Abstract:
A method of tracking an object of interest preferably includes (i) acquiring a first image and a second image representing different viewpoints of the object of interest; (ii) processing the first image into a first image data set and the second image into a second image data set; (iii) processing the first image data set and the second image data set to generate a background data set associated with a background; (iv) generating a first difference map by determining differences between the first image data set and the background data set and a second difference map by determining differences between the second image data set and the background data set; (v) detecting a first relative position of the object of interest in the first difference map and a second relative position of the object of interest in the second difference map; and (vi) producing an absolute position of the object of interest from the first and second relative positions of the object of interest.

Description:
This application is a continuation of U.S. patent application Ser. No. 12/118,407, filed May 9, 2008, which is a continuation of U.S. patent application Ser. No. 11/248,166, filed Oct. 13, 2005 (abandoned), which is a continuation of U.S. patent application Ser. No. 10/408,671, filed Apr. 8, 2003 (abandoned), which is a continuation of U.S. patent application Ser. No. 09/610,481, filed Jul. 5, 2000, now U.S. Pat. No. 6,803,906, which issued Oct. 12, 2004, all of which are incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention related generally to input devices and in particular to a passive touch system and method of detecting use input. 
     BACKGROUND OF THE INVENTION 
     Touch systems are well known in the art and typically include a touch screen having a touch surface on which contacts are made using a pointer in order to generate user input. Pointer contacts with the touch surface are detected and are used to generate corresponding output depending on areas of the contact surface where the contacts are made. There are basically two general types of touch systems available and they can be broadly classified as “active” touch systems and “passive” touch systems. 
     Active touch systems allow a user to generate user input by contacting the touch surface with a special pointer that usually requires some form of on-board power source, typically batteries. The special pointer emits signals such as infrared light, visible light, ultrasonic frequencies, electromagnetic frequencies, etc. that activate the touch surface. 
     Passive touch systems allow a user to generate user input by contacting the touch surface with a passive pointer and do not require the use of a special pointer in order to activate the touch surface. A passive pointer can be a finger, a cylinder of some material, or any suitable object that can be used to contact some predetermined area of interest on the touch surface. 
     Passive touch systems provide advantages over active touch systems in that any suitable pointing device, including a user&#39;s finger, can be used as a pointer to contact the touch surface. As a result, user input can easily be generated. Also, since special active pointers are not necessary in passive touch systems, battery power levels and/or pointer damage, theft, or misplacement are of no concern to users. 
     Passive touch systems have a number of applications relating to computer operation and video display. For example, in one interactive application, as is disclosed in U.S. Pat. No. 5,448,263 to Martin, assigned to the assignee of the present invention, the passive touch system is coupled to a computer and the computer display is projected onto the touch surface of the touch screen. The coordinates representing specific locations on the touch surface are mapped to the computer display. When a user contacts the touch surface, the coordinates of the contact are fed back to the computer and mapped to the computer display thereby allowing the user to operate the computer in a manner similar to using a computer mouse simply by contacting the touch surface. Furthermore, the coordinates fed back to the computer can be recorded in an application and redisplayed at a later time. Recording contact coordinates is typically done when it is desired to record information written or drawn on the touch surface by the user. 
     The resolution of a passive touch screen determines if the touch system is suitable for recording information written or drawn on the touch screen or only useful for selecting areas on the touch screen mapped to large regions on the computer or video display in order to manipulate the computer or video display. Resolution is typically measured in dots per inch (DPI). The DPI is related to the size of the touch screen and the sampling ability of the touch system hardware and software used to detect contacts on the touch surface. 
     Low-resolution passive touch screens only have enough DPI to detect contacts on the touch surface within a large group of pixels displayed by the computer or video system. Therefore, these low-resolution passive touch screens are useful only for manipulating the computer or video display. 
     On the other hand, high-resolution passive touch screens have sufficient DPI to detect contacts that are proportional to a small number of pixels or sub-pixels of the computer or video display. However, a requirement for high-resolution touch screens is the ability to detect when the pointer is in contact with the touch surface. This is necessary for writing, drawing, mouse-click operations, etc. Without the ability to detect pointer contact with the touch screen, writing and drawing would be one continues operation, and mouse clicks would not be possible thereby making computer display manipulation impossible. A secondary requirement is the ability to detect when the pointer is “hovering” above the touch surface. Although not required for writing or drawing, today&#39;s computer operating systems are increasingly using hover information to manipulate computer or video displays or pop-up information boxes. 
     Passive touch screens are typically either of the analog resistive type, Surface Acoustic Wave (SAW) type or capacitive type. Unfortunately, these touch screens suffer from a number of problems or shortcomings as will be described. 
     Analog resistive touch screens typically have a high-resolution. 
     Depending on the complexity of the touch system, the resolution of the touch screen can produce 4096×4096 DPI or higher. Analog resistive touch screens are constructed using two flexible sheets that are coated with a resistive material and arranged as a sandwich. The sheets do not come into contact with each other until a contact has been made. The sheets are typically kept separated by insulating microdots or by an insulating air space. The sheets are constructed from ITO, which is mostly transparent. Thus, the touch screen introduces some image distortion but very little parallax. 
     During operation of an analog resistive passive touch screen, a uniform voltage gradient is applied in one direction along a first of the sheets. The second sheet measures the voltage along the first sheet when the two sheets contact one another as a result of a contact made on the touch surface. Since the voltage gradient of the first sheet can be translated to the distance along the first sheet, the measured voltage is proportional to the position of the contact on the touch surface. When a contact coordinate on the first sheet is acquired, the uniform voltage gradient is then applied to the second sheet and the first sheet measures the voltage along the second sheet. The voltage gradient of the second sheet is proportional to the distance along the second sheet. These two contact coordinates represent the X-Y position of the contact on the touch surface in a Cartesian coordinate system. 
     Since mechanical pressure is required to bring both sheets into contact, analog resistive touch screens can only detect contact when there is sufficient pressure to bring the two sheets together. Analog resistive passive touch screens cannot sense when a pointer is hovering over the touch surface. Therefore, contact events and positions can only be detected when actual contacts are made with the touch surface. 
     Surface Acoustic Wave (SAW) touch screens typically provide for medium resolution and are not suitable for recording good quality writing. SAW touch screens employ transducers on the borders of a glass surface to vibrate the glass and produce acoustic waves that ripple over the glass surface. When a contact is made on the glass surface, the waves reflect back and the contact position is determined from the signature of the reflected waves. 
