PATENT ABSTRACT
A motion detection and interpretation system comprising a camera plus an infrared transmitter/receiver paired with a single reflective surface that records image data from two vantage points. The camera is connected to a computer and a display screen. The system creates a virtual touch screen for interaction with the display screen. The components of the system can be protected behind a transparent barrier while the virtual touch screen is provided for user interaction thus preventing user interference with, deterring vandalism and theft of, and prolonging the usable life of the equipment. In addition to finite hand movements detected by the virtual touch screen, the system can also simultaneously perform facial recognition and body movement recognition. The system is capable of interpreting multi-touch inputs. All recognitions are defined in the computer to carry out preprogrammed responses.

PATENT DESCRIPTION
CROSS REFERENCE TO RELATED APPLICATION 
       [0001]    This application is a continuation of U.S. application Ser. No. 14/535,823 filed Nov. 7, 2014, which is a continuation-in-part of U.S. application Ser. No. 13/890,709 filed May 9, 2013. The above identified patent applications are incorporated herein by reference in their entirety to provide continuity of disclosure. 
     
    
     FIELD OF THE INVENTION 
       [0002]    This disclosure relates to the field of automated motion detection. More particularly this disclosure relates to computer vision systems registering body motion inputs and translating such inputs into computer instructions. 
       BACKGROUND OF THE INVENTION 
       [0003]    Interactive motion detection and interpretation is useful in many modern computing applications such as gaming, retail, bank teller machines, and communications. In the prior art, a video camera, an infrared (IR) emitter/detector, a display screen and a computer processor are required to translate body motion inputs into computer instructions. In the prior art, a single camera only works sufficiently in applications that recognize broad movements, such as gaming, but not in applications that require inputs from small or discrete movements or that require an obstructed view of the user. In many applications, such as gaming, the display may block some portion of the camera&#39;s view of the user. In other applications, such as bank teller machines, physical security of the system often times requires an obstructed view of the user. To compensate for an obstructed view, the prior art requires additional cameras placed behind, above, or to the side of the display to provide an unobstructed view of the user. However, multiple cameras increase complexity and cost. 
         [0004]    For example, U.S. Pat. No. 7,598,942 to Underkoffler, et al. discloses a gestural interface to visually presented elements on a display screen. Multiple cameras capture movement and detect location and orientation and generate output signals to processors connected to a computer. The processors translate the camera outputs into gestural signals which are interpreted as input information. The computer uses the input information to generate commands to control computer functions. 
         [0005]    U.S. Pat. No. 7,034,807 to Maggioni discloses a system for interaction with a display. The system includes a recording unit for recording a pointer object in the vicinity of the display. A computer is connected to the recording unit and is used to determine a position of the pointer object. The system requires multiple cameras and multiple reflective surfaces. 
         [0006]    U.S. Patent Application Publication No. 2012/0212413 to Plagemann, et al. discloses a system for receiving image information and translating it into computer instructions. Image information is received for a single predetermined action space to identify motion. A camera combined with mirrors, prisms, or optic cables is used to gather the image information. However, only one action area is monitored at any given time. 
         [0007]    U.S. Patent Application Publication No. 2012/0162077 to Sze, et al. discloses an input device used to detect locations and motions of objects in a virtual working area. A camera is directed to a region of interest. A region of interest is illuminated by a “flat” beam of light. An object is placed in the region of interest and illuminated. The camera captures an image of the object and sends it to the processor. The processor processes the image to obtain locations and movements. Based on the movements, the processor produces computer instructions. 
         [0008]    Therefore, there is a need for a system of motion detection which requires only a single camera to gather video data from an obstructed viewpoint and to create a virtual touch screen for interpreting fine motor movements and translating them into computer instructions. There is also a need to provide physical security for such a system to prevent vandalism and theft. 
       SUMMARY 
       [0009]    In a preferred embodiment, a system for purchasing a set of products is disclosed. The system includes a network, a computer connected to the network, a third party connected to the network, a user device connected to the network, a feedback display connected to the computer, a camera connected to the computer, and a mirror adjacent to the camera. The computer is programmed to store and execute instructions that cause the system to perform a method. The method includes the steps of defining an action area adjacent to the camera, defining a set of sub-action areas for the action area, receiving a perceived position in the action area, calculating an actual position from the perceived position, determining a sub-action position from the actual position, executing a set of actions based on the sub-action position and a predetermined time, and receiving a set of purchase information in response to the set of actions. 
         [0010]    In another embodiment, the system disclosed gathers video data and depth information from around an obstruction with a single camera. A single mirror is geometrically positioned in such a way as to provide the camera a reflected view around the obstruction. The system creates a virtual touch screen for interaction with the computer from behind a glass barrier which prevents any physical contact between the user and the system. 
         [0011]    Unlike the prior art, it is not required that the single camera of the system disclosed have an unobstructed view of the user. A novel positioning of the camera and the mirror provides a view of body movements and image recognition and a view around the obstruction to capture fine motor movements of, for example, a user&#39;s hands interacting with a virtual touch screen. The system also provides a novel component positioning which allows the components of the system to be protected behind glass, while still being accessible to the user via the virtual touch screen. 
         [0012]    The system can simultaneously react to fine motor inputs and perform facial recognition. For example, it is possible for the system to identify a user by his facial characteristics and query the user for a manually entered personal identification number (PIN) at the same time. Other examples of useful embodiments include adaptive advertising displays in store windows, automatic teller machines requiring secure financial transactions, and building entrance security. 
         [0013]    The virtual touch screen is a predefined three-dimensional set of coordinates in which movements and positions behind an obstruction are recognized. The action area can be comprised of a plurality of separately defined actions areas each corresponding to a different function. When an object is detected in the action area, it is recognized and interpreted as a set of specific computer instructions. In one embodiment, a signal is sent to a display screen that confirms the interpretations to the user as they are being made. 
         [0014]    The present disclosure provides a system which embodies significantly more than an abstract idea including technical advancements in the field of data processing and a transformation of data which is directly related to real world objects and situations. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0015]    Reference will now be made to the following drawings: 
           [0016]      FIG. 1  is a schematic diagram of the components of a preferred embodiment. 
           [0017]      FIG. 2A  is an elevation view of a preferred embodiment. 
           [0018]      FIG. 2B  is an elevation view of a preferred embodiment. 
           [0019]      FIG. 2C  is an elevation view of a preferred embodiment. 
           [0020]      FIG. 3  is a ray diagram of a preferred embodiment. 
           [0021]      FIG. 4  is a schematic of a field of view of a camera of a preferred embodiment. 
           [0022]      FIG. 5  is an isometric view of an action area of a preferred embodiment. 
           [0023]      FIG. 6  is a flow chart of steps involved in the setup of a preferred embodiment. 
           [0024]      FIG. 7  is a flow chart of the steps involved in the use of a preferred embodiment. 
           [0025]      FIG. 8  is a flow chart of the steps involved in the facial recognition routine of a preferred embodiment. 
           [0026]      FIG. 9  is a flow chart of the steps involved for interaction with a virtual touch screen in a preferred embodiment. 
           [0027]      FIG. 10  is an elevation view of a display screen of a preferred embodiment. 
           [0028]      FIG. 11  is a schematic diagram of the components of a preferred embodiment. 
           [0029]      FIG. 12  is an elevation view of a preferred embodiment. 
           [0030]      FIG. 13  is a detail elevation view of a preferred embodiment. 
           [0031]      FIG. 14  is a field of view of a camera of preferred embodiment. 
           [0032]      FIG. 15  is a flow chart of a method for calibrating the system of a preferred embodiment. 
           [0033]      FIG. 16  is a flow chart of a method for converting a set of positions of a preferred embodiment. 
           [0034]      FIG. 17  is a flow chart of a method for converting a set of y positions of a preferred embodiment. 
           [0035]      FIG. 18A  is a flowchart of a method for converting a set of x positions of a preferred embodiment. 
           [0036]      FIG. 18B  is a flowchart of a method for mapping a matrix to a square matrix of a preferred embodiment. 
           [0037]      FIG. 19  is a flow chart of a method for interaction with a virtual touch screen of a preferred embodiment. 
       
    
    
