Abstract:
The present invention pertains generally to the field of computer graphics user interfaces. More specifically, the present invention discloses a video image based tracking system that allows a computer to robustly locate and track an object in three dimensions within the viewing area of two or more cameras. The preferred embodiment of the disclosed invention tracks a person&#39;s appendages in 3D allowing touch free control of interactive devices but the method and apparatus can be used to perform a wide variety of video tracking tasks. The method uses at least two cameras that view the volume of space within which the object is being located and tracked. It operates by maintaining a large number of hypotheses about the actual 3D object location.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application is based on and claims priority to U.S. Provisional Application No. 60/426,574, filed Nov. 15, 2002, which is fully incorporated herein by reference. 

   FEDERALLY SPONSORED RESEARCH 
   Not Applicable 
   SEQUENCE LISTING OR PROGRAM 
   Not Applicable 
   BACKGROUND OF THE INVENTION 
   Field of the Invention 
   The present invention pertains generally to the field of computer graphics user interfaces. More specifically, the present invention discloses a video image based tracking system that allows a computer to robustly locate and track an object in three dimensions within the viewing area of two or more cameras. The preferred embodiment of the disclosed invention tracks a person&#39;s appendages in 3D allowing touch free control of interactive devices but the method and apparatus can be used to perform a wide variety of video tracking tasks. 
   BACKGROUND OF THE INVENTION 
   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 method of Harakawa, U.S. Pat. No. 6,434,255, also utilizes two video sensors, but 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 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. It is well known in the art, that this feature matching approach takes a lot of computational resources and that it easily fails in situations where no or very few clean feature sets can be extracted, where occlusion prevents pairing of a feature in one image with a point in the second image. It is common to pair two features that do not correspond to the same location in space, yielding an entirely incorrect 3D location estimate. Finally, their method requires additional processing based on the stereo information calculated to determine the actual location of the object to be tracked, with many more computational steps as the present invention. 
   The method of Darrell et. al, US 2001/0000025 A1, is also based on two cameras but also requires the calculation of a disparity image, which is faced with exactly the same challenges as the above described method of Hildreth et. al. 
   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. The use of a single camera does not yield any 3D coordinates of the objects that are being tracked. Furthermore, it is well known, that the use of only color information and a single camera 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. In particular, their method will fail, if for example the user holds his hand in front of his face. 
   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 use of a single camera does not yield any 3D coordinates of the objects that are being tracked. 
   The method of Jolly et. al, U.S. Pat. No. 6,259,802, is also based on a single camera and requires a means to extract and process contour information from an image. Contour extraction is both time consuming and prone to error 
   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 also based on a single camera, yielding no 3D information, utilizes only color information and is highly specialized to head tracking, making it unsuitable for alternative application domains and targets. 
   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 Moeslund T. B., et al., 4th IEEE Int. Conf. Automatic Face and Gesture Rec., 2000, p. 362-367, utilizes color segmentation of the hand and the head in two cameras. This approach fails if the segments of head and hand come too close to each other. 
   The methods of Goncalves L., et al., Proc. International Conference on Computer Vision, 1995, p. 764-770, and Filova V., et al., 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, 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 A., et al., 4th IEEE Int. Conf. Automatic Face and Gesture Rec., 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 S., 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. 
   SUMMARY 
   A method for locating and tracking objects is disclosed. The method uses at least two cameras that view the volume of space within which the object is being located and tracked. It operates by maintaining a large number of hypotheses about the actual 3D object location. The set of hypotheses is continuously updated based on incoming video information. First, each hypothesis is evaluated based on information obtained from the video cameras such as motion and color. Based on the obtained values, a new set of hypothesis is generated and the location of each hypothesis is randomly varied. The mean of the hypothesis set forms the final 3D object location result. The covariance of the set gives an estimate of the location uncertainty. 

   
     DRAWINGS 
     Figures 
       FIG. 1  illustrates a preferred embodiment of the presented invention where a person&#39;s hand is tracked in 3D by two cameras. 
       FIG. 2  is a block diagram showing the hardware components of the tracking system. 
