Abstract:
The present invention is a system and method for detecting and analyzing motion patterns of individuals present at a multimedia computer terminal from a stream of video frames generated by a video camera and the method of providing visual feedback of the extracted information to aid the interaction process between a user and the system. The method allows multiple people to be present in front of the computer terminal and yet allow one active user to make selections on the computer display. Thus the invention can be used as method for contact-free human-computer interaction in a public place, where the computer terminal can be positioned in a variety of configurations including behind a transparent glass window or at a height or location where the user cannot touch the terminal physically.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application is entitled to the benefit of Provisional Patent Application Ser. No. 60/369,279, filed Apr. 2, 2002. 

   FEDERALLY SPONSORED RESEARCH 
   Not Applicable 
   SEQUENCE LISTING OR PROGRAM 
   Not Applicable 
   BACKGROUND OF THE INVENTION 
   Field of the Invention 
   The present invention relates to a system and method for detecting and analyzing motion patterns of individuals present at a computer vision-enabled multimedia terminal and the method of providing visual feedback of the extracted information to aid the contact-free human-computer interaction process between a user and the system. 
   BACKGROUND OF THE INVENTION 
   There is a significant need in the art for a system and method for robustly tracking human body motion and to develop means of providing suitable visual feedback of said human movements during an interaction process with a multimedia the system controlled by said human motions. 
   Prior Art 
   Several video tracking systems are well known in the art. However, video tracking systems heretofore known, lack many of the functional, performance and robustness capabilities as the present invention. 
   The methods of Bradski, U.S. Pat. No. 6,394,557 and U.S. Pat. No. 6,363,160, are based on using color information to track the head or hand of a person in the view of a single camera. It is well known, that the use of only color information in general is insufficient to track small, fast moving objects in cluttered environment, their method is hence much less general and only workable in certain specialized environments. No advanced feedback mechanism is in place to improve the interaction between a user and the system. 
   The method of Crabtree et. al, U.S. Pat. No. 6,263,088, is also based on a single camera and designed to track people in a room seen from above. The concept of track feedback visualization does not apply to their application. 
   The method of Qian et. al, U.S. Pat. No. 6,404,900, is designed to track human faces in the presence of multiple people. The method is highly specialized to head tracking, making it unsuitable for alternative application domains and targets, such at human hands. No advanced feedback mechanism is in place to improve the interaction between a user and the system. 
   The method of Sun et. al, U.S. Pat. No. 6,272,250, is also based on a single camera or video and requires an elaborate color clustering approach, making their method computationally expensive and not suitable for tracking general targets in 3D. 
   The method of Harakawa, U.S. Pat. No. 6,434,255, utilizes two video sensors, and requires specialized infrared cameras. Furthermore, additional hardware is required to provide infrared illumination of the user. Finally, the system needs a large mechanized calibration apparatus that involves moving a large marking plate through the space that is later occupied by the user. During the calibration procedure, the movement of the plate has to be precisely controlled by the computer. 
   The method of Hildreth et. al, International Patent. WO 02/07839 A2, determines the 3D locations of objects in the view of multiple cameras by first extracting salient features from each image and then to pair up these two sets to find points in each of the two images that correspond to the same point in space. Their method does not work with only a single camera. 
   The method of Darrell et. al, US 2001/0000025 A1, is also based on two cameras and is faced with exactly the same challenges as the above described method of Hildreth et. al. 
   The method of Moeslund et. al, “Multiple Cues used in Model-Based Human Motion Capture”, in Fourth IEEE International Conference on Automatic Face and Gesture Recognition, 2000, p. 362-367, utilizes color segmentation of the hand and the head and requires the use of two cameras. In addition, their approach fails if the segments of head and hand come too close to each other. 
   The methods of Goncalves et. al, “Monocular tracking of the human arm in 3D”, in Proc. International Conference on Computer Vision, 1995, p. 764-770, and Filova et. al, “Automatic reconstruction of 3D human arm motion from a monocular image sequence”, Machine Vision and Application, 1998, 10: p. 223-231, perform model based tracking of a human arm in a single camera view. This approach obtains 3D information even in a single camera image, which yields robust tracking, potentially making feedback visualization unnecessary. However, model based tracking as described in their paper is computationally extremely expensive and not suitable for practical application. Furthermore, the operating conditions are very constrained requiring the person whose arm is tracked to assume a very specific pose with respect to the camera. 