     DETAILED DESCRIPTION 
       [0038]    In the descriptions that follow, like parts are marked throughout the specification and drawings with the same numerals, respectively. The drawing figures are not necessarily drawn to scale and certain figures may be shown in exaggerated or generalized form in the interest of clarity and conciseness. 
         [0039]    It will be appreciated by those skilled in the art that aspects of the present disclosure may be illustrated and described herein in any of a number of patentable classes or context including any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof. Therefore, aspects of the present disclosure may be implemented entirely in hardware or combining software and hardware implementation that may all generally be referred to herein as a “circuit,” “module,” “component,” or “system” (including firmware, resident software, micro-code, etc.). Further, aspects of the present disclosure may take the form of a computer program product embodied in one or more computer readable media having computer readable program code embodied thereon. 
         [0040]    Any combination of one or more computer readable media may be utilized. The computer readable media may be a computer readable signal medium or a computer readable storage medium. For example, a computer readable storage medium may be, but not limited to, an electronic, magnetic, optical, electromagnetic, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples of the computer readable storage medium would include, but are not limited to: a portable computer diskette, a hard disk, a random access memory (“RAM”), a read-only memory (“ROM”), an erasable programmable read-only memory (“EPROM” or Flash memory), an appropriate optical fiber with a repeater, a portable compact disc read-only memory (“CD-ROM”), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. Thus, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. 
         [0041]    A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. The propagated data signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. Program code embodied on a computer readable signal medium may be transmitted using any appropriate medium, including but not limited to wireless, wire line, optical fiber cable, RF, or any suitable combination thereof. 
         [0042]    Computer program code for carrying out operations for aspects of the present disclosure may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Scala, Smalltalk, Eiffel, JADE, Emerald, C++, C#, VB.NET, Python or the like, conventional procedural programming languages, such as the “C” programming language, Visual Basic, Fortran 2003, Perl, COBOL 2002, PHP, ABAP, dynamic programming languages such as Python, Ruby and Groovy, or other programming languages. 
         [0043]    Aspects of the present disclosure are described herein with reference to flowchart illustrations and/or block diagrams of methods, systems and computer program products according to embodiments of the disclosure. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable instruction execution apparatus, create a mechanism for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. 
         [0044]    These computer program instructions may also be stored in a computer readable medium that when executed can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions when stored in the computer readable medium produce an article of manufacture including instructions which when executed, cause a computer to implement the function/act specified in the flowchart and/or block diagram block or blocks. The computer program instructions may also be loaded onto a computer, other programmable instruction execution apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatuses or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. 
         [0045]    Referring to  FIG. 1 , components of motion detection and interpretation system  100  include computer  101  connected to camera  102 . Camera  102  is known in the art and includes firmware for movement interpretation and image recognition. An example is the Carmine 1.08 3D sensor from PrimeSense of Tel-Aviv, Israel. Another example is the Xbox Kinect from Microsoft of Redmond, Wash. Camera  102  provides image data in the form of streaming video at the rate of 30 frames per second in a standard 640×480 VGA. The focal length of the camera is 525 pixels with a field of view of approximately 63°. The camera also provides distance-to-target information from an on-board infrared transmitter/receiver pair. The focal length of the infrared transmitter/receiver is 580 pixels with a field of view of approximately 58°. The infrared data is provided as a 16 bit number at a refresh rate of 200 μs. 
         [0046]    Computer  101  contains processor  104 , memory  105 , and software module  107 . Software module  107  includes hardware drivers  108 . In a preferred embodiment, hardware drivers include an image capturing program such as Kinect for Windows available from Microsoft in Software Development Kit 1.7. Software module  107  includes executable routine  109  for coordination and execution of the system functions as will be further described. The software module includes a database  110 . In a preferred embodiment, the database is a SQL database which resides in memory. The software module also includes facial recognition routine  111 . 
         [0047]    Computer  101  is connected to display  106 . Display  106  in the preferred embodiment is a flat panel LCD screen provided by LG Electronics of South Korea. Mirror  112  is positioned within view of camera  102  as will be further described. 
         [0048]    Referring to  FIG. 2A , the relative positions of the views of camera  102  are shown. In general, camera  102  is positioned to achieve field of view  220 . In the preferred embodiment, field of view  220  can range from 55°-110°. Glass  208  separates the user from camera  102  and display  106 . Mirror  112  is positioned behind glass  208 . In other preferred embodiments, when security is of lesser concern, mirror  112  can be positioned in front of glass  208 . In a preferred embodiment, the mirror is a front silvered planar mirror having an optical coating to prevent distortion. 
         [0049]    Display  106  is positioned a typical distance above the ground, usually about eye level. In order to be at eye level, the display necessarily blocks a portion of field of view  220 , as shown by obstructed view  216 . In an alternate preferred embodiment, field of view  220  may be narrow and/or the position of the camera relative to the display may be situated such that field of view  220  is not obstructed by the display. Partial field of view  222  represents the limited unobstructed view from camera  102 . Reflected field of view  217  represents the portion of the total field returned by mirror  112 . It is important to note that reflected field of view  217  allows the camera to compensate for the obstructed field of view  216  adjacent the display, thereby allowing actions that take place in the obstructed field of view to be recognized. Overlap area  234  represents the field of view visible to the camera that otherwise would be obstructed. It is also important to note that overlap area  234  is directly adjacent the display. 
         [0050]    In a preferred embodiment, the camera is mounted a distance “g” from the floor and a distance “h” from the display. The visual axis of the camera is maintained at an angle α with respect to horizontal. The mirror is typically positioned a distance “i” from the camera and a distance ‘j’ from the floor. The mirror is mounted at a fixed angle β from horizontal. The display is typically mounted at about eye level, at a distance “k” from the floor. The display is typically a distance “l” from the glass. The camera and mirror are shown positioned above the display; however, the camera and the mirror may also be positioned below or to the side of the display and still function as intended, so long as the relative positions of the devices provide for the overlap area. Table 1 summarizes the angles and distances as approximate ranges of the preferred embodiments: 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                   
                 Range 
                 Preferred 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 g 
                 3.5-14  
                 ft. 
                 7  
                 ft. 
               
               
                   
                 h 
                 1 in.-8  
                 ft. 
                 14  
                 in. 
               
               
                   
                 i 
                 1 in.-2  
                 ft. 
                 4  
                 in. 
               
               
                   
                 j 
                 6-14  
                 ft. 
                 7 ft. 1  
                 in. 
               
               
                   
                 k 
                 3-9  
                 ft. 
                 6  
                 ft. 
               
               
                   
                 l 
                 1-6  
                 in. 
                 2  
                 in. 
               
             
          
           
               
                   
                 α 
                 (−27)°-27° 
                 −5° 
               
               
                   
                 β 
                 0°-110° 
                 45° 
               
               
                   
                   
               
             
          
         
       
     
         [0051]    Referring to  FIGS. 2B and 2C , other preferred embodiments are described. Curved mirror  212  is a curved mirror having a focal length f and a center curvature  2   f.  In a preferred embodiment, the curved mirror has a focal length of between about 1 and 4 inches. The curved mirror may be convex or concave. Further, the curved mirror may be curved in one or more planes, that is, it may spherical or cylindrical. The convex mirror in these embodiments is a front silvered mirror having an optical coating to reduce distortion. Curved mirror  212  provides the camera with a reflected field of view  217 . Reflected field of view  217  results in overlap area  254 . If the curved mirror is of a convex nature, overlap area  254  is significantly larger and overlap area  234 . The larger overlap enables the system to track gross motor movements over a larger area. If the curved mirror is of a concave nature, overlap area  274  is significantly smaller, thus allowing the system to track fine motor movements more accurately than the prior art as will be further described. 
         [0052]    Referring to  FIG. 3 , the relative positions of action area  214  and user  210  are described. Action area  214  is a 3-dimensional space defined by the software module. In general, the action area is positioned adjacent glass  208  and between user  210  and display  106 . The action area is located in the overlap area, that is both in the reflected field of view and the obstructed field of view. A ray diagram shows incident light  302  reflected from user  210  into camera  102 . Similarly, incident light  304  is reflected from hand  306  of user  210  to mirror  112  where it is further reflected to camera  102 . Camera  102  reports distance “A+A”&#39; as the distance to hand  306  and distance “B” as the distance from the facial image of user  210  to the computer, as will be further described. 
         [0053]    Referring to  FIG. 4 , the image data gathered by camera  102  includes image  450 . Image  450  also includes reflected image  460 . Reflected image  460  reflects light from mirror  112 . In use, image  450  includes that portion of the user not blocked by display  106 . In use, reflected image  460  includes both a view of the user&#39;s hands (which are obstructed from the view of the camera) and action area  214 . 
         [0054]    The reflected image alters the reference coordinates in the image data gathered by the camera. The camera receives data according to coordinate system reference  455  for the image  450 . For example, the x axis represents horizontal. The y axis represents vertical and the z axis is out of the page. However, reflected image  460  is reported to the camera according to coordinate system  465 . In coordinate system  465 , the x axis is horizontal, the y axis is out of the page and the z axis is vertical. Hence, the y and z axes are reversed between coordinate systems  455  and  465 . Action area  214 , as will be further described later, is defined in reflected image  460 . Facial recognition area  215 , as will be described further later, is defined in image  450 . 
         [0055]    Referring to  FIG. 5 , action area  214  is described in more detail. Action area  214  is sub-divided into a series of three-dimensional geometric shapes within coordinate system  465 . Each of the geometric shapes is bounded by a series of points which form lines enclosing certain discrete volumes. For example, sub-action area  214 A is bounded by a set of points including X 1 , Y 1 , Z 1 ; X 2 , Y 1 , Z 1 ; X 1 , Y 2 , Z 1 ; X 2 , Y 2 , Z 1 ; and function  505 . Function  505 , in this example, is a hyperbolic function defined by the equation 
         [0000]        C≈x   2   +y   2   Eq. 1
 
         [0000]    Of course, other hyperbolic functions or linear functions may be used to define any set of points, in the X, Y, or Z directions, defining a general shape, so long as the function is closed with respect to the discrete area. 
         [0056]    As further shown in  FIG. 5 , the various “widths,” “lengths” and “depths” for each sub-action item can vary. For example, sub-action area  214 B comprises a relatively “shallow” depth. Such shallow depths are useful to directly “mimic” a prior art touch screen, thereby conveying to the user a sensation that touching the glass surface causes the interaction. Sub-action areas  214 C and  214 D comprise “medium” depth areas. The medium depth areas convey to the user a sense that a computer function can be activated without actually touching the glass surface. Sub-action areas  214 E and  215 F comprise relatively “deep” action areas. Deep action areas, such as are shown in  214 E and  214 F are useful to record 3-dimensional paths indicated by a user, such as path  510 . 
         [0057]    Referring to  FIG. 6 , method  600  of calibrating the system is described. In order to correctly interpret images from the camera, it is necessary to calibrate actual locations within the action area to theoretical locations stored in memory. The following preferred method is used by the system to calibrate the boundaries of action area  214  and facial recognition area  215 . 
         [0058]    The method begins at step  602 . At step  604 , the processor is instructed to set an initial point X, Y, Z in the obstructed view to define a corner of the action area. At step  606 , a pointer, such as a finger or stylus, is moved to the actual location X, Y, Z. At step  608 , the processor queries the camera for the perceived image location X′, Y′, Z′. At step  610 , the processor calculates the difference between the actual location X, Y, Z and the perceived location at X′, Y′, Z′ to arrive at a difference ΔX, ΔY, ΔZ. 
         [0059]    At step  612 , ΔX, ΔY, and ΔZ are used to derive a translation function. In a preferred embodiment, the translation function is: 
         [0000]        X=X′+ΔX    Eq. 2
 