     Unfortunately, SAW touch screens exhibit noticeable parallax due to the thickness of the vibrating glass which is placed over the surface of the video or computer display. Also, contact events and positions can only be detected when actual contacts are made with the glass surface. Furthermore, SAW touch screens do not scale beyond a few feet diagonal. 
     Capacitive touch screens provide for low resolution because contacts can only be determined in large areas (approximately ½″×½″). As a result, capacitive touch screens cannot be used for recording writing or drawing and are suitable for selecting areas on the touch screen corresponding to computer generated buttons displayed on the video or computer display. These touch screens also suffer disadvantages in that they are sensitive to temperature and humidity. Similar to analog resistive touch screens and SAW touch screens, capacitive touch screens can also only detect contact events and positions when actual contacts are made with the touch surface. 
     Scalability of passive touch screens is important since the demand for larger electronic digitizers is increasing. Where digitizers were once small desktop appliances, today they have found there way onto electronic whiteboarding applications. The need to build a passive touch sensitive “wall” has become a requirement for new touch screen applications. Existing passive touch screens of the types discussed above are all limited in the maximum size where they are still functional. 
     As will be appreciated, improvements to passive touch systems are desired. It is therefore an object of the present invention to provide a novel passive touch system and method of detecting user input. 
     SUMMARY OF THE INVENTION 
     According to one aspect of the present invention there is provided a passive touch system comprising: 
     a passive touch surface; 
     at least two cameras associated with said touch surface, said at least two cameras acquiring images of said touch surface from different locations and having overlapping fields of view; and 
     a processor receiving and processing images acquired by said at least two cameras to detect the existence of a pointer therein and to determine the location of said pointer relative to said touch surface. 
     In a preferred embodiment, the at least two cameras are two-dimensional image sensor and lens assemblies having fields of view looking along the plane of the touch surface. The processor determines the location of the pointer relative to the touch screen using triangulation. The processor also determines when the pointer is in contact with the touch surface and when the pointer is hovering above the touch surface. 
     In one embodiment, the processor selects pixel subsets of images acquired by the image sensor and lens assemblies and processes the pixel subsets to determine the existence of the pointer. The processor includes a digital signal processor associated with each image sensor and lens assembly and a master digital signal processor in communication with the digital signal processors. The digital signal processors associated with each image sensor and lens assembly select the pixel subsets and process the pixel subsets to determine the existence of the pointer. The master digital signal processor receives pixel characteristic data from the digital signal processors and triangulates the pixel characteristic data to determine the location of the pointer relative to the touch surface. 
     According to another aspect of the present invention there is provided a method of detecting the position of a pointer relative to a passive touch surface comprising the steps of: 
     acquiring images of said touch surface from different locations using cameras having overlapping fields of view; and 
     processing said images to detect the existence of a pointer therein and to determine the location of said pointer relative to said touch surface. 
     The present invention provides advantages in that the passive touch system is of high resolution and allows actual pointer contacts with the touch surface as well as pointer hovers above the touch surface to be detected and corresponding output generated. Also, the present passive touch system provides advantages in that it does not suffer from parallax, image distortion, pointer position restrictions, image projection and scalability problems that are associated with prior art passive touch systems. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       An embodiment of the present invention will now be described more fully with reference to the accompanying drawings in which: 
         FIG. 1  is a schematic diagram of a passive touch system in accordance with the present invention; 
         FIG. 2  is an isometric view of a touch screen forming part of the passive touch system of  FIG. 1 ; 
         FIG. 3  is an isometric view of a corner portion of the touch screen of  FIG. 2 ; 
         FIG. 4  is a schematic diagram of a camera assembly forming part of the touch screen of  FIG. 2 ; 
         FIG. 5  is a front lavational view of the touch screen of  FIG. 2  showing the fields of view of two camera assemblies; 
         FIG. 6  is a schematic diagram of a master controller forming part of the passive touch system of  FIG. 1 ; 
         FIG. 7  is case diagram showing functions executed by the camera assemblies; 
         FIG. 8  is a flowchart showing the steps performed during execution of a findPointerMotion( ) function; 
         FIG. 9  is a flowchart showing the steps performed during execution of an autoSelectThres( ) function; 
         FIG. 10  is a flowchart showing the steps performed during execution of an extractPointer function; 
         FIG. 11  is a flowchart showing the steps performed during execution of a centerOfMass( ) function; 
         FIG. 12  is a flowchart showing the steps performed during execution of a processROI( ) function; 
         FIG. 13  is a flowchart showing the steps performed during execution of a getHighestRegion( ) function; 
         FIG. 14  shows an acquired image and a pixel subset of the image that is processed; 
         FIG. 15  shows a region of interest within the pixel subset; 
         FIG. 16  shows the triangulation geometry used to calculate a pointer contact position on the touch surface of the touch screen; 
         FIG. 17  shows an image acquired by an image sensor and lens assembly including the pointer and its median line; and 
         FIG. 18  shows pointer contact and pointer hover for different orientations of the pointer. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Turning now to  FIG. 1 , a passive touch system in accordance with the present invention is shown and is generally indicated to by reference numeral  50 . As can be seen, passive touch system  50  includes a touch screen  52  coupled to a master controller  54 . Master controller  54  is also coupled to a computer  56 . Computer  56  executes one or more application programs and provides display output that is projected onto the touch screen  52  via a projector  58 . The touch screen  52 , master controller  54 , computer  56  and projector  58  form a closed-loop so that user contacts with the touch screen  52  can be recorded as writing or drawing or used to control execution of application programs executed by the computer  56 . 
       FIGS. 2 to 4  better illustrate the touch screen  52 . Touch screen  52  includes a touch surface  60  bordered by a frame  62 . Touch surface  60  is passive and is in the form of a rectangular planar sheet of material. Camera subsystems are associated with each corner of the touch screen  52 . Each camera subsystem includes a camera assembly  63  mounted adjacent a different corner of the touch screen  52  by a frame assembly  64 . Each frame assembly  64  includes an angled support plate  66  on which the camera assembly  63  is mounted. Supporting frame elements  70  and  72  are mounted on the plate  66  by posts  74  and secure the plate  66  to the frame  62 . 
     Each camera assembly  63 , in this embodiment, includes a camera in the form of a two-dimensional CMOS camera image sensor and associated lens assembly  80 , a first-in-first-out (FIFO) buffer  82  coupled to the image sensor and lens assembly  80  by a data bus and a digital signal processor (DSP)  84  coupled to the FIFO  82  by a data bus and to the image sensor and lens assembly  80  by a control bus. A boot EPROM  86  and a power supply subsystem  88  are also included. 