   The method of Wu et. al, “A Virtual 3D blackboard: 3D finger tracking using a single camera”, in Fourth IEEE International Conference on Automatic Face and Gesture Recognition, 2000, p. 536-542, is also a model-based approach and requires the detection of a users elbow and shoulder, which is difficult to perform outside of very constrained environments. More specifically, their method is based on skin color cues and implicitly assumes that the user, whose arm is being tracked, wears short-sleeved shirts, thus very much limiting the domain in which their method would be useful. 
   The method of Ahmad, “A Usable Real-Time 3D Hand Tracker”, IEEE Asian Conference, 1994, is able to track a human hand held between a camera and a table, where the camera is pointed at the table with the imaging sensor parallel to the table surface. Their method is very specific in that it is only usable in a situation where the user, whose hand is being tracked, is sitting at a table with his hand at a particular location held in a particular pose and thus lacks generality. No advanced feedback mechanism is in place to improve the interaction between a user and the system. 
   The method of Struman et. al, “Hands-on Interaction With Virtual Environments”, in Proceedings of the ACM SIGGRAPH Symposium on User Interfaces, 1989: Williamsburg, Va. p. 19-24, also discusses contact free interaction with a virtual environment. However, their method requires the user to wear a special data glove whose 3D position is sensed through non-visual means. Their method is hence less general than our method and the concept of track feedback visualization does not apply. 
   The method of Davis et. al, “Determining 3-D Hand Motion”, Proceedings of the 28th asilomar conference on signals, systems, and computer, 1994, discusses tracking a person&#39;s hand in 3D based on a single camera view. The method models the fingertips and assumes a clear planar top view of the hand with the fingers stretched out. This type of hand tracking would not be applicable for the type of applications aimed at in this patent and no feedback mechanism is discussed. 
   In a very early work, Bolt, “‘put-that-there’: Voice and gesture at the graphics interface”, In SIGGRAPH &#39;80 Proceedings, volume 14, 1980, presented a virtual interactive environment. Interaction was performed via two joysticks rather then using vision-based approaches, which eliminates the need for advanced feedback visualization. 
   The method of Freeman et. al, “Computer Vision for Interactive Computer Graphics”, IEEE Computer Graphics and Applications, Vol. 18, Issue 3, pp. 42-53, May-June 1998, utilizes a 2D template based approach for interacting with a television display. They explicitly mention the use of feedback for their application, but only display a simple hand cursor at the location of the hand as perceived by the system. Their approach hence only maintains a single hand location hypothesis and therefore lacks the robustness offers by the work disclosed in this patent. 
   In Krahnstoever et. al, “Multimodal Human Computer Interaction for Crisis Management Systems,” IEEE Workshop on Applications of Computer Vision, The Orlando World Center Marriott Orlando, Fla. USA, Dec. 3-4, 2002, and Krahnstoever et. al, “A Real-Time Framework for Natural Multimodal Interaction with Large Screen Displays,” Fourth International Conference on Multimodal Interfaces (ICMI &#39;2002), Pittsburgh, Pa. USA, Oct. 14-16, 2002, a large screen interactive system is presented by Krahnstoever et. al, which also utilizes single camera head and hand tracking. However, as the previous method, only a single hand location hypothesis is estimated and no advanced visual feedback is provided. 
   SUMMARY 
   The present invention operates to process a sequence of input images received from a camera monitoring one or multiple users in front of, for example, a large screen information access terminal. In a preferred embodiment, the present invention collects data that is useful for analyzing and managing user interaction with an information access terminal. 
   The present invention is directed to a system and method for detecting human movement patterns such as hand and arm movements with respect to an information terminal by generating a sequence of video frames containing images of the user. The image information in the video frames is processed by a processor, such as a computer, to identify regions of the video frame representing a user or body parts of a user such as the arm(s) or hand(s). 
   The obtained region information is processed to obtain estimates of the location of the user&#39;s body parts of interest in the view of the camera which can be used in the interaction process by mapping the obtained location information to the video screen on the terminal in a form similar to a mouse pointer commonly used in graphical user interfaces but in a way that takes uncertainty of the obtained location information into consideration. 
   The invention is the methodology for extracting the location information and the associated visual display of the location information that provides effective visual feedback to the user about the user&#39;s body part location as perceived by the processing unit and the uncertainty that the processing unit associates with this location. The feedback of location information and uncertainty information is essential for providing the user with a satisfactory interaction experience. 
   The above and other objects and advantages of the present invention will become more readily apparent when reference is made to the following description, taken in conjunction with the following drawings. 