         [0000]        Y=Y′+ΔY    Eq. 3
 
         [0000]        Z=Z′+ΔZ    Eq. 4
 
         [0000]    At step  614 , the translation function is stored. At step  616 , the processor sets X, Y, Z in t 1  reflected view. At step  618 , the pointer is moved to the corresponding physical location in the reflected view. At step  619  the camera queried for the X, Y, Z location of the image. At step  620 , a transform function is derived. Calibration of additional points is required if the transform function is nonlinear. Nonlinear transform functions may arise in embodiments where concave, convex or non-planar mirrors are used. If so, at step  624 , the processor increments to the next point to be calibrated, and returns to step  616 . If not, the processor moves to step  625  and stores the transform function. At step  626 , the process is complete. 
         [0060]    Referring to  FIG. 7 , method  700  of calibrating a path is described. The method begins at step  702 . At step  704 , the chosen predefined path, such as path  510 , is loaded into memory by the processor. At step  706 , a pointer is moved to the start of the path. A step  708 , the processor activates the camera and begins recording video data and storing it in memory. At step  709 , the processor starts an internal timer to record the time it takes for the pointer to move along the path. At step  710 , the pointer is moved through the path in action area  112  from the beginning of the path to the end of the path within a time “t”. At step  712 , upon the arrival of the pointer at the end of the path, the processor stops the timer. 
         [0061]    At step  714 , the processor then stops recording video images from the camera. At step  716 , the processor calculates the equation of the path of “A” over the variables X, Y, Z and t, based on the recorded pointer movements. At step  716 , the processor calculates the difference between the original path A and the stored path A′. At step  718 , the new path A′ is stored in memory. At step  720 , the processor determines if all paths have been calibrated. If not, at step  724 , the processor increments to the next path to be calibrated and returns to step  704 . If all paths have been calibrated at step  720 , the processor proceeds to step  722  and the process of path calibration is complete. 
         [0062]    Referring to  FIG. 8 , facial recognition routine  800  will be described. At step  801 , the process starts. At step  802 , the camera is queried for the locations of facial features including eye location and color, ear location, chin location and hair color. In a preferred embodiment, the query is accommodated by Microsoft SKD Rel. 7.1 .LIB file Microsoft.Kinect.Toolkit.FaceTracking. In a preferred embodiment, at least 121 different locations are determined. At step  804 , the distances between facial features are measured. A “facial map” is created at step  806 . The facial map includes a table of the facial features and the distances between them. At step  808 , the facial map is compared to a set of digital images stored in database  110 . If the map is not recognized, then the process returns to step  801 . If the facial map is recognized, then the process moves to step  810 . At step  810 , the user identification demographic is returned. At step  812 , the process concludes. 
         [0063]    Referring to  FIG. 9 , the steps involved in method  900  of use of motion detection system are described. At step  902 , the processor is activated and loads the executable routine. A display signal is sent to the display at step  903  by the executable routine. In a preferred embodiment, the display signal includes a graphical and text picture which corresponds to a two-dimensional representation of the access area and sub-areas. At step  904 , the camera is queried for motion presence in facial recognition area. At step  905 , if no presence is detected, the processor returns to step  904 . If a presence is detected, the process moves to step  906  and initiates the facial recognition routine to determine the identity of the user. In a preferred embodiment, the facial recognition routine sorts through the database to identify facial features which match a predetermined pattern. The database then is queried for associated user information, such as the user&#39;s name, and account status, which is stored in the memory for later use by the processor. 
         [0064]    The processor then moves to step  908  where it begins monitoring the action area. At step  910 , the camera is queried for image data within the action area. 
         [0065]    At step  912 , image data and distance data are perceived in the action area and returned from the camera as coordinates X, Y, Z. At step  914 , the processor executes the translation function to translate the perceived coordinates into the actual coordinates. At step  916 , the processor executes the transform function to interpret the coordinates of the reflected view into the coordinates of the unobstructed view so that “Y” and “Z” dimension information is accurately reported to the processor. At step  918 , if the action position is no in a sub-action area then the process returns to step  912 . If it is in a sub-action area, then the processor proceeds to step  920 . At step  920 , the processor receives path data from the action area including a set of path variables X, Y, Z over a defined time period, Δt. At step  922 , the processor executes the translation function to translate the perceived path to the actual path. At step  924 , the processor, executes the transform function to change the coordinates of the reflected view into the coordinates of the unobstructed view so that the path information is accurately reported to the processor. At step  926 , the processor determines if a path defined by the action position corresponds to a path within a predefined tolerance and predefined time period. If the path is not within a predefined tolerance and a predefined time period, the processor returns to step  912 . If the path is within a predetermined tolerance and a predefined time period, the processor proceeds to step  928 . At step  928 , a look-up table is queried for a predetermined instruction, if an action is within an action area and/or a motion is within a predefined path tolerance and time period. At step  930 , the processor performs the instruction according to the look-up table. At step  932 , the processor displays the results of and feedback from the instruction. After the instruction is displayed, the processor returns to step  904  and again queries the camera for the presence of a subject in the facial recognition area. 
         [0066]      FIG. 10  shows display  106  as viewed by a user outside glass  208 . Selections  1016 A-F are shown on display  106 . A user can see the selections available on the display but cannot physically touch the display because it is behind glass  208 . Feedback display  1017  provides visual confirmation of the system interface to the user. Confirming, that is, that actions have been recognized and correctly interpreted by the system. For example, an interaction with sub-action area  214 B results in selection  1016 B shown to the user to be selected as a radio button. 
         [0067]    Referring to  FIG. 11  in another embodiment, system  1100  includes computer  1101  connected to camera  1102  and to network  1112 . Third party  1113  and user device  1114  are connected to network  1112 . Display  1106  is connected to computer  1101 . Mirror  1112  is positioned adjacent to and in view of camera  1102 , as will be further described below. 
         [0068]    Computer  1101  includes processor  1104 , memory  1105  connected to processor  1104 , and software module  1107 . Software module  1107  includes hardware drivers  1108 , executable routine  1109 , database  1110 , and facial recognition routine  1111 . Executable routine  109  for coordinates and executes system functions, as will be further described. 
         [0069]    In a preferred embodiment, third party  1113  is a financial entity, such as a bank, a credit card company, a credit union, a payment processor such as PayPal, or a payment system such as Bitcoin. Any financial entity and/or payment system known in the art may be employed. 
         [0070]    In a preferred embodiment, network  1112  is the Internet. In another embodiment, network  1112  is a local area network and a wide area network. 
         [0071]    In one embodiment, user device  1114  is a smartphone. In another embodiment, user device  1114  is a tablet computer. Any computing device known in the art may be employed. 
         [0072]    In a preferred embodiment, database  1110  is a SQL database which resides in memory  1105 . Any database known in the art may be employed. 
         [0073]    In a preferred embodiment, display  1106  in the preferred embodiment is a flat panel LCD screen provided by LG Electronics of South Korea. Any type of display known in the art may be employed. 
         [0074]    In a preferred embodiment, hardware drivers  1108  include an image capturing program such as Kinect for Windows available from Microsoft in Software Development Kit 1.7. 
         [0075]    Camera  1102  is known in the art and includes firmware for movement interpretation and image recognition. An example is the Carmine 1.08 3D sensor from PrimeSense of Tel-Aviv, Israel. Another example is the Xbox Kinect from Microsoft of Redmond, Wash. Camera  1102  provides image data in the form of streaming video at the rate of 30 frames per second in a standard 640×480 VGA. The focal length of the camera is 525 pixels with a field of view of approximately 63°. The camera also provides distance-to-target information from an on-board infrared transmitter/receiver pair. The focal length of the infrared transmitter/receiver is 580 pixels with a field of view of approximately 58°. The infrared data is provided as a 16 bit number at a refresh rate of 200 μs. 
         [0076]    Referring to  FIGS. 12 and 13 , the relative positions of the views of camera  1102  are shown. Camera  1102  is positioned to achieve field of view  1203  adjacent to product shelf  1201 . Mirror  1112  is positioned adjacent to camera  1102 . 
         [0077]    Partial field of view  1205  represents the limited unobstructed view from camera  1102 . Reflected field of view  1202  represents the portion of the total field returned by mirror  1112 . Overlap area  1206  represents the field of view visible to the camera from field of view  1203  and reflected field of view  1202 . 
         [0078]    In the preferred embodiment, field of view  1203  can range from 55°-110°. In a preferred embodiment, the mirror is a front silvered planar mirror having an optical coating to prevent distortion. 
         [0079]    In a preferred embodiment, camera  1102  is mounted a distance “g” from the floor. Camera  1102  is positioned with respect to product shelf  1201  such that no portion of product shelf  1201  interferes with reflected field of view  1202 . The visual axis of camera  1102  is maintained at an angle α with respect to horizontal. Mirror  1112  is typically positioned a distance “i” from camera  1102  and a distance “j” from floor  1207 . Mirror  1207  is mounted at a fixed angle β from horizontal. Table 2 summarizes the angles and distances as approximate ranges of the preferred embodiments: 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                   
                 Range 
                 Preferred 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 g 
                 3.5-14  
                 ft. 
                 7  
                 ft. 
               
               
                   
                 i 
                 1 in.-2  
                 ft. 
                 4  
                 in. 
               
               
                   
                 j 
                 6-14  
                 ft. 
                 7 ft. 1  
                 in. 
               