     In the present embodiment, the CMOS camera image sensor is a Photobit PB300 image sensor configured for a 20×640 pixel subarray that can be operated to capture image frames at rates in excess of 200 frames per second. The FIFO buffer  82  is manufactured by Cypress under part number CY7C4211V and the DSP  84  is manufactured by Analog Devices under part number ADSP2185M. 
     The DSP  84  provides control information to the image sensor and lens assembly  80  via the control bus. The control information allows the DSP  84  to control parameters of the image sensor and lens assembly  80  such as exposure, gain, array configuration, reset and initialization. The DSP  84  also provides clock signals to the image sensor and lens assembly  80  to control the frame rate of the image sensor and lens assembly  80 . 
     As shown in  FIG. 5 , each image sensor and lens assembly  80  has a 55° field of view. The angle of the plate  66  is selected so that the field of view of each image and lens assembly  80  includes at least the majority of a different peripheral edge of the touch surface  60 . In this way, the entire touch surface  60  is within the fields of view of the image sensor and lens assemblies  80 . 
     Master controller  54  is best illustrated in  FIG. 6  and includes a DSP  90 , a boot EPROM  92 , a serial line driver  94  and a power supply subsystem  95 . The DSP  90  communicates with the DSPs  84  of the camera assemblies  63  over a data bus through a serial port  96  and communicates with the computer  56  over a data bus through a serial port  98  and the serial line driver  94 . In this embodiment, the DSP  90  is also manufactured by Analog Devices under part number ADSP2185M. The serial line driver  94  is manufactured by Analog Devices under part number ADM222. 
     The master controller  54  and each camera assembly  63  follow a communication protocol that enables bi-directional communications via a common serial cable similar to a universal serial bus (USB). The transmission bandwidth is divided into thirty-two (32) 16-bit channels. Of the thirty-two channels, five (5) channels are assigned to each of the DSPs  84  in the camera assemblies  63  and to the DSP  90  in the master controller  54  and the remaining seven (7) channels are unused. The master controller  54  monitors the twenty (20) channels assigned to the camera assembly DSPs  84  while the DSPs  84  in the camera subsystems  63  monitor the five (5) channels assigned to the master controller DSP  90 . Communications between the master controller  54  and the camera assemblies  63  are performed as background processes in response to interrupts. 
     The general operation of the passive touch system  50  will now be described. Each camera assembly  63  acquires images of the touch surface  60  within the field of view of its image sensor and lens assembly  80  at the frame rate established by the DSP clock signals and processes the images to determine if a pointer is in the acquired images. If a pointer is in the acquired images, the images are further processed to determine characteristics of the pointer contacting or hovering above the touch surface  60 . Pointer characteristics are then converted into pointer information packets (PIPs) and the PIPs are queued for transmission to the master controller  54 . 
     The camera assemblies  63  also receive and respond to diagnostic PIPs generated by the master controller  54 . 
     The master controller  54  polls the camera assemblies  63  at a set frequency (in this embodiment  70  times per second) for PIPs and triangulates pointer characteristics in the PIPs to determine pointer position data. The master controller  54  in turn transmits pointer position data and/or status information to the personal computer  56 . In this manner, the pointer position data transmitted to the personal computer  56  can be recorded as writing or drawing or can be used to control execution of application programs executed by the computer  56 . The computer  56  also updates the display output conveyed to the projector  58  so that information projected onto the touch surface  60  reflects the pointer activity. 
     The master controller  54  also receives commands from the personal computer  56  and responds accordingly as well as generates and conveys diagnostic PIPs to the camera assemblies  63 . 
     Specifics concerning the processing of acquired images and the triangulation of pointer characteristics in PIPs will now be described with particular reference to  FIGS. 7 to 13 . 
     Initially, an alignment routine is performed to align the image sensor and lens assemblies  80 . During the alignment routine, a pointer is held in the approximate center of the touch surface  60 . Subsets of the pixels of the image sensor and lens assemblies  80  are then selected until a subset of pixels for each image sensor and lens assembly  80  is found that captures the pointer and the pointer tip on the touch surface  60 . This alignment routine allows for a relaxation in mechanical mounting of the image sensor and lens assemblies on the frame assemblies  64 . The identification of the pointer tip on the touch surface  60  also gives a calibration that determines the row of pixels of each image sensor and lens assembly  80  that detects actual contacts made with the touch surface. Knowing these pixel rows allows the difference between pointer hover and pointer contact to be determined. 
     In this embodiment, since a computer display is projected onto the touch surface  60 , during the alignment routine several known coordinate locations are also displayed and the user is required to touch these coordinate locations in sequence using the pointer so that the subset of pixels for each of image sensor and lens assembly  80  includes all of the coordinate locations as well. Calibration data is then stored for reference so that pointer contacts on the touch surface  60  can be mapped to corresponding areas on the computer display. 
     As mentioned above, each camera assembly  63  acquires images of the touch surface  60  within its field of view. The images are acquired by the image and lens assembly  80  at intervals in response to the clock signals received from the DSP  84 . Each image acquired by the image and lens assembly  80  is sent to the FIFO buffer  82 . 
     The DSP  84  in turn reads each image from the FIFO buffer  82  and processes the image to determine if a pointer is located in the image and if so, to extract the pointer and related pointer statistical information. To avoid processing significant numbers of pixels containing no useful information, only the subset of the pixels in the image determined during the alignment routine are actually processed as is shown in  FIG. 14 . 
     In order to determine if a pointer is located in the image and extract pointer and related pointer statistical information, the DSP  84  executes a main findPointerMotion( ) function  120  that calls a number of other functions, namely an autoSelectThres( ) function  122 , an extractPointer function  124 , a centerOfMass( ) function  126 , and a processROI( ) function  128  (see  FIG. 7 ). The extractPointer( ) function  128  also calls a getHighestRegion( ) function  130 . 
     The findPointerMotion( ) function  120  is used to extract the pointer from the image. Turning now to  FIG. 8 , the steps performed during execution of the findPointerMotion( ) function  120  is shown. When the findPointerMotion( ) function is called, a check is made to determine if a previous image iPrev including a pointer exists (step  150 ). If no previous image iPrev exists, center of mass parameters Cx and Cz are assigned zero values (step  152 ). The current image iCurr being processed is then designated as the previous image iPrev (step  154 ) to complete the findPointerMotion( ) function. 
     At step  150 , if a previous image iPrev exists, the current image iCurr is subtracted from the previous image iPrev and the absolute value of the difference image iDiff is taken (step  156 ). By forming the difference image iDiff, background features and noise are removed. The autoSelectThres( ) function  122  is then called to select a threshold value tValue for the difference image iDiff (step  158 ) based on the histogram of the difference image iDiff. The threshold iThres of the difference image iDiff is then taken (step  160 ) to highlight further the pointer within the current image iCurr. During thresholding a grayscale image is mapped to the binary difference image iDiff. Pixels in the difference image with values equal to or less than the threshold value tValue are made black while all other pixels are made white. The result is a binary image containing the pointer and some noise both designated by white pixels. 