   
     DRAWINGS—FIGURES 
     FIG.  1 —Figure of the overall system. 
     FIG.  2 —View of the user as seen by the system. 
     FIG.  3 —View of the system as seen by the user. 
     FIG.  4 —Flow of information. 
     FIG.  5 —Uncertainty factors that can lead to ambiguities. 
     FIG.  6 —Activity extraction from video frames. 
     FIG.  7 —Body part location confidence image generation. 
     FIG.  8 —Color motion extraction. 
     FIG.  9 —Confidence Estimation. 
     FIG.  10 —Creation of Body Part Feedback Particle System Image. 
     FIG.  11 —Feedback visualization. 
     FIG.  12 —Interaction with system using feedback visualization. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   A preferred embodiment of the invention is now described in detail. Referring to the drawings, like numbers indicate like components and/or steps throughout the views. 
     FIG. 1  shows the overall system that provides the hardware and application context for the present invention. The hardware components of the system consist of a display terminal  120 , preferably a large screen display, that displays information or multi-media content to the user  130  standing at a distance that allows comfortable viewing of the displayed information. The information that is displayed is supplied by a central processing unit (CPU)  140 , such as a computer. A video camera  110  that can also be coupled to the central processing unit  140  is preferably mounted on top of the display terminal  120  and is directed at a location where the user  130 , in the view of the camera  101 , would normally stand to view the display terminal  120 . All components are non-customized off-the-shelf hardware components; for example, video camera  110  can comprise a SONY EVI D30 Pan-Tilt camera; display terminal  120  can comprise a SONY LCD Projection Data Monitor KL-X9200; and CPU  140  can comprise a DELL Precision 420 Workstation. A physical enclosure (not shown) that contains the components  110 ,  120  and  140  can be provided if desired; such enclosure would typically be custom made and could be configured in numerous shapes and sizes. 
   A typical view  101  that the camera  110  acquires of the user  130  is shown in  FIG. 2 . The camera  110  can capture an image of the entire user  130  or might only capture an image of the upper body of the user  130  as shown in  FIG. 2 . The user  130  is able to interact with the multi-media content displayed on the display terminal  120  using body gestures that can consist of gestures with the (e.g., right) hand  131  or the arm  133 . The user might use the index finger  132  to point at items displayed on the display terminal screen  120 . Since the system can detect the presence of the user  130  by detection his or her face in front of the display, a view of the user&#39;s face  134  can be required. 
     FIG. 3  shows an example display of information that can be shown on the display terminal  120  as seen by the user  130 . The information is presented in the form of text, graphics, videos and/or computer animations. The display might include navigational features such as buttons  141 - 144  that allow the user  130  to make selections  144 , indicate desired actions  142  or to navigate to other parts of the application  141  and  143 , all of which represent typical content found on an interactive display. 
   In the following, the processing and visualization components are described in more detail with reference to  FIG. 4 . The camera  110  is connected to the (CPU)  140 . The signal of the camera (typically NTSC or PAL) is converted to binary data for processing by CPU  140 . This conversion is achieved by a conventional frame grabber  441  that can comprise MATROX Meteor-II frame grabber and that is typically a component directly integrated in connected to the CPU  140 . A processor  443  can comprise a processor (e.g., an Intel Pentium III processor) found in an industry standard personal computer (PC) running a conventional operating system (e.g., the Microsoft Windows 2000® operating system). The individual functions of the overall system are preferably implemented by a software program that may be installed in the memory  442  of the computer, stored on CD-ROM, floppy disk(s), hard disk, etc., or it may be downloaded via a network or satellite connection or reside in system ROM. The system is implemented by several software modules (that can comprise modules developed using the C++ programming language using the C++ Microsoft Visual Studio Development system Version 6.0) each compromising a plurality of executable instructions which, when stored in memory  442 , cause the processor  443  to perform the processes shown and described hereinafter. However, one with ordinary skills in the art will appreciate that several components of the system could be implemented by one or more application specific integrated circuits, digital signal processors or other suitable signal processing architectures. 
   The camera signal is converted into digital images of sizes typically 640×480 or in general Width×Height picture elements (pixels). The converted images are transferred into the memory  442  where they are processed by the processor  443  and the desired information about the user&#39;s presence and actions (e.g., hand and arm gestures as described above) is extracted. This information is used to detect selection and pointing events that can be used as human-computer interaction events, similar to the way that a mouse device can make selections and point at items on a computer screen. The application that is running on the processing unit uses the user activity information to manage the displayed content, which is sent to a graphics card  444  that can comprise an ATI Technologies Inc., Fire GL2 graphics card connected to the display terminal  120 . 
   The system needs to obtain dynamic body pose parameters from the user as seen by the camera. These pose parameters consist preferably of the 3D (x,y,z) location of the user&#39;s hand and pointing direction (described by two angles) with respect to a global system coordinate frame. The system could also extract only the 2D (x,y) location of, for example, the user&#39;s hand in the view of the camera. 