             
          
           
               
                   
                 α 
                 (−27)°-27° 
                 −5° 
               
               
                   
                 β 
                 0°-110° 
                 45° 
               
               
                   
                   
               
             
          
         
       
     
         [0080]    Referring to  FIG. 14 , product shelf  1401  includes shelves  1402 ,  1403 ,  1404 , and  1405 . Camera  1102  is mounted to product shelf  1401 . Action area  1400  includes center point  1413  and is defined by corner points  1414 ,  1415 ,  1416 , and  1417 . Action area  1400  includes a set of sub-action areas defined by lines  1406 ,  1407 ,  1408 ,  1409 ,  1410 ,  1411 , and  1412 . For example, sub-action area  1418  is a rectangle defined by lines  1408 ,  1409 ,  1410 , and  1411  and sub-action area  1419  is a rectangle adjacent to sub-action area  1418  and is defined by lines  1408 ,  1409 ,  1411 , and  1412 . 
         [0081]    In a preferred embodiment, lines  1406 ,  1407 ,  1408 ,  1409 ,  1410 ,  1411 , and  1412  are predetermined distances from center  1413 . 
         [0082]    In a preferred embodiment, action area  1400  is a two-dimensional plane defined by corner points  1414 ,  1415 ,  1416 , and  1417 , as will be further described below. In a preferred embodiment, action area  1400  is a rectangle or quadrilateral. In other embodiments, action area  1400  is any polygon. In this embodiment, display  1106  provides feedback information. In this embodiment, a user defines action area  1400  by moving a pointer, such as a finger or stylus, from center  1413  to a corner until the pointer is no longer in view of camera  1102 . Once the pointer is no longer in the field of view of camera  1102 , display  1106  displays a red signal, telling the user to stop moving the pointer. The process is repeated until all corners are defined. 
         [0083]    In a preferred embodiment, each sub-action area corresponds to a different product displayed on product shelf  1401 . For example, sub-action area  1418  corresponds to a book and sub-action area  1419  corresponds to a Blu-ray movie. In this example, the information corresponding to the book, including the sub-action area location, title, author, page numbers, publisher, and price are stored in the database of the system. The information for the Blu-ray movie, including the sub-action area location, title, credits, and price are stored in the database of the system. Any product or combination of products may be employed. 
         [0084]    In a preferred embodiment, the system detects the presence of a user using the facial recognition routine, as previously described, and a user&#39;s hand in any of the sub-action areas. Based on the length of time a user&#39;s hand is present in a sub-action area, the system executes a predetermined action, as will be further described below. 
         [0085]    Referring to  FIG. 15 , method  1500  for defining and calibrating an action area for the system is described. The process starts at step  1501 . At step  1502 , a pointer is centered and the center point X, Y is set. At step  1503 , the pointer is moved to a corner of a set of corners that will define the action area. At step  1504 , the system queries the camera for the perceived pointer location. At step  1505 , the system determines whether the image of the pointer is in view of the camera. If the pointer is in view of the camera, then a “go” signal is sent to the display at step  1506 . In one embodiment, the “go” signal is a green light signal. In another embodiment, the “go” signal is a text display. Any type of signal may be employed. If the pointer is in view of the camera, then method  1500  proceeds to step  1507 . 
         [0086]    At step  1507 , a “stop” signal is sent to the display. In one embodiment, the “stop” signal is a red light display. In another embodiment, the “stop signal is a text display. Any type of signal may be employed. 
         [0087]    At step  1508 , the pointer is moved towards the center in response to the “stop” signal. At step  1509 , the camera is queried for the perceived pointer image location. At step  1510 , the system determines whether the image of the pointer is in view of the camera. If the pointer is not in view of the camera, then a “go” signal is sent to the display at step  1511 . If the pointer is in view of the camera, then a “stop” signal is sent to the display at step  1512 . At step  1513 , the movement of the pointer is stopped at the corner location. 
         [0088]    At step  1514 , the system records the X, Y position of the pointer at the corner. At step  1515 , the pointer is moved back to the center. At step  1516 , the position of the pointer is recorded. At step  1517 , a determination is made as to whether all corners of the set of corners for the action area have been recorded. If not, then method  1500  returns to step  1502 . If so, method  1500  proceeds to step  1518 . At step  1518 , the recorded positions of the set of corners and the center position are calculated and saved, as will be further described below. At step  1519 , method  1500  ends. Method  1500  is repeated to defined and calibrate each of the set of sub-action areas. 
         [0089]    Referring to  FIG. 16 , step  1518  will be further described as method  1600 . In method  1600 , the perceived camera points are translated to a screen to transform each action/or sub-action area into a quadrilateral, or other polygon, that fits into the pixel dimensions of a computer screen. In this way, each point of the action and/or sub-action area becomes “selectable” in the same manner as a point on the computer screen. 
         [0090]    At step  1601 , the camera-perceived action position x c , y c  is retrieved. At step  1602 , the y coordinate of the actual position, y s , is calculated in relation to a screen using the position x c , y c  by 
         [0000]        y   s   =x   c   ·l   s     2     +y   c   ·l   s     4   +1· l   s     6      Eq. 5
 
         [0000]    where l s     2   , l s     4   , l s     6    are defined by a least squares matrix, 
         [0000]    
       
         
           
             
               
                 
                   
                     M 
                     ls 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               l 
                               
                                 s 
                                 1 
                               
                             
                           
                           
                             
                               l 
                               
                                 s 
                                 2 
                               
                             
                           
                         
                         
                           
                             
                               l 
                               
                                 s 
                                 3 
                               
                             
                           
                           
                             
                               l 
                               
                                 s 
                                 4 
                               
                             
                           
                         
                         
                           
                             
                               l 
                               
                                 s 
                                 5 
                               
                             
                           
                           
                             
                               l 
                               
                                 s 
                                 6 
                               
                             
                           
                         
                       
                       ] 
                     
                     . 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   6 
                 
               
             
           
         
       
     
         [0000]    The least squares matrix, M ls , will be further defined below. 
         [0091]    At step  1603 , the x coordinate of the actual position, x s , is calculated in relation to the screen using position x c , y c  by 
         [0000]        x   s   =m   1   ·x   c   +m   2   ·y   c   +m   3 ,   Eq. 7
 
         [0000]    where m 1 , m 2 , and m 3  are defined by a multiplied matrix, M m    
         [0000]    
       
         
           
             
               
                 
                   
                     M 
                     m 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               m 
                               1 
                             
                           
                           
                             
                               m 
                               2 
                             
                           
                           
                             
                               m 
                               3 
                             
                           
                         
                         
                           
                             
                               m 
                               4 
                             
                           
                           
                             
                               m 
                               5 
                             
                           
                           
                             
                               m 
                               6 
                             
                           
                         
                         
                           
                             
                               m 
                               7 
                             
                           
                           
                             
                               m 
                               8 
                             
                           
                           
                             
                               m 
                               9 
                             
                           
                         
                       
                       ] 
                     
                     . 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   8 
                 
               
             
           
         
       
     
         [0000]    The multiplied matrix, M m , will be further defined below. 
         [0092]    At step  1604 , the actual position of X, Y is set as the actual position and saved in memory. 
         [0093]    Referring to  FIG. 17 , step  1602  will be further described as method  1700  for determining a set of y coordinates for each of a set of positions. At step  1701 , a set of recorded points is retrieved from memory. At step  1702 , a camera points matrix is created from the set of recorded points. In a preferred embodiment, the camera points matrix is defined as 
         [0000]    
       
         
           
             
               
                 
                   
                     M 
                     c 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             x 
                             ctl 
                           
                         
                         
                           
                             y 
                             ctl 
                           
                         
                         
                           1 
                         
                       
                       
                         
                           
                             x 
                             cbl 
                           
                         
                         
                           
                             y 
                             cbl 
                           
                         
                         
                           1 
                         
                       
                       
                         
                           
                             x 
                             cbr 
                           
                         
                         
                           
                             y 
                             cbr 
                           
                         
                         
                           1 
                         
                       
                       
                         
                           
                             x 
                             ctr 
                           
                         
                         
                           
                             y 
                             ctr 
                           
                         
                         
                           1 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   9 
                 
               
             
           
         
       
     
         [0000]    where M C  is the camera points matrix, x ctl , y ctl , 1 is the x, y, z position of a top left corner of a camera view, x chl , y cbl , 1 is the x, y, z position of a bottom left corner of the camera view, x cbr , y cbr , 1 is the x, y, z position of a bottom right corner of the camera view, and x ctr , y ctr , 1 is the x, y, z position of a top right corner of the camera view. A 1 is added as a z coordinate for each corner point of the same plane. 
         [0094]    At step  1703 , the camera points matrix, M c , is transposed. The transposed camera points matrix, M ct , is defined as 
         [0000]    
       
         
           
             
               
                 
                   
                     M 
                     ct 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               x 
                               ctl 
                             
                           
                           
                             
                               x 
                               cbl 
                             
                           
                           
                             
                               x 
                               cbr 
                             
                           
                           
                             
                               x 
                               ctr 
                             
                           
                         
                         
                           
                             
                               y 
                               ctl 
                             
                           
                           
                             
                               y 
                               cbl 
                             
                           
                           
                             
                               y 
                               cbr 
                             
                           
                           
                             
                               y 
                               ctr 
                             
                           
                         
                         
                           
                             1 
                           
                           
                             1 
                           
                           
                             1 
                           
                           
                             1 
                           
                         
                       
                       ] 
                     
                     . 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   10 
                 
               
             
           
         
       
     
         [0095]    At step  1704 , a screen points matrix, M s , is created. The screen points matrix is defined as 
         [0000]    
       
         
           
             
               
                 
                   
                     M 
                     s 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             x 
                             stl 
                           
                         
                         
                           
                             y 
                             stl 
                           
                         
                       
                       
                         
                           
                             x 
                             sbl 
                           
                         
                         
                           
                             y 
                             sbl 
                           
                         
                       
                       
                         
                           
                             x 
                             sbr 
                           
                         
                         
                           
                             y 
                             sbr 
                           
                         
                       
                       
                         
                           
                             x 
                             str 
                           
                         
                         