     Once the difference image has been thresholded, the extractPointer function  124  is called (step  162 ) to extract the pointer ptr from the difference image iDiff and ignore the noise. The size of the pointer ptr is then examined to determine if it is greater than a threshold value MIN_PTR_SIZE (step  164 ). 
     If the size of the pointer is greater than the threshold value MIN_PTR_SIZE, the centerOfMass( ) function  126  is called (step  166 ) to determine the center of the pointer. Following this, the processROI( ) function  128  is called (step  168 ) to select a region of interest ROI within the difference image iDiff and extract the pointer from the region of interest. 
     Once the pointer has been extracted from the region of interest ROI, the size of the extracted pointer is determined (step  170 ). If the pointer size is greater than zero, a medianLine function is called (step  172 ). During execution of the medianLine function, the median line of the pointer (i.e. the pointer location within the region of interest) is calculated using linear least squares. The current image iCurr is then designated as the previous image iPrev to complete the findPointerMotion( ) function. 
     At step  164 , if the pointer size is equal to zero, the center of mass parameters Cx and Cz are examined (step  174 ). If both of the center of mass parameters Cx and Cz have values greater zero, the processROI( ) function  128  is called (step  168 ) to select a region of interest ROI within the difference image iDiff and extract the pointer from the region of interest. At step  174 , if one or both of the center of mass parameters Cx and Cz have values equal to zero or at step  170 , if the size of the pointer is less than zero, a no pointer found condition is determined (step  176 ). At this stage, the current image iCurr is designated as a calibration image glRef. The findPointerMotion( ) function then proceeds to step  152  where the center of mass parameters Cx and Cz are assigned zero values. 
     As mentioned above, at step  158 , when the findPointerMotion( ) function  120  calls the autoSelectThres( ) function  122 , a threshold value for the difference image iDiff is selected based on the histogram of the difference image so that when the difference image iDiff is thresholded, the pointer is further highlighted from background features and noise. Selection of the threshold value in this manner is more robust than hardcoding the threshold value. 
     Turning now to  FIG. 9 , the steps performed during execution of the autoSelectThres( ) function  122  are illustrated. As can be seen, in order to select the threshold level, a histogram of the difference image iDiff is taken and the number of pixels in each bin of the histogram are counted (step  200 ). The number of pixels in the bin having the highest count is used as a peak parameter and the threshold value is initially assigned a value of one (step  202 ). The number of bins having non-zero counts is then examined to determine if more than eight (8) bins have non-zero counts (step  204 ). If less than eight (8) bins have non-zero counts, the threshold value remains at its initially assigned value and the autoSelectThres( ) function is completed. 
     At step  204 , if more than eight (8) bins have non-zero counts, the number of non-zero bins is checked again to determine if an entire difference image is being processed (i.e. the autoSelectThres( ) function was called by the findPointerMotion( ) function  120 ) or if a region of interest ROI within the difference image is being processed (i.e. the autoSelecThres( ) function was called by the processROI( ) function  128 ) (step  206 ). If the entire difference image iDiff is being processed, a threshold minimum parameter (tMin) is set to a value of twelve (12) and a Peak_Div parameter is set to a value of eight (8) (step  208 ). A minimum count parameter minCount is then calculated by dividing the peak parameter determined at step  202  by the Peak_Div parameter (step  210 ). If a region of interest is being processed, the threshold minimum parameter (tMin) is set to a value of forty (40) and the Peak_Div parameter is set to a value of thirty-two (32) (step  212 ) before proceeding to step  210 . 
     Once minCount has been determined, the peak level is checked to determine if it is greater than the threshold minimum tmin (step  214 ). Peak level is the grayscale level that contains the most pixels. In the case of a tie, the grayscale level with the highest numerical value (i.e. the closest to 255) is chosen. If the peak level is greater than the threshold minimum tMin, a startLevel parameter is assigned a value equal to the peak level+1 (step  216 ). At step  214 , if the peak level is less than the threshold minimum tMin, the startLevel parameter is assigned a value equal to the threshold minimum tMin (step  218 ). 
     Following step  216  or  218 , a loop is entered. During the loop, the levCount for each bin having a bin number between the value of the startLevel parameter and two hundred and fifty-five (255) is examined to determine if it is greater than zero and if it is less than the minCount parameter determined at step  210  (step  220 ). If the condition is met during the loop, the loop is exited and the threshold value is assigned a value equal to the bin number having the levCount that resulted in the loop being exited+1 (step  222 ). If the condition is not met, the loop is exited after the levCount for bin number  255  has been checked. 
     Once the loop has been exited, the threshold value is checked to determine if it is less than the minimum threshold value tMin (step  224 ). If not, a check is again made to determine if an entire difference image is being processed or whether a region of interest ROI is being processed (step  226 ). If the threshold value is less than the minimum threshold value tMin, the threshold value is set equal to the minimum threshold value tMin (step  228 ) before the check is made to determine if an entire difference image is being processed or whether a region of interest is being processed (step  226 ). 
     At step  226 , if a difference image iDiff is being processed, the autoSelectThres( ) function is completed. However, if a region of interest is being processed, a parameter p is assigned a value corresponding to the first grayscale level at which 90% or more of the pixels will go black (step  230 ). The parameter p is then compared to the threshold level (step  232 ). If the parameter p is less than the threshold level, the autoSelectThres( ) function is completed. If the parameter p is greater than the threshold level, the threshold value is set to the value of parameter p (step  234 ) and the autoSelectThres( ) function is completed. 
     As mentioned above, at step  162  the findPointerMotion( ) function  120  calls the extractPointer( ) function  124  to extract the pointer from the binary image and ignore the noise. This is done by selecting the “white region” in the binary image that is greater than or equal to a certain minimum size and is the highest region (i.e. the largest in the y-axis (20 pixel axis)). Specifically, when the extractPointer( ) function  124  is called, the extractPointer( ) function calls the getHighestRegion( ) function  130  (step  250 ). The getHighestRegion( ) function  130  uses the threshold value and tol parameters to select the appropriate white region szRegion in the thresholded difference image. The tol parameter is used to avoid situations where board surface noise is mistaken as a pointer.  FIG. 13  shows the steps performed during this function. 
     Once the white region szRegion has been selected, the white region szRegion is checked to see if it is greater than zero (step  252 ). If not, a no pointer condition is determined (step  254 ). If the white region szRegion is greater than zero, morphological operator of erosion and dilation are used on the white region to reduce further noise (steps  256  to  264 ) and the extractPointer( ) function is completed. 
     As mentioned above, at step  166  the findPointerMotion( ) function  120  calls the centerOfMass( ) function  126  to determine the center of the pointer. During this function, the black pixels in the binary image are treated as having a mass of zero (0) and the white pixel are treated as having a mass of one (1). The physics formulae for center-of-mass are used. The equation below gives the center of mass in the x-direction:
 