   If the extracted 2D or 3D information is inaccurate or there is some inaccuracy in the systems calibration, the spatial correspondence between user&#39;s movements (such as hand or pointing gestures) and elements on the screen can be degraded or lost. This intuitively leads to situations in which the user is pointing at an item at the screen, but the processing unit “sees” (perceives that) the user pointing at a different location. Hence it is desirable to provide the user with visual feedback about the current state of the body part detection procedure by, for example, displaying a graphical element such as an iconic hand symbol or mouse pointer on the display terminal  120  on top of the information content. This visual feedback is analogous to the feedback that a user is given in graphical user interfaces on a PC operated with a mouse. There is no direct spatial correspondence of the location of the computer mouse with the location on the computer screen that the user would like to reach. However, by providing visual feedback in the form of a mouse pointer, a user applies subconsciously a mapping between the movements of the hand that operates the mouse and the desired movements of the mouse pointer. 
   One with skills in the art will appreciate the difficulties of extracting reliable location information about a user&#39;s body part in the view of a single camera by a computer program. Several factors can distract and confuse a computer program and cause erroneous judgments to be made that can lead to a deteriorated user experience and ultimately in a dissatisfied and frustrated user. In the following explanation, the body part “hand” is used as an example of a body-part that the system might use for the interaction process, but can also mean “hands”, “arm”, “head”, “finger”, etc. 
   It is in general difficult to utilize higher-level domain knowledge of human anatomy, shape and appearance in extracting the desired information. These factors, while easily utilized by humans to locate another person&#39;s hand, show large variability that are not easily discerned from non-hand objects by a computer program operating on standard video data. Computer programs commonly use indirect features such as color or motion information to detect and track a user&#39;s hand. This approach can be distracted by items in an image such as those shown in  FIG. 5 . A background object  150  that has the same color as the user&#39;s hand  131  can cause the processing unit to confuse object  150  with the actual hand  131  of the user. This event is commonly called a false negative (FN) in the art. Other FN&#39;s can be caused by, for example, the user&#39;s own face  134 , or by standers  135  that do not interact with the system but might still be visible in the view of the camera. 
   Due to these challenges, the system can encounter FN detections of for example the object  150  with the hand  131 , without the system having any knowledge about this FN confusion. The present invention, among other things, presents an innovative way of providing the user with a special kind of visual feedback about the current state of the system&#39;s “body part detected” procedure. This visual feedback puts the responsibility for judging the current “body part detected” status, especially with respect to a FN situation, on the user, who is able to make an intuitive and sub-conscious decision and adjust his or her movement patterns to help the system to recover. 
     FIG. 6  shows the overall processing pipeline of the system. The camera  110  captures a video stream of the user  130  interacting in front of the display  120 . The video stream is digitized by the frame grabber  441 , which yields a digitized image  650 . From this image an auxiliary image is generated (described hereinafter) by the processor that gives, for every image location, a measure of the systems confidence that the desired body part is present at that location in the screen. This confidence image contains pixels of value between zero and one with high values denoting high confidence and low values denoting low confidence. For example a scene as shown in  FIG. 5  would give high confidence values to the hand  131  of the user  130  and potentially medium values to other items such as the background object  150  or body parts of bystanders  135 . From this image, suitable visual feedback in the form of an additional visual feedback image  170  is generated in an innovative way (described hereinafter) and displayed on display terminal  120 , to guide the user&#39;s interaction process with the system. 
     FIG. 7  shows a preferred embodiment of the process that generates the body part location confidence image (BPLCI)  160  from the stream of digitized video images  151  provided by the frame grabber  441 . The frame grabber  441  stores the digitized images in memory  442  that can then be accessed by the processor  443 , which generates the BPLCI from this data as described hereinafter. The processor operates in two stages. In the first step, described below with reference to  FIG. 8 , a motion energy image (MEI)  161  and a color segmentation image (CSI)  162  are generated. In the second step, described below with reference to  FIG. 9 , these two images are combined to yield the BPLCI 
   At a given time t, the memory contains digitized video images I t  for time t  152  and a previous I t−1  for a time slice t−1  153 . These two images are analyzed to yield the MEI and the CSI. The MEI image contains pixels of value between zero and one with high values denoting high confidence and low values denoting low confidence that the observed motion that occurred between images  152  and  153  was caused by the desired body part. The CSI image contains pixels of value between zero and one with high values denoting high confidence and low values denoting low confidence that the observed color in the  152  arises from the desired body part. In the presented embodiment of the invention, these motion oriented and color oriented pixel confidence are calculated as follows: 
   Given a second order statistical color model of the hand color with average color με            and covariance matrix ΣεM(3×3,          ). This color model can originate from a skin color sample representing the average population, a skin color sample extracted from the user, e.g., during and initialization phase, or originate from an adaptive skin color extraction procedure. A pixel at location x in the image at time t  152  is now assigned a confidence according to the equation:
                     CSI   t   ′     ⁡     (   x   )       =     e       -     1   2       ⁢       (         I   t     ⁡     [   x   ]       -   μ     )     T     ⁢       ∑     -   1       ⁢     (         I   t     ⁡     [   x   ]       -   μ     )                   (   1.1   )               
This image has values equal to one for pixels that correspond very well to the average skin color and goes towards zero for pixels that show poor correspondence.
 