                           
                             y 
                             str 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   11 
                 
               
             
           
         
       
     
         [0000]    where M s  is the screen points matrix, x stl , y stl  is the x, y position of a top left corner of a display screen, x sbl , y sbl  is the x, y position of a bottom left corner of the display screen, x sbr , y sbr  is the x, y position of a bottom right corner of the display screen, and x str , y str  is the x, y position of a top right corner of the display screen. 
         [0096]    At step  1705 , the transposed camera points matrix, M ct , is multiplied by the camera points matrix, M c . 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             M 
                             ct 
                           
                            
                           
                             M 
                             c 
                           
                         
                         = 
                           
                          
                         
                           
                             [ 
                             
                               
                                 
                                   
                                     x 
                                     ctl 
                                   
                                 
                                 
                                   
                                     x 
                                     cbl 
                                   
                                 
                                 
                                   
                                     x 
                                     cbr 
                                   
                                 
                                 
                                   
                                     x 
                                     ctr 
                                   
                                 
                               
                               
                                 
                                   
                                     y 
                                     ctl 
                                   
                                 
                                 
                                   
                                     y 
                                     cbl 
                                   
                                 
                                 
                                   
                                     y 
                                     cbr 
                                   
                                 
                                 
                                   
                                     y 
                                     ctr 
                                   
                                 
                               
                               
                                 
                                   1 
                                 
                                 
                                   1 
                                 
                                 
                                   1 
                                 
                                 
                                   1 
                                 
                               
                             
                             ] 
                           
                            
                           
                             [ 
                             
                               
                                 
                                   
                                     x 
                                     ctl 
                                   
                                 
                                 
                                   
                                     y 
                                     ctl 
                                   
                                 
                                 
                                   1 
                                 
                               
                               
                                 
                                   
                                     x 
                                     cbl 
                                   
                                 
                                 
                                   
                                     y 
                                     cbl 
                                   
                                 
                                 
                                   1 
                                 
                               
                               
                                 
                                   
                                     x 
                                     cbr 
                                   
                                 
                                 
                                   
                                     y 
                                     cbr 
                                   
                                 
                                 
                                   1 
                                 
                               
                               
                                 
                                   
                                     x 
                                     ctr 
                                   
                                 
                                 
                                   
                                     y 
                                     ctr 
                                   
                                 
                                 
                                   1 
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           [ 
                           
                             
                               
                                 
                                   a 
                                   = 
                                   
                                     
                                       x 
                                       ctl 
                                       2 
                                     
                                     + 
                                     
                                       x 
                                       cbl 
                                       2 
                                     
                                     + 
                                     
                                       x 
                                       cbr 
                                       2 
                                     
                                     + 
                                     
                                       x 
                                       ctr 
                                       2 
                                     
                                   
                                 
                               
                               
                                 
                                   b 
                                   = 
                                   
                                     
                                       
                                         x 
                                         ctl 
                                       
                                        
                                       
                                         y 
                                         ctl 
                                       
                                     
                                     + 
                                     
                                       
                                         x 
                                         cbl 
                                       
                                        
                                       
                                         y 
                                         cbl 
                                       
                                     
                                     + 
                                     
                                       
                                         x 
                                         cbr 
                                       
                                        
                                       
                                         y 
                                         cbr 
                                       
                                     
                                     + 
                                     
                                       
                                         x 
                                         ctr 
                                       
                                        
                                       
                                         y 
                                         ctr 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   c 
                                   = 
                                   
                                     
                                       x 
                                       ctl 
                                     
                                     + 
                                     
                                       x 
                                       cbl 
                                     
                                     + 
                                     
                                       x 
                                       cbr 
                                     
                                     + 
                                     
                                       x 
                                       ctr 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   d 
                                   = 
                                   
                                     
                                       
                                         y 
                                         ctl 
                                       
                                        
                                       
                                         x 
                                         ctl 
                                       
                                     
                                     + 
                                     
                                       
                                         y 
                                         cbl 
                                       
                                        
                                       
                                         x 
                                         cbl 
                                       
                                     
                                     + 
                                     
                                       
                                         y 
                                         cbr 
                                       
                                        
                                       
                                         x 
                                         cbr 
                                       
                                     
                                     + 
                                     
                                       
                                         y 
                                         ctr 
                                       
                                        
                                       
                                         x 
                                         ctr 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   e 
                                   = 
                                   
                                     
                                       y 
                                       ctl 
                                       2 
                                     
                                     + 
                                     
                                       y 
                                       cbl 
                                       2 
                                     
                                     + 
                                     
                                       y 
                                       cbr 
                                       2 
                                     
                                     + 
                                     
                                       y 
                                       ctr 
                                       2 
                                     
                                   
                                 
                               
                               
                                 
                                   f 
                                   = 
                                   
                                     
                                       y 
                                       ctl 
                                     
                                     + 
                                     
                                       y 
                                       cbl 
                                     
                                     + 
                                     
                                       y 
                                       cbr 
                                     
                                     + 
                                     
                                       y 
                                       ctr 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   g 
                                   = 
                                   1 
                                 
                               
                               
                                 
                                   h 
                                   = 
                                   1 
                                 
                               
                               
                                 
                                   i 
                                   = 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   12 
                 
               
             
           
         
       
     
         [0097]    At step  1706 , the resulting matrix M ct M c  is inverted, (M ct M c ) −1 . 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             ( 
                             
                               
                                 M 
                                 ct 
                               
                                
                               
                                 M 
                                 c 
                               
                             
                             ) 
                           
                           
                             - 
                             1 
                           
                         
                         = 
                           
                          
                         
                           
                             [ 
                             
                               
                                 
                                   a 
                                 
                                 
                                   b 
                                 
                                 
                                   c 
                                 
                               
                               
                                 
                                   d 
                                 
                                 
                                   e 
                                 
                                 
                                   f 
                                 
                               
                               
                                 
                                   g 
                                 
                                 
                                   h 
                                 
                                 
                                   i 
                                 
                               
                             
                             ] 
                           
                           
                             - 
                             1 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             1 
                             
                               det 
                                
                               
                                 ( 
                                 
                                   
                                     M 
                                     ct 
                                   
                                    
                                   
                                     M 
                                     c 
                                   
                                 
                                 ) 
                               
                             
                           
                            
                           
                             [ 
                             
                               
                                 
                                   
                                     ( 
                                     
                                       ei 
                                       - 
                                       fh 
                                     
                                     ) 
                                   
                                 
                                 
                                   
                                     - 
                                     
                                       ( 
                                       
                                         bi 
                                         - 
                                         ch 
                                       
                                       ) 
                                     
                                   
                                 
                                 
                                   
                                     ( 
                                     
                                       bf 
                                       - 
                                       ce 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 
                                   
                                     - 
                                     
                                       ( 
                                       
                                         di 
                                         - 
                                         fg 
                                       
                                       ) 
                                     
                                   
                                 
                                 
                                   
                                     ( 
                                     
                                       ai 
                                       - 
                                       cg 
                                     
                                     ) 
                                   
                                 
                                 
                                   
                                     - 
                                     
                                       ( 
                                       
                                         af 
                                         - 
                                         cd 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     ( 
                                     
                                       dh 
                                       - 
                                       eg 
                                     
                                     ) 
                                   
                                 
                                 
                                   
                                     - 
                                     
                                       ( 
                                       
                                         ah 
                                         - 
                                         bg 
                                       
                                       ) 
                                     
                                   
                                 
                                 
                                   
                                     ( 
                                     
                                       ae 
                                       - 
                                       bd 
                                     
                                     ) 
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   13 
                 
               
             
           
         
       
     
         [0000]    where det(M ct M c ) is computed by Sarrus&#39; Rule, 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           M 
                           ct 
                         
                          
                         
                           M 
                           c 
                         
                       
                       ) 
                     
                     
                       - 
                       1 
                     
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             A 
                           
                           
                             D 
                           
                           
                             G 
                           
                         
                         
                           
                             B 
                           
                           
                             E 
                           
                           
                             H 
                           
                         
                         
                           
                             C 
                           
                           
                             F 
                           
                           
                             I 
                           
                         
                       
                       ] 
                     
                     . 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   14 
                 
               
             
           
         
       
     
         [0000]    Any method for calculating a determinant known in the art may be employed. 
         [0098]    At step  1707 , a new camera points matrix, M nc , is calculated by multiplying the inverted matrix, (M ct M c ) −1 , by the transposed matrix, M ct , from step  1703 . 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           M 
                           nc 
                         
                         = 
                           
                          
                         
                           
                             
                               ( 
                               
                                 
                                   M 
                                   ct 
                                 
                                  
                                 
                                   M 
                                   c 
                                 
                               
                               ) 
                             
                             
                               - 
                               1 
                             
                           
                            
                           
                             M 
                             ct 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             [ 
                             
                               
                                 
                                   A 
                                 
                                 
                                   D 
                                 
                                 
                                   G 
                                 
                               
                               
                                 
                                   B 
                                 
                                 
                                   E 
                                 
                                 
                                   H 
                                 
                               
                               
                                 
                                   C 
                                 
                                 
                                   F 
                                 
                                 
                                   I 
                                 
                               
                             
                             ] 
                           
                            
                           
                             [ 
                             
                               
                                 
                                   
                                     x 
                                     ctl 
                                   
                                 
                                 
                                   
                                     x 
                                     cbl 
                                   
                                 
                                 
                                   
                                     x 
                                     cbr 
                                   
                                 
                                 
                                   
                                     x 
                                     ctr 
                                   
                                 
                               
                               
                                 
                                   
                                     y 
                                     ctl 
                                   
                                 
                                 
                                   
                                     y 
                                     cbl 
                                   
                                 
                                 
                                   
                                     y 
                                     cbr 
                                   
                                 
                                 
                                   
                                     y 
                                     ctr 
                                   
                                 
                               
                               
                                 