 C   x =sum(( X   i )/ M )
 
where:
 
     X i  are the x-coordinates of the white pixels in the binary image; and 
     M is the number of white pixels in the binary image. 
     Initially, once the centerOfMass( ) function is executed, the center of mass parameters massX, massZ and a mass parameter are assigned zero values (see step  300  in  FIG. 11 ). A loop is then entered to calculate the center of mass parameters massX and massZ using the above equation and to calculate the mass parameter (step  302 ). 
     Upon exiting the loop, the mass parameter is checked to determine if its value is greater than zero (step  304 ). If the value of the mass parameter is equal to zero, the center of mass parameters Cx and Cz are assigned values of zero (step  306 ) and the centerOfMass( ) function  126  is completed. At step  304 , if the value of the mass parameter is greater than zero, the center of mass coordinates Cx and Cz are calculated (step  308 ) using the equations:
 
 Cx =mass X /mass; and
 
 Cz =mass Z /mass.
 
     Once the center of mass coordinates have been calculated, the centerOfMass( ) function  126  is completed. 
     As mentioned above, at step  168  the findPointerMotion( ) function  120  calls the processROI( ) function  128  to process the region-of-interest in a manner similar to the findPointerMotion( ) function  120  except, here the image size is 100×20 pixels and a calibration image including only background (i.e. no pointer) is used in place of the previous image. Upon execution of the processROI( ) function  128 , xLeft and xRight parameters are calculated by subtracting and adding fifty (50) to the center of mass parameter Cx (step  350 ). The value of parameter xLeft is then checked to determine if it is less than one (1) (step  352 ). If the parameter xLeft has a value less than one (1), the parameter xRight is recalculated and the parameter xLeft is assigned a value of one (1) (step  354 ) to define boundaries of the region of interest as shown in  FIG. 15 . A difference image iDiff of the region of interest is then calculated by subtracting the region of interest of the current image from the region of interest of the calibration image glRef determined at step  176  of the findPointerMotion( ) function  120  and taking the absolute value of the difference (step  356 ). 
     At step  352 , if the parameter xLeft has a value greater than one (1), the parameter xRight is checked to determine if it has a value greater than 640 (step  358 ). If the parameter xRight has a value greater than 640, the parameter xLeft is recalculated and the parameter xRight is assigned a value of one (1) (step  360 ) to define boundaries of the region of interest. The processROI( ) function  128  then proceeds to step  356  to calculate the difference image iDiff of the region of interest. At step  358 , if the parameter xRight has a value less than 640, the processROI( ) function  128  proceeds directly to step  356  to calculate the difference image iDiff of the region of interest. 
     Once the difference image iDiff of the region of interest has been calculated, the autoSelectThres( ) function  122  is called to select a threshold value for the difference image iDiff of the region of interest (step  362 ) in the manner described above with reference to  FIG. 9 . The difference image iDiff of the region of interest is then thresholded (step  364 ). Following this, the extractPointer( ) function  124  is called to extract the pointer from the difference image iDiff of the region of interest (step  366 ) in the manner described above with reference to  FIG. 10 . 
     Once the acquired image has been processed in the above manner, a PIP for the acquired image is created by the DSP  84 . The PIP is a five (5) word packet and has a layout including camera identification, an LRC checksum to ensure data integrity and a valid tag to ensure zero packets are not valid. The valid tag indicates whether the PIP relates to a pointer characteristic packet ( 10 ), a diagnostic packet for a specific camera assembly  63  ( 01 ) or a diagnostic packet for all camera assemblies  63  ( 11 ). Table 1 below shows the PIP layout. 
     