   The MEI  161  is calculated as follows: For each pixel x from I t  and I t−1 , a difference value is calculated as:
 
Δ I   t ( x )=√{square root over (( I   t ( x )− I   t−1 ( x )) T ( I   t ( x )− I   t−1 ( x )))}{square root over (( I   t ( x )− I   t−1 ( x )) T ( I   t ( x )− I   t−1 ( x )))}{square root over (( I   t ( x )− I   t−1 ( x )) T ( I   t ( x )− I   t−1 ( x )))}{square root over (( I   t ( x )− I   t−1 ( x )) T ( I   t ( x )− I   t−1 ( x )))}.  (1.2)
 
From these differences, MEI t ′ is calculated as
 
                       MEI   t   ′     ⁡     (   x   )       =     CLAMP   ⁡     (         Δ   ⁢           ⁢       I   t     ⁡     (   x   )           σ   MEI       ,   1     )         ,           (   1.3   )               
with σ MEI  a scale factor that controls the weight of observed motion energy values. The function CLAMP ensures that all values are clamped to one. Pixels that now show high confidence both in terms of color and motion energy should lead to a high overall confidence in the final confidence image. However, due to noise, pixels that show high motion energy might not spatially correspond to pixels with high color confidence in terms precise pixel location but usually are close to each other if they arise from the same actual body part. Hence, both CSI t ′ and MEI t ′ need to be smoothed spatially in order to resolve this phenomenon:
 MEI t =G σ     m   {circle around (x)}MEI t ′  (1.4) and CSI t =G σ     c   {circle around (x)} CSI   t ′  (1.5) 
where G σ     m    and G σ     c    correspond to suitable (e.g., Gaussian) smoothing kernels and {circle around (x)} a convolution of the kernel with the image. These two images MEI t  and CSI t  can now be merged into the combined body part location confidence image BPLCI t    160 , which is described hereinafter.
 
     FIG. 9  shows the combination of MEI t  and CSI t . For each pixel location x a pixel in BPLCI t  is assigned the value
   BPLCI   t ( x )= w   m   MEI   t ( x )+ w   cm   MEI   t ( x ) CSI   t ( x )+ w   c   CSI   t ( x ),  (1.6) 
where the variables w m , w cm  and w c  weight the contributions of the different confidence sources. The weights are chosen such that w cm =1−w c −w m .
 
   Equation (1.6) expresses the following logical combination of confidences: A pixel in BPLCI t  should have high confidence, if there is a high confidence that there is motion energy arising from the body part (weighted with w m ) or there is a high confidence that there is color match with the body part (weighted with w c ) or there is high confidence both in terms of motion and color (weighted with w cm ). 
   The BPLCI will in general show high confidence at the actual locations of the user&#39;s body part of interest but may also show large values at locations in the image that contain distracters as described in the foregoing description and  FIG. 5 . One hypothetical location of the body part of interest could now be obtained by choosing the location in the BPLCI that has the highest confidence when compared to all other locations in the image, but many high confidence areas might make the choice of location ambiguous. The best possible scenario is when the user&#39;s body part of interest, say the right hand  131 , is clearly visible in the view of the camera  101  and the hand is in gentle motion, because this yields high confidences in all three terms in equation (1.6). Hence a user that has experience, knows to always give the system a clear view of the hand and to make gentle hand movements in order to help the system see the hand location as well as possible. However, a user is not inherently experienced and it is difficult and undesirable to explicitly train a user to interact in this manner with the system. Hence this invention presents a method for providing visual feedback in the form of a dynamic visual representation of the BPLCI that helps the user grasp the concept of location ambiguities. Every user consciously or subconsciously wants to optimize the interaction process with the system and will adjust his or her motions and actions to get the best possible result. The visual feedback will, mostly without any conscious knowledge of the user, teach the user to perform actions and motions that makes it as easy as possible for the system to locate the user&#39;s hand. 