                                   1 
                                 
                                 
                                   1 
                                 
                                 
                                   1 
                                 
                                 
                                   1 
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             [ 
                             
                               
                                 
                                   
                                     α 
                                     = 
                                     
                                       
                                         Ax 
                                         ctl 
                                       
                                       + 
                                       
                                         Dy 
                                         ctl 
                                       
                                       + 
                                       G 
                                     
                                   
                                 
                                 
                                   
                                     β 
                                     = 
                                     
                                       
                                         Ax 
                                         cbl 
                                       
                                       + 
                                       
                                         Dy 
                                         cbl 
                                       
                                       + 
                                       G 
                                     
                                   
                                 
                                 
                                   
                                     γ 
                                     = 
                                     
                                       
                                         Ax 
                                         cbr 
                                       
                                       + 
                                       
                                         Dy 
                                         cbr 
                                       
                                       + 
                                       G 
                                     
                                   
                                 
                                 
                                   
                                     δ 
                                     = 
                                     
                                       
                                         Ax 
                                         ctr 
                                       
                                       + 
                                       
                                         Dy 
                                         ctr 
                                       
                                       + 
                                       G 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     ɛ 
                                     = 
                                     
                                       
                                         Bx 
                                         ctl 
                                       
                                       + 
                                       
                                         Ey 
                                         ctl 
                                       
                                       + 
                                       H 
                                     
                                   
                                 
                                 
                                   
                                     λ 
                                     = 
                                     
                                       
                                         Bx 
                                         cbl 
                                       
                                       + 
                                       
                                         Ey 
                                         cbl 
                                       
                                       + 
                                       H 
                                     
                                   
                                 
                                 
                                   
                                     μ 
                                     = 
                                     
                                       
                                         Bx 
                                         cbr 
                                       
                                       + 
                                       
                                         Ey 
                                         cbr 
                                       
                                       + 
                                       H 
                                     
                                   
                                 
                                 
                                   
                                     ρ 
                                     = 
                                     
                                       
                                         Bx 
                                         ctr 
                                       
                                       + 
                                       
                                         Ey 
                                         ctr 
                                       
                                       + 
                                       H 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     σ 
                                     = 
                                     
                                       
                                         Cx 
                                         ctl 
                                       
                                       + 
                                       
                                         Fy 
                                         ctl 
                                       
                                       + 
                                       I 
                                     
                                   
                                 
                                 
                                   
                                     ϕ 
                                     = 
                                     
                                       
                                         Cx 
                                         cbl 
                                       
                                       + 
                                       
                                         Fy 
                                         cbl 
                                       
                                       + 
                                       I 
                                     
                                   
                                 
                                 
                                   
                                     ψ 
                                     = 
                                     
                                       
                                         Cx 
                                         cbr 
                                       
                                       + 
                                       
                                         Fy 
                                         cbr 
                                       
                                       + 
                                       I 
                                     
                                   
                                 
                                 
                                   
                                     ω 
                                     = 
                                     
                                       
                                         Cx 
                                         ctr 
                                       
                                       + 
                                       
                                         Fy 
                                         ctr 
                                       
                                       + 
                                       I 
                                     
                                   
                                 
                               
                             
                             ] 
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   15 
                 
               
             
           
         
       
     
         [0099]    At step  1708 , a least squares matrix, M ls , is calculated by multiplying the new camera points matrix by the screen points matrix created in step  1704 . 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           M 
                           ls 
                         
                         = 
                           
                          
                         
                           
                             M 
                             nc 
                           
                            
                           
                             M 
                             S 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             [ 
                             
                               
                                 
                                   α 
                                 
                                 
                                   β 
                                 
                                 
                                   γ 
                                 
                                 
                                   δ 
                                 
                               
                               
                                 
                                   ɛ 
                                 
                                 
                                   λ 
                                 
                                 
                                   μ 
                                 
                                 
                                   ρ 
                                 
                               
                               
                                 
                                   σ 
                                 
                                 
                                   ϕ 
                                 
                                 
                                   ψ 
                                 
                                 
                                   ω 
                                 
                               
                             
                             ] 
                           
                            
                           
                             [ 
                             
                               
                                 
                                   
                                     x 
                                     stl 
                                   
                                 
                                 
                                   
                                     y 
                                     stl 
                                   
                                 
                               
                               
                                 
                                   
                                     x 
                                     sbl 
                                   
                                 
                                 
                                   
                                     y 
                                     sbl 
                                   
                                 
                               
                               
                                 
                                   
                                     x 
                                     sbr 
                                   
                                 
                                 
                                   
                                     y 
                                     sbr 
                                   
                                 
                               
                               
                                 
                                   
                                     x 
                                     str 
                                   
                                 
                                 
                                   
                                     y 
                                     str 
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       l 
                                       
                                         s 
                                         1 
                                       
                                     
                                     = 
                                     
                                       
                                         α 
                                          
                                         
                                             
                                         
                                          
                                         
                                           x 
                                           stl 
                                         
                                       
                                       + 
                                       
                                         β 
                                          
                                         
                                             
                                         
                                          
                                         
                                           x 
                                           sbl 
                                         
                                       
                                       + 
                                       
                                         γ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           x 
                                           sbr 
                                         
                                       
                                       + 
                                       
                                         δ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           x 
                                           str 
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       l 
                                       
                                         s 
                                         2 
                                       
                                     
                                     = 
                                     
                                       
                                         α 
                                          
                                         
                                             
                                         
                                          
                                         
                                           y 
                                           stl 
                                         
                                       
                                       + 
                                       
                                         β 
                                          
                                         
                                             
                                         
                                          
                                         
                                           y 
                                           sbl 
                                         
                                       
                                       + 
                                       
                                         γ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           y 
                                           sbr 
                                         
                                       
                                       + 
                                       
                                         δ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           y 
                                           str 
                                         
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       l 
                                       
                                         s 
                                         3 
                                       
                                     
                                     = 
                                     
                                       
                                         ɛ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           x 
                                           stl 
                                         
                                       
                                       + 
                                       
                                         λ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           x 
                                           sbl 
                                         
                                       
                                       + 
                                       
                                         μ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           x 
                                           sbr 
                                         
                                       
                                       + 
                                       
                                         ρ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           x 
                                           str 
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       l 
                                       
                                         s 
                                         4 
                                       
                                     
                                     = 
                                     
                                       
                                         ɛ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           y 
                                           stl 
                                         
                                       
                                       + 
                                       
                                         λ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           y 
                                           sbl 
                                         
                                       
                                       + 
                                       
                                         μ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           y 
                                           sbr 
                                         
                                       
                                       + 
                                       
                                         ρ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           y 
                                           str 
                                         
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       l 
                                       
                                         s 
                                         5 
                                       
                                     
                                     = 
                                     
                                       
                                         σ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           x 
                                           stl 
                                         
                                       
                                       + 
                                       
                                         ϕ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           x 
                                           sbl 
                                         
                                       
                                       + 
                                       
                                         ψ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           x 
                                           sbr 
                                         
                                       
                                       + 
                                       
                                         ω 
                                          
                                         
                                             
                                         
                                          
                                         
                                           x 
                                           str 
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       l 
                                       
                                         s 
                                         6 
                                       
                                     
                                     = 
                                     
                                       
                                         σ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           y 
                                           stl 
                                         
                                       
                                       + 
                                       
                                         ϕ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           y 
                                           sbl 
                                         
                                       
                                       + 
                                       
                                         ψ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           y 
                                           sbr 
                                         
                                       
                                       + 
                                       
                                         ω 
                                          
                                         
                                             
                                         
                                          
                                         
                                           y 
                                           str 
                                         
                                       
                                     
                                   
                                 
                               
                             
                             ] 
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   16 
                 
               
             
           
         
       
     
         [0100]    Referring to  FIG. 18A , step  1603  will be further described for determining a set of x coordinates for each of a set of positions as method  1800 . At step  1801 , the set of recorded points is retrieved from memory. At step  1802 , a camera points matrix is created from the set of recorded points. 
         [0000]    
       
         
           
             
               
                 
                   
                     M 
                     c 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             x 
                             ctl 
                           
                         
                         
                           
                             y 
                             ctl 
                           
                         
                       
                       
                         
                           
                             x 
                             cbl 
                           
                         
                         
                           
                             y 
                             cbl 
                           
                         
                       
                       
                         
                           
                             x 
                             cbr 
                           
                         
                         
                           
                             y 
                             cbr 
                           
                         
                       
                       
                         
                           
                             x 
                             ctr 
                           
                         
                         
                           
                             y 
                             ctr 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   17 
                 
               
             
           
         
       
     
         [0101]    where M C  is the camera points matrix, x ctl , y ctl  is the x, y position of a top left corner of a camera view, x cbl , y cbl  is the x, y position of a bottom left corner of the camera view, x chr , y cbr  is the x, y position of a bottom right corner of the camera view, and x ctr , y ctr  is the x, y position of a top right corner of the camera view. 
         [0102]    At step  1803 , a screen points matrix is created. 
         [0000]    
       
         
           
             
               
                 
                   
                     M 
                     s 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             x 
                             stl 
                           
                         
                         
                           
                             y 
                             stl 
                           
                         
                       
                       
                         
                           
                             x 
                             sbl 
                           
                         
                         
                           
                             y 
                             sbl 
                           
                         
                       
                       
                         
                           
                             x 
                             sbr 
                           
                         
                         
                           
                             y 
                             sbr 
                           
                         
                       
                       
                         
                           
                             x 
                             str 
                           
                         
                         
                           
                             y 
                             str 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   18 
                 
               
             
           
         
       
     