       
         
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
             
               
               
               
             
               
               
               
             
               
               
               
               
             
               
             
               
               
               
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Word 
                 15 
                 14 
                 13 
                 12 
                 11 
                 10 
                 9 
                 8 
                 7 
                 6 
                 5 
                 4 
                 3 
                 2 
                 1 
                 0 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Pointer Characteristics packet (generated by Camera) 
               
             
          
           
               
                 0 
                 Valid 
                 Camera 
                 X Intercept (at Y0) 
               
               
                   
                 tag 
                 # 
               
             
          
           
               
                 1 
                 Frame rate 
                 intensity/color 
               
             
          
           
               
                 2 
                 Packet # 
                 pointer area 
               
               
                 3 
                 Unused 
                 X intercept (at Y19) 
               
             
          
           
               
                 4 
                 Unused 
                 Z position 
                 LRC checksum 
               
             
          
           
               
                 Diagnostic Packet (generated by Camera or Master) 
               
             
          
           
               
                 0 
                 Valid 
                 Camera 
                   
               
               
                   
                 tag 
                 # 
               
               
                 1 
               
             
          
           
               
                 2 
                 Packet # 
                   
               
               
                 3 
               
             
          
           
               
                 4 
                   
                 LRC checksum 
               
               
                   
               
             
          
         
       
     
     As mentioned above, each camera assembly  63  acquires and processes an image in the manner described above in response to each clock signal generated by its DSP  84 . The PIPs created by the DSPs  84  are only sent to the master controller  54  when the camera assemblies  63  are polled by the master controller. The DSPs  84  create PIPs faster than the master controller  54  polls the camera assemblies  63 . PIPs that are not sent to the master controller  54  are overwritten. 
     When the master controller  54  polls the camera assemblies  63 , frame sync pulses are sent to the camera assemblies  63  to initiate transmission of the PIPs created by the DSPs  84 . Upon receipt of a frame sync pulse, each DSP  84  transmits the PIP to the master controller  54  over the data bus. The PIPs transmitted to the master controller  54  are received via the serial port  96  and auto-buffered into the DSP  90 . 
     After the DSP  90  has polled the camera assemblies  63  and has received PIPs from each of the camera assemblies, the DSP  90  processes the PIPs using triangulation to determine the location of the pointer relative to the touch surface  60  in (x,y) coordinates. Specifically, the PIPs from pairs of camera assemblies  63  are processed using triangulation. 
       FIG. 16  shows that two angles φ 1  and φ 2  are needed to triangulate the position (x 0 ,y 0 ) of the pointer relative to the touch screen  60 . The PIPs generated by each camera assembly  63  include a number θε[0,sensorResolution−1] (see  FIG. 17 ) identifying the median line of the pointer. The sensor Resolution, in the case of the Photobit PB300 image sensor, is 640. The equations below relate the angle φ to the position θ taking into account the field-of-view of the image sensor and lens assembly  80 : 
     
       
         
           
             
               
                 
                   ϕ 
                   = 
                   
                     
                       
                         θ 
                         sensorResolution 
                       
                       × 
                       
                         F 
                         ov 
                       
                     
                     - 
                     δ 
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   ϕ 
                   = 
                   
                     
                       
                         
                           SensorResolution 
                           - 
                           θ 
                         
                         sensorResolution 
                       
                       × 
                       
                         F 
                         
                           ov 
                           ⁢ 
                           
                               
                           
                         
                       
                     
                     - 
                     δ 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     The above equations subtract away an angle δ that allows the image sensor and lens assembly  80  to have some overlap with the frame  62 . The overlap with the frame  62  is desired due to mechanical tolerance issues in the frame assemblies  64  (i.e. the angle of the plate  66  can have an error of 1° to 2°). The angle δ is allowed to be negative, meaning that there is no overlap with the frame  62 , in fact part of the touch surface  60  along the frame  62  is missed. Equation 1 or 2 is used to determine. φ, depending on the mounting and/or optical properties of the image sensor and lens assembly  80 . If the image acquired by the camera assembly  63  is rotated as a result of the mounting and/or optical properties of the image sensor and lens assembly  80 , then equation 2 is used. Equation 1 is used otherwise. In the present embodiment, equation 1 is used with the camera assemblies  63  positioned at the top left and bottom right corners of the touch screen  52  and equation 2 is used with the camera assemblies  63  positioned at the bottom left and top right corners of the touch screen  52 . 
     As discussed above, equations 1 and 2 allow the pointer median line data included in the PIPs to be converted by the DSP  90  into an angle φ with respect to the x-axis. When two such angles are available, the intersection of the median lines extending at these angles from their respective camera assemblies  63  yields the location of the pointer relative to the touch surface  60 . 
     In this embodiment, since the touch screen  52  includes four camera assemblies  63 , six pairs of camera assemblies can be used for triangulation. The following discussion describes how a pointer position is determined by triangulation for each pair of the camera assemblies  63 . 
     In order to determine a pointer position using the PIPs received from the camera assemblies  63  along the left side of the touch screen  52 , the following equations are used to determine the (x 0 ,y 0 ) coordinates of the pointer position given the angles φ 0  and φ 1  for the upper and lower camera assemblies: 
                     x   0     =       h   w     ×     1       tan   ⁡     (     ϕ   0     )       +     tan   ⁡     (     ϕ   1     )                     (   3   )                 y   0     =       tan   ⁡     (     ϕ   0     )           tan   ⁡     (     ϕ   0     )       +     tan   ⁡     (     ϕ   1     )                   (   4   )               
where:
 
     h is the height of the touch screen  52  i.e. the vertical distance from camera assembly focal point-to-focal point; 
     w is the width of the touch screen  52  i.e. the horizontal distance from camera assembly focal point-to-focal point; and 
     φ i  is the angle with respect to the horizontal, measured using camera assembly i and equation 1 or 2. 
     For the camera assemblies  63  along on the right side of the touch screen  52 , the following equations are used to determine the (x 0 , y 0 ) coordinates of the pointer position given the angles φ 2  and φ 3  for the upper and lower camera assemblies: 
     