   The key aspect of the feedback visualization is to generate and display a, normally large, number of small particles from the BPLCI. Each particle can be viewed to represent a certain amount of confidence that the system has in the user&#39;s hand being at the location of the particle. It can furthermore be viewed as a mouse pointer that represents the location of the hand of the user according to the analogy described above. However, a large number of such particles are used. Rather than the location of a single graphical element, the collection of many particles represent the location and confidence of the body part location. The more particles are shown on a certain area of the screen, the higher the confidence of the system that the user&#39;s hand is within that area. An optimal situation with the least amount of ambiguity now corresponds to the situation where a large number of particles are located in a very small region on the display, showing that there is little spatial ambiguity about the location, and high confidence. A less optimal situation corresponds to multiple, spread out clouds of particles with low density. Hence a user attempts to perform actions and movements that yield a single highly localized and dense cloud of particles. 
   Each particle is a small graphical element that has an intensity value. The intensity can be visually represented in several forms; examples of this are color change, area change (shape and size), or transparency value change. When several particles are shown on the screen, they conform what will be defined as Body Part Feedback Particle System Image (BPFPSI)  170 .  FIG. 9  illustrates an example BPFPSI that was obtained from the BPLCI  160  used in the previous figures. In this case the particles are small circles whose intensity is represented by color (a color in the grayscale), being black the maximum intensity, and white the minimum. As noted, the distribution and intensity of the particles give a good reference of what the vision system is interpreting. The cloud with more particles  171  represents the moving hand  131 , and there are a small number of particles with low intensity in the other body parts that are not taking part on the interaction. At each frame, particles are created randomly from a probabilistic distribution that is obtained from the corresponding BPLCI. The particles are created with an initial intensity value that is also obtained from the BPLCI. The lifespan of the particle can be of several frames; the intensity value is decreased at each frame for every particle, and those that reach zero intensity are eliminated. 
   The intensity of a particle is defined to be in the range [0,1]. For each pixel x in the BPLCI, at each frame a particle is created with probability: 
             P   ⁡     (       p   ❘   x     ,   t   ,   ϕ   ,   ω     )       =         n     BPLCI   t       ⁢       BPLCI   t     ⁡     (   x   )           ϕ   ⁢           ⁢   ω             
where ω is the number of desired particles per frame in normal interaction conditions; n BPLCI  is the number of pixels in the BPLCI; and φ is the expected total activity when there is a normal interaction with the screen. This value can be calculated in a calibration phase by training the system in normal condition, from a sample of k frames:
 