         [0000]    where M s  is the screen points matrix, x stl , y stl  is the x, y position of a top left corner of a display screen, x sbl , y sbl  is the x, y position of a bottom left corner of the display screen, x sbr , y sbr  is the x, y position of a bottom right corner of the display screen, and x str , y str  is the x, y position of a top right corner of the display screen. 
         [0103]    At step  1804 , a tolerance for each matrix is determined. In a preferred embodiment, the tolerance is a standard deviation of the difference between the number of pixels of the camera and the number of pixels of the screen. Any tolerance or error computation or analysis known in the art may be employed. At step  1805 , the camera points matrix is mapped to a camera square matrix, M c     s   . 
         [0000]    
       
         
           
             
               
                 
                   
                     M 
                     
                       c 
                       s 
                     
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             c 
                             
                               s 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                         
                           
                             c 
                             
                               s 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                         
                           
                             c 
                             
                               s 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       
                         
                           
                             c 
                             
                               s 
                                
                               
                                   
                               
                                
                               4 
                             
                           
                         
                         
                           
                             c 
                             
                               s 
                                
                               
                                   
                               
                                
                               5 
                             
                           
                         
                         
                           
                             c 
                             
                               s 
                                
                               
                                   
                               
                                
                               6 
                             
                           
                         
                       
                       
                         
                           
                             c 
                             
                               s 
                                
                               
                                   
                               
                                
                               7 
                             
                           
                         
                         
                           
                             c 
                             
                               s 
                                
                               
                                   
                               
                                
                               8 
                             
                           
                         
                         
                           
                             c 
                             
                               s 
                                
                               
                                   
                               
                                
                               9 
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   19 
                 
               
             
           
         
       
     
         [0104]    At step  1806 , the screen points matrix is mapped to a screen square matrix, M s     s   . 
         [0000]    
       
         
           
             
               
                 
                   
                     M 
                     
                       s 
                       s 
                     
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             s 
                             
                               s 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                         
                           
                             s 
                             
                               s 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                         
                           
                             s 
                             
                               s 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       
                         
                           
                             s 
                             
                               s 
                                
                               
                                   
                               
                                
                               4 
                             
                           
                         
                         
                           
                             s 
                             
                               s 
                                
                               
                                   
                               
                                
                               5 
                             
                           
                         
                         
                           
                             s 
                             
                               s 
                                
                               
                                   
                               
                                
                               6 
                             
                           
                         
                       
                       
                         
                           
                             s 
                             
                               s 
                                
                               
                                   
                               
                                
                               7 
                             
                           
                         
                         
                           
                             s 
                             
                               s 
                                
                               
                                   
                               
                                
                               8 
                             
                           
                         
                         
                           
                             s 
                             
                               s 
                                
                               
                                   
                               
                                
                               9 
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   20 
                 
               
             
           
         
       
     
         [0105]    Steps  1805  and  1806  will be further described below with reference to  FIG. 18B . 
         [0106]    At step  1807 , the screen square matrix from step  1806  is adjugated to create an adjugated screen matrix. 
         [0000]    
       
         
           
             
               
                 
                   
                     M 
                     
                       a 
                       s 
                     
                   
                   = 
                   
                       
                     
                       [ 
                       
                         
                           
                             
                               
                                 a 
                                 
                                   s 
                                   1 
                                 
                               
                               = 
                               
                                 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       5 
                                     
                                   
                                   · 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       6 
                                     
                                   
                                 
                                 - 
                                 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       8 
                                     
                                   
                                   · 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       9 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 a 
                                 
                                   s 
                                   2 
                                 
                               
                               = 
                               
                                 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       8 
                                     
                                   
                                   · 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       9 
                                     
                                   
                                 
                                 - 
                                 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                   · 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       3 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 a 
                                 
                                   s 
                                   3 
                                 
                               
                               = 
                               
                                 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                   · 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       3 
                                     
                                   
                                 
                                 - 
                                 
                                   
                                     s 
                                     s5 
                                   
                                   · 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       6 
                                     
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 a 
                                 
                                   s 
                                   4 
                                 
                               
                               = 
                               
                                 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       6 
                                     
                                   
                                   · 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       4 
                                     
                                   
                                 
                                 - 
                                 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       9 
                                     
                                   
                                   · 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       7 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 a 
                                 
                                   s 
                                   5 
                                 
                               
                               = 
                               
                                 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       9 
                                     
                                   
                                   · 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       7 
                                     
                                   
                                 
                                 - 
                                 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       3 
                                     
                                   
                                   · 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 a 
                                 
                                   s 
                                   6 
                                 
                               
                               = 
                               
                                 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       3 
                                     
                                   
                                   · 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                 
                                 - 
                                 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       6 
                                     
                                   
                                   · 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       4 
                                     
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 a 
                                 
                                   s 
                                   7 
                                 
                               
                               = 
                               
                                 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       4 
                                     
                                   
                                   · 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       5 
                                     
                                   
                                 
                                 - 
                                 
                                   
                                     s 
                                     s7 
                                   
                                   · 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       8 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 a 
                                 
                                   s 
                                   8 
                                 
                               
                               = 
                               
                                 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       7 
                                     
                                   
                                   · 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       8 
                                     
                                   
                                 
                                 - 
                                 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                   · 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 a 
                                 
                                   s 
                                   9 
                                 
                               
                               = 
                               
                                 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                   · 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                 
                                 - 
                                 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       4 
                                     
                                   
                                   · 
                                   
                                     s 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       5 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   21 
                 
               
             
           
         
       
     
         [0107]    At step  1808 , the camera square matrix, M c     s   , and the adjugated screen matrix, M a     s   , are multiplied into a multiplied matrix, M m . 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       M 
                       m 
                     
                     = 
                     
                       
                         
                           M 
                           
                             c 
                             s 
                           
                         
                         · 
                         
                           M 
                           
                             a 
                             s 
                           
                         
                       
                       = 
                       
                         
                           [ 
                           
                             
                               
                                 
                                   c 
                                   
                                     s 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                               
                               
                                 
                                   c 
                                   
                                     s 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                 
                               
                               
                                 
                                   c 
                                   
                                     s 
                                      
                                     
                                         
                                     
                                      
                                     3 
                                   
                                 
                               
                             
                             
                               
                                 
                                   c 
                                   
                                     s 
                                      
                                     
                                         
                                     
                                      
                                     4 
                                   
                                 
                               
                               
                                 
                                   c 
                                   
                                     s 
                                      
                                     
                                         
                                     
                                      
                                     5 
                                   
                                 
                               
                               
                                 
                                   c 
                                   
                                     s 
                                      
                                     
                                         
                                     
                                      
                                     6 
                                   
                                 
                               
                             
                             
                               
                                 
                                   c 
                                   
                                     s 
                                      
                                     
                                         
                                     
                                      
                                     7 
                                   
                                 
                               
                               
                                 
                                   c 
                                   
                                     s 
                                      
                                     
                                         
                                     
                                      
                                     8 
                                   
                                 
                               
                               
                                 
                                   c 
                                   
                                     s 
                                      
                                     
                                         
                                     
                                      
                                     9 
                                   
                                 
                               
                             
                           
                           ] 
                         
                         · 
                         
                           [ 
                           
                             
                               
                                 
                                   a 
                                   
                                     s 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                               
                               
                                 
                                   a 
                                   
                                     s 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                 
                               
                               
                                 
                                   a 
                                   
                                     s 
                                      
                                     
                                         
                                     
                                      
                                     3 
                                   
                                 
                               
                             
                             
                               
                                 
                                   a 
                                   
                                     s 
                                      
                                     
                                         
                                     
                                      
                                     4 
                                   
                                 
                               
                               
                                 
                                   a 
                                   
                                     s 
                                      
                                     
                                         
                                     
                                      
                                     5 
                                   
                                 
                               
                               
                                 
                                   a 
                                   
                                     s 
                                      
                                     
                                         
                                     
                                      
                                     6 
                                   
                                 
                               
                             
                             
                               
                                 
                                   a 
                                   
                                     s 
                                      
                                     
                                         
                                     
                                      
                                     7 
                                   
                                 
                               
                               
                                 
                                   a 
                                   
                                     s 
                                      
                                     
                                         
                                     
                                      
                                     8 
                                   
                                 
                               
                               
                                 
                                   a 
                                   
                                     s 
                                      
                                     
                                         
                                     
                                      
                                     9 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                    
                   
                       
                   
                    
                   
                     
                       M 
                       m 
                     
                     = 
                     
                       [ 
                       
                         
                           
                             
                               
                                 m 
                                 1 
                               
                               = 
                               
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       4 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       3 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       7 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 m 
                                 2 
                               
                               = 
                               
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       5 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       3 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       8 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 m 
                                 3 
                               
                               = 
                               
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       3 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       6 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       3 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       9 
                                     
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 m 
                                 4 
                               
                               = 
                               
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       4 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       5 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       4 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       6 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       7 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 m 
                                 5 
                               
                               = 
                               
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       4 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       5 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       5 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       6 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       8 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 m 
                                 6 
                               
                               = 
                               
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       4 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       3 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       5 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       6 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       6 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       9 
                                     
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 m 
                                 7 
                               
                               = 
                               
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       7 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       8 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       4 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       9 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       7 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 m 
                                 8 
                               
                               = 
                               
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       7 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       8 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       5 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       9 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       8 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 m 
                                 9 
                               
                               = 
                               
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       7 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       3 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       8 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       6 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       9 
                                     
                                   
                                   · 
                                   
                                     a 
                                     
                                       s 
                                        
                                       
                                           
                                       
                                        
                                       9 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   22 
                 
               
             
           
         
       
     
         [0108]    Referring to  FIG. 18B , each of steps  1805  and  1806  are performed using method  1809 , which will now be described. At step  1810 , a matrix, M i , is retrieved. 
         [0000]    
       
         
           
             
               
                 
                   
                     M 
                     i 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             x 
                             itl 
                           
                         
                         
                           
                             y 
                             itl 
                           
                         
                       
                       
                         
                           
                             x 
                             ibl 
                           
                         
                         