       
         
           
             
               
                 
                   
                     x 
                     0 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         h 
                         w 
                       
                       × 
                       
                         1 
                         
                           
                             tan 
                             ⁡ 
                             
                               ( 
                               
                                 ϕ 
                                 2 
                               
                               ) 
                             
                           
                           + 
                           
                             tan 
                             ⁡ 
                             
                               ( 
                               
                                 ϕ 
                                 3 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   
                     y 
                     0 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         tan 
                         ⁡ 
                         
                           ( 
                           
                             ϕ 
                             2 
                           
                           ) 
                         
                       
                       
                         
                           tan 
                           ⁡ 
                           
                             ( 
                             
                               ϕ 
                               2 
                             
                             ) 
                           
                         
                         + 
                         
                           tan 
                           ⁡ 
                           
                             ( 
                             
                               ϕ 
                               3 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     The similarity between equations 3 and 5, i.e. equation 5=1-equation 3 once φ 2  and φ 3  have been substituted into equation 3 for φ 1  and φ 2  respectively should be apparent. Equations 4 and 6 are related in a similar manner. 
     In order to determine a pointer position using the camera assemblies  63  along the bottom of the touch screen  52 , the following equations are used to determine the (x 0 , y 0 ) coordinates of the pointer position given the angles φ 0  and φ 3  for bottom left and bottom right camera assemblies: 
     
       
         
           
             
               
                 
                   
                     x 
                     0 
                   
                   = 
                   
                     
                       tan 
                       ⁡ 
                       
                         ( 
                         
                           ϕ 
                           3 
                         
                         ) 
                       
                     
                     
                       
                         tan 
                         ⁡ 
                         
                           ( 
                           
                             ϕ 
                             0 
                           
                           ) 
                         
                       
                       + 
                       
                         tan 
                         ⁡ 
                         
                           ( 
                           
                             ϕ 
                             3 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           y 
                           0 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             w 
                             h 
                           
                           × 
                           
                             
                               tan 
                               ⁡ 
                               
                                 ( 
                                 
                                   ϕ 
                                   3 
                                 
                                 ) 
                               
                             
                             
                               
                                 tan 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     ϕ 
                                     0 
                                   
                                   ) 
                                 
                               
                               + 
                               
                                 tan 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     ϕ 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                           × 
                           
                             tan 
                             ⁡ 
                             
                               ( 
                               
                                 ϕ 
                                 0 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             w 
                             h 
                           
                           × 
                           
                             x 
                             0 
                           
                           × 
                           
                             tan 
                             ⁡ 
                             
                               ( 
                               
                                 ϕ 
                                 0 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     In order to determine a pointer position using the camera assemblies  63  along the top of the touch screen  52 , the following equations are used to determine the (x 0 , y 0 ) coordinates of the pointer position given the angles φ 1  and φ 2  for the top left and top right camera assemblies: 
     
       
         
           
             
               
                 
                   
                     x 
                     0 
                   
                   = 
                   
                     
                       tan 
                       ⁡ 
                       
                         ( 
                         
                           ϕ 
                           2 
                         
                         ) 
                       
                     
                     
                       
                         tan 
                         ⁡ 
                         
                           ( 
                           
                             ϕ 
                             1 
                           
                           ) 
                         
                       
                       + 
                       
                         tan 
                         ⁡ 
                         
                           ( 
                           
                             ϕ 
                             2 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           y 
                           0 
                         
                         = 
                           
                         ⁢ 
                         
                           1 
                           - 
                           
                             
                               w 
                               h 
                             
                             × 
                             
                               
                                 tan 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     ϕ 
                                     2 
                                   
                                   ) 
                                 
                               
                               
                                 
                                   tan 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       ϕ 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 + 
                                 
                                   tan 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       ϕ 
                                       2 
                                     
                                     ) 
                                   
                                 
                               
                             
                             × 
                             
                               tan 
                               ⁡ 
                               
                                 ( 
                                 
                                   ϕ 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           1 
                           - 
                           
                             
                               w 
                               h 
                             
                             × 
                             
                               x 
                               0 
                             
                             × 
                             
                               tan 
                               ⁡ 
                               
                                 ( 
                                 
                                   ϕ 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     The similarity between equations 7 and 9, i.e. equation 9=equation 7 once φ 1  and φ 2  have been substituted into equation 7 for φ 0  and φ 3  should be apparent. Equations 8 and 10 have the following relationship: equation 10=1-equation 8 once φ 1  and φ 2  have been substituted into equation 8 for φ 0  and φ 3  respectively. 
     In order to determine a pointer position using the camera assemblies  63  across the bottom left to top right corner diagonal, the following equations are used to determine the (x 0 ,y 0 ) coordinates of the pointer position given the angles φ 0  and φ 2  for bottom left and top right camera assemblies: 
     
       
         
           
             
               
                 
                   
                     x 
                     0 
                   
                   = 
                   
                     
                       
                         h 
                         w 
                       
                       - 
                       
                         tan 
                         ⁡ 
                         
                           ( 
                           
                             ϕ 
                             2 
                           
                           ) 
                         
                       
                     
                     
                       
                         tan 
                         ⁡ 
                         
                           ( 
                           
                             ϕ 
                             0 
                           
                           ) 
                         
                       
                       - 
                       
                         tan 
                         ⁡ 
                         
                           ( 
                           
                             ϕ 
                             2 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                     y 
                     0 
                   
                   = 
                   
                     
                       
                         1 
                         - 
                         
                           w 
                           h 
                         
                         - 
                         
                           tan 
                           ⁡ 
                           
                             ( 
                             
                               ϕ 
                               2 
                             
                             ) 
                           
                         
                       
                       
                         
                           tan 
                           ⁡ 
                           
                             ( 
                             
                               ϕ 
                               0 
                             
                             ) 
                           