   
     
       
         
           ϕ 
           = 
           
             
               1 
               k 
             
             ⁢ 
             
               
                 ∑ 
                 
                   t 
                   = 
                   1 
                 
                 k 
               
               ⁢ 
               
                 [ 
                 
                   
                     ∑ 
                     
                       y 
                       ∈ 
                       
                         BPLCI 
                         t 
                       
                     
                   
                   ⁢ 
                   y 
                 
                 ] 
               
             
           
         
       
     
   
   The initial intensity of the created particle p at time t is simply defined as the value of the pixel in the corresponding BPLCI:
 
 Y   p,t   =BPLCI   t ( x )
 
   The initial position of the particle is the position of pixel x according to the position of the pixel. Once a particle is created, the intensity is decreased over time, until it reaches zero. Particles with zero intensity are eliminated from the BPFPSI. The position of the particle can be slightly changed to produce visual effects, but should remain close to the original position to indicate the location of the body part movement. 
   When the BPFPSI  170  is displayed as visual feedback on the display  120  overlaid on top of information  145  that is displayed to the user  130 , the user might see the combined information  180  that is illustrated in  FIG. 11 . As the user is standing in front of the display  120 , he or she might be pointing at one of the buttons  144 . The overall interaction experience provided by the feedback mechanism is illustrated in  FIG. 12 , which shows the main components of the system together with the combined information  180 . The body part feedback particle system has a high density at the location that the user is pointing to. Actual interaction between the user and the system is provided by making graphical elements of the information that is displayed on the on the screen sensitive to the presence of feedback particles. If a sufficient number of particles are being detected at a selectable graphical element, say one of the buttons  144 , the system assumes that the user wants to select the element (i.e., press one of the displayed virtual buttons  144 ), which triggers a change in the displayed information. In the preferred illustrative embodiment, the user might after a selection be taken to a screen that displays customer service options. 
   While the invention has been illustrated and described in detail, in the drawings and foregoing description, such an illustration and description is to be considered as exemplary and not restrictive in character, it being understood that only the preferred embodiment has been shown and described and that all changes and modifications that come within the spirit of the invention are desired to be protected.