                           
                             y 
                             ibl 
                           
                         
                       
                       
                         
                           
                             x 
                             ibr 
                           
                         
                         
                           
                             y 
                             ibr 
                           
                         
                       
                       
                         
                           
                             x 
                             itr 
                           
                         
                         
                           
                             y 
                             itr 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   23 
                 
               
             
           
         
       
     
         [0000]    For step  1805 , the matrix M i  is the camera points matrix M c . For step  1806 , the matrix M i  is the screen points matrix M s . 
         [0109]    At step  1811 , a set of arrays, px and py, are created from matrix M i  for x and y coordinates. 
         [0000]        px=x   itl   −x   ibl   +x   ibr   −x   itr    Eq. 24
 
         [0000]        py=y   itl   −y   ibl   +y   ibr   −y   itr    Eq. 25
 
         [0110]    At step  1812 , each array is compared to the tolerance. If both arrays are within the tolerance, then method  1809  proceeds to step  1813 . Both arrays are within the tolerance if all the following relationships are true: 
         [0000]        px&lt;t    Rel. 1
 
         [0000]        px&gt;−t    Rel. 2
 
         [0000]        py&lt;t    Rel. 3
 
         [0000]        py&gt;−t    Rel. 4
 
         [0000]    where t is the tolerance. 
         [0111]    At step  1813 , a tolerance square matrix, M s     t   , is calculated from the matrix M i . 
         [0000]    
       
         
           
             
               
                 
                   
                     M 
                     
                       s 
                       t 
                     
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             
                               x 
                               ibl 
                             
                             - 
                             
                               x 
                               itl 
                             
                           
                         
                         
                           
                             
                               x 
                               ibr 
                             
                             - 
                             
                               x 
                               ibl 
                             
                           
                         
                         
                           
                             x 
                             itl 
                           
                         
                       
                       
                         
                           
                             
                               y 
                               ibl 
                             
                             - 
                             
                               y 
                               itl 
                             
                           
                         
                         
                           
                             
                               y 
                               ibr 
                             
                             - 
                             
                               y 
                               ibl 
                             
                           
                         
                         
                           
                             y 
                             itl 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           1 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   26 
                 
               
             
           
         
       
     
         [0112]    At step  1815 , the tolerance square matrix is saved. 
         [0113]    If both arrays are not within the tolerance, then method  1809  proceeds to step  1814 . At step  1814 , a determinant square matrix, M s     d    is calculated. In this step, a set of determinant arrays are calculated from the matrix M i . 
         [0000]        d   x     1     =x   ibl   −x   ibr    Eq. 27
 
         [0000]        d   x     2     =x   itr   −x   ibr    Eq. 28
 
         [0000]        d   y     1     =y   ibl   −y   ibr    Eq. 29
 
         [0000]        d   y     2     =y   itr   −y   ibr    Eq. 30
 
         [0000]    The determinant of the set of arrays is calculated by 
         [0000]      del=det( d   x     1     ·d   x     2     −d   y     1     ·d   y     2   ).   Eq. 31
 
         [0000]    The determinant square matrix, M s     d   , is then calculated from the set of determinant arrays, matrix M i , and the determinant of the set of arrays as defined by 
         [0000]    
       
         
           
             
               
                 
                   
                     M 
                     
                       s 
                       d 
                     
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             
                               x 
                               ibl 
                             
                             - 
                             
                               x 
                               itl 
                             
                             + 
                             
                               
                                 x 
                                 ibl 
                               
                                
                               
                                 ( 
                                 
                                   
                                     det 
                                      
                                     
                                       ( 
                                       
                                         px 
                                         , 
                                         
                                           d 
                                           
                                             x 
                                             2 
                                           
                                         
                                         , 
                                         py 
                                         , 
                                         
                                           d 
                                           
                                             y 
                                             2 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                   del 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               x 
                               itr 
                             
                             - 
                             
                               x 
                               itl 
                             
                             + 
                             
                               
                                 x 
                                 itr 
                               
                                
                               
                                 ( 
                                 
                                   
                                     det 
                                      
                                     
                                       ( 
                                       
                                         
                                           d 
                                           
                                             x 
                                             1 
                                           
                                         
                                         , 
                                         px 
                                         , 
                                         
                                           d 
                                           
                                             y 
                                             1 
                                           
                                         
                                         , 
                                         py 
                                       
                                       ) 
                                     
                                   
                                   del 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             x 
                             itl 
                           
                         
                       
                       
                         
                           
                             
                               y 
                               ibl 
                             
                             - 
                             
                               y 
                               itl 
                             
                             + 
                             
                               
                                 y 
                                 ibl 
                               
                                
                               
                                 ( 
                                 
                                   
                                     det 
                                      
                                     
                                       ( 
                                       
                                         px 
                                         , 
                                         
                                           d 
                                           
                                             x 
                                             2 
                                           
                                         
                                         , 
                                         py 
                                         , 
                                         
                                           d 
                                           
                                             y 
                                             2 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                   del 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               y 
                               itr 
                             
                             - 
                             
                               y 
                               itl 
                             
                             + 
                             
                               
                                 y 
                                 itr 
                               
                                
                               
                                 ( 
                                 
                                   
                                     det 
                                      
                                     
                                       ( 
                                       
                                         
                                           d 
                                           
                                             x 
                                             1 
                                           
                                         
                                         , 
                                         px 
                                         , 
                                         
                                           d 
                                           
                                             y 
                                             1 
                                           
                                         
                                         , 
                                         py 
                                       
                                       ) 
                                     
                                   
                                   del 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             y 
                             itl 
                           
                         
                       
                       
                         
                           
                             
                               det 
                                
                               
                                 ( 
                                 
                                   px 
                                   , 
                                   
                                     d 
                                     
                                       x 
                                       2 
                                     
                                   
                                   , 
                                   py 
                                   , 
                                   
                                     d 
                                     
                                       y 
                                       2 
                                     
                                   
                                 
                                 ) 
                               
                             
                             del 
                           
                         
                         
                           
                             
                               det 
                                
                               
                                 ( 
                                 
                                   
                                     d 
                                     
                                       x 
                                       1 
                                     
                                   
                                   , 
                                   px 
                                   , 
                                   
                                     d 
                                     
                                       y 
                                       1 
                                     
                                   
                                   , 
                                   py 
                                 
                                 ) 
                               
                             
                             del 
                           
                         
                         
                           1 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   32 
                 
               
             
           
         
       
     
         [0114]    At step  1815 , the determinant square matrix is saved. 
         [0115]    Referring to  FIG. 19 , method  1900  for interacting with an action area is described. The method begins at step  1901 . At step  1902 , the camera is queried for motion presence in facial recognition area. At step  1903 , if no presence is detected, the processor returns to step  1902 . If a presence is detected, the process moves to step  1904  and initiates the facial recognition routine to determine the identity of the user. In a preferred embodiment, the facial recognition routine sorts through the database to identify facial features which match a predetermined pattern. The database then is queried for associated user information, such as the user&#39;s name, account status, and contact information including an email address and phone number, which is stored in the memory for later use by the processor. 
         [0116]    At step  1905 , the system begins monitoring the action area. At step  1906 , the camera is queried for image data within the action area. At step  1907 , image data and distance data are perceived in the action area and returned from the camera as coordinates X, Y. At step  1908 , an actual position is calculated to translate the perceived position in the perceived coordinates into the coordinates of a screen using method  1600 . In a preferred embodiment, the actual position is calculated using method  1600  at a rate of 30 times per second. 
         [0117]    At step  1909 , if the action position is not in a sub-action area then the process returns to step  1907 . If it is in a sub-action area, then the processor proceeds to step  1910 . At step  1910 , the system determines if the action is a dwell action or a touch action. In a preferred embodiment, the system determines a time for the action position. For example, how long a user&#39;s hand is in the sub-action area. The system then compares the time with a predetermined time. In one embodiment, the predetermined time is 1.2 seconds. If the time is less than 1.2 seconds, then the action is a touch action. If the time is greater than or equal to 1.2 seconds, then the action is a dwell action. Other times may be employed. 
         [0118]    At step  1911 , a dwell look-up table is queried for a predetermined instruction, if an action is within a sub-action action area and time period. For example, the dwell action is purchase request for the product displayed in the sub-action area. The system queries the database and retrieves the product information of the product associated with the sub-action area. The purchase request is sent to the display and via email or text message to the user device as a hyperlink. The email address and phone number is retrieved from the user&#39;s profile during the facial recognition process. 
         [0119]    At step  1912 , a touch look-up table is queried for a predetermined instruction, if an action is within a sub-action area and time period. For example, the touch action is a coupon or other advertisement for the product displayed in the sub-action area. The system queries the database and retrieves the product information of the product associated with the sub-action area. A link to purchase the product is included. 
         [0120]    At step  1913 , a set of response data is received in the form of a selected link from the purchase request and purchase information entered by a user including name, address, and credit card information. At step  1914  in one embodiment, the purchase information is retrieved from a third party server. At step  1915 , the purchase is processed and a receipt is emailed or sent via text message to the user device. At step  1916 , a feedback message is displayed on the display. For example, the feedback message states, “Thank you for your purchase.” 
         [0121]    It will be appreciated by those skilled in the art that the disclosed embodiments provide a system which embodies significantly more than an abstract idea including technical advancements in the field of data processing and a transformation of data which is directly related to real world objects and situations. Specifically, the disclosed system and methods increase the efficiency of a computer network by identifying a target audience for advertisements without collecting and parsing consumer information. Further, the disclosed system and methods increases the speed of processing purchases by eliminating the wait time in order to complete the purchases. 
         [0122]    It will be appreciated by those skilled in the art that changes could be made to the embodiments described above without departing from the broad inventive concept. It is understood, therefore, that this disclosure is not limited to the particular embodiments herein, but it is intended to cover modifications within the spirit and scope of the present disclosure as defined by the appended claims.