                         
                         - 
                         
                           tan 
                           ⁡ 
                           
                             ( 
                             
                               ϕ 
                               2 
                             
                             ) 
                           
                         
                       
                     
                     × 
                     
                       tan 
                       ⁡ 
                       
                         ( 
                         
                           ϕ 
                           0 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     In order to determine a pointer position using the camera assemblies  63  across the bottom right to top left diagonal, the following equations are used to determine the (x 0 ,y 0 ) coordinates of the pointer position given the angles φ 1  and φ 3  for the bottom right and top left camera assemblies: 
     
       
         
           
             
               
                 
                   
                     x 
                     0 
                   
                   = 
                   
                     
                       
                         h 
                         w 
                       
                       - 
                       
                         tan 
                         ⁡ 
                         
                           ( 
                           
                             ϕ 
                             3 
                           
                           ) 
                         
                       
                     
                     
                       
                         tan 
                         ⁡ 
                         
                           ( 
                           
                             ϕ 
                             1 
                           
                           ) 
                         
                       
                       - 
                       
                         tan 
                         ⁡ 
                         
                           ( 
                           
                             ϕ 
                             3 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
             
               
                 
                   
                     y 
                     0 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           1 
                           - 
                           
                             w 
                             h 
                           
                           - 
                           
                             tan 
                             ⁡ 
                             
                               ( 
                               
                                 ϕ 
                                 3 
                               
                               ) 
                             
                           
                         
                         
                           
                             tan 
                             ⁡ 
                             
                               ( 
                               
                                 ϕ 
                                 1 
                               
                               ) 
                             
                           
                           - 
                           
                             tan 
                             ⁡ 
                             
                               ( 
                               
                                 ϕ 
                                 3 
                               
                               ) 
                             
                           
                         
                       
                       × 
                       
                         tan 
                         ⁡ 
                         
                           ( 
                           
                             ϕ 
                             1 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     The similarity between equations 11 and 13, i.e. equation 13=equation 11 once °1 and °3 have been substituted into equation 11 for φ 0  and φ 2  should be apparent. Equations 12 and 14 have the following relationship: equation 14=1-equation 12 once φ 1  and φ 3  have been substituted into equation 12 for φ 0  and φ 2  respectively. 
     As will be appreciated, the above equations generate the coordinates x 0  and y 0  on a scale of [0, 1]. Therefore, any appropriate coordinate scale can be reported by multiplying x 0  and y 0  by the maximum X and maximum Y values respectively. 
     In the present embodiment, the DSP  90  calculates the pointer position using triangulation for each camera pair excluding the diagonal pairs. The resulting pointer positions are then averaged and the resulting pointer position coordinates are queued for transmission to the personal computer  56  via the serial port  98  and the serial line driver  94 . Since the rows of pixels of the image sensor and lens assemblies  80  that correspond to actual contacts with the touch surface  60  are known, any Z-position in a PIP that does not correspond with one of these rows is by definition a pointer hover event. 
     If desired, pointer velocity and angle can be calculated by the DSP  90  as shown in  FIG. 18 . The velocity of the pointer is calculated by examining the changes in the Z-position (or X-intercept) of the pointer in successive PIPs and knowing the camera frame rate. For example, if the camera frame rate is 200 frames per second and the Z-position changes by 1 pixel per frame, the pointer velocity is 200 pixels per second. 
     The angle of the pointer can be determined due to the fact that the PIP includes the X-intercept at pixel rows 0 and 19 of the median line. Since the X distance (the difference between X-intercepts) and the Y distance (the number of pixel rows) are known, all of the information necessary to calculate the pointer angle is available. 
     The present invention provides advantages in that the passive touch system  50  does not suffer parallax and/or image distortion problems due to the fact that a glass or other transparent overlay over a computer or video display is not required. In addition, the present passive touch system  50  allows both pointer contact and pointer hover over the touch surface  60  to be detected by using two-dimensional image sensor and lens assemblies  80  in the plane of the touch surface  60 . Pointer contact with the touch surface  60  is defined only when the pointer is in very close proximity of the touch surface. The present invention also provides advantages in that the pointer position with respect to the touch surface is not restricted since the image sensor and lens assemblies  80  look along the plane of the touch surface  60 . 
     With respect to resolution, the resolution of the passive touch system is a function of the distances of the pointer with respect to the image sensor and lens assemblies  80 , the number of pixel elements in the image sensor and lens assemblies and the fields of view of the image sensor and lens assemblies. Since image sensor and lens assemblies are available with pixel elements that range in number from tens of thousand to many millions and since the number of pixel elements in image sensors and lens assemblies of this nature is only expected to increase, the resolution of the present passive touch system  50  is high. 
     The passive touch system  50  also provides advantages in that alignment is automatically corrected since only pixel subsets of images that include the touch surface and the pointer are processed. In addition, the present passive touch system allows for very fast acquisition of image data since the image sensor and lens assemblies can be triggered to capture images at rates exceeding two hundred frames per second. 
     The present passive touch system  50  is scalable and can include a touch surface  60  of arbitrary size. When used in conjunction with a projected computer image, the number of pixels of the image sensor and lens assemblies should be proportional to the number of pixels being displayed on the touch surface  60 . For example, if a projected computer image is 1024×768 pixels, the size of the projected image is not be of concern provided the image sensor and lens assemblies  80  are able to resolve the (x,y) coordinates with sufficient accuracy with respect to the displayed pixels. 
     Although the passive touch system  50  is shown including camera assemblies  63  associated with each corner of the touch screen  52 , those of skill in the art will appreciate that only two camera assemblies are required. In this case, the fields of view of the image sensor and lens assemblies are preferably selected so that the entire touch surface  60  is encompassed since the locations of pointer contacts are determined only when they occur within the overlapping fields of view of the camera assemblies  63 . 
     Also, although the passive touch system  50  is described as including a projector to display the computer display output onto the touch surface  60 , this is not required. No information need be displayed on the touch surface. 
     Although a preferred embodiment of the present invention has been described, those of skill in the art will appreciate that variations and modifications may be made without departing from the spirit and scope thereof as defined by the appended claims.