       FIG. 3  illustrates a typical view of one of the system cameras. 
       FIG. 4  illustrates the viewing geometry of the two cameras looking at the target hand that is being tracked in 3D. Shown also are the images that are being captured by the cameras. 
       FIG. 5  illustrates the challenge of simply combining confidence estimates based on color and motion cues. 
       FIG. 6  illustrates how to spatial spread out a cue response image. 
       FIG. 7  illustrates how two spread out cue response images are combined into a single combined cue response image. 
       FIG. 8  illustrates how two cameras that capture confidence images can determined whether a point in space is located inside the hand or not. 
       FIG. 9  shows a calibration target in the view of one of the system cameras. 
       FIG. 10  shows the algorithm that is used to calibrate a camera. 
       FIG. 11  illustrates hypotheses that are being used to determine the location of the target. 
       FIG. 12  illustrates the estimated target location together with a sphere that illustrates uncertainty of the target location. 
       FIG. 13  shows the overview of the tracking algorithm. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   A method and apparatus for tracking an object in three dimensions is disclosed. Although the presented embodiment describes tracking a person&#39;s hand, one with ordinary skills in the art understands that the presented invention not only pertains to tracking a person&#39;s hand but also general objects if the color of the object to be tracked is known. Furthermore, it will be apparent for one skilled in the art that certain details are not required in order to practice the present invention. 
   Object Tracking System Overview 
   A preferred embodiment of the disclosed invention is shown is illustrated in  FIG. 1 . Two color cameras  110  and  120  are connected to a computer system  130 . The cameras are pointed at and capture a plurality of images of a hand  100  of a person  140  that is in the viewing area of the cameras. In the illustrated embodiment, the cameras are located on top of a stand looking down at the object  100  to be tracked. However, other viewing configurations such as the cameras being located on the floor, looking up, or asymmetrical configurations with one camera on top and the other camera on the floor are possible. The disclosed method and apparatus continuously determines the 3D hand location in a coordinate system  150  from the video data captured by the cameras. 
   The embodiment in  FIG. 1 , which uses the teachings of the present invention, enables a person to point at the terminal display  160  and to perform selections of items shown on the screen. The method enables this remote control of the terminal by tracking the users hand in 3D and by showing a hand symbol  170  on the screen that represents the location of the users hand with respect to the terminal. Selection can be performed by moving the hand towards the screen. 
   As illustrated in  FIG. 1  and shown in more detail in  FIG. 2 , the cameras  110  and  120  are connected to a computer system  130 . The computer system  130  contains an apparatus  200  for capturing the video data that is captured by the cameras. In the preferred embodiment, this apparatus  200  is an IEEE 1394 digital video interface and the cameras  110  and  120  IEEE 1394 compatible cameras. However for one with ordinary skills in the art it will be apparent that other embodiments, for example using television cameras and frame grabbers, are possible and equivalent. The video capture apparatus transfers the images to a computer memory  210  of the computer system that is accessible by a processing device  220 . 
     FIG. 3  illustrates a typical task that the disclosed invention solves. It shows a typical camera view  300  that is captured by either of the cameras  110  and  120  showing the person  140  stretching out the arm and hand  100 . Tracking the target object (the hand  100 ) is challenging because of the presence of other distracting objects in the camera view such as objects in the background  310  that have similar color as the hand  100 , other people  320  and also the face  330  of the user  310  as the color of the skin of the person  310  and other people  320  can closely match the color of the target object  310 . 
   As  FIG. 4  illustrates, a volume in space  400  is defined that is visible in both cameras  110  and  120 . Locations in this space, for example a point  410  on the palm of the users hand  100  is visible at the image location  410   b  in the image  420  as captured by the Left camera  110  and at location  410   c  in the image  430  as captured by the right camera  120 . The location of the point  410  is related to the locations  410   b  and  410   c  by a mathematical projection functions that projects 3D space locations in the coordinate system  150  to 2D locations  410   b  and  410   c  in images  420  and  430  respectively. For illustration, these projections map a point in space along the viewing rays  440  and  450  onto the image sensors of the camera. 
   More specifically, we assume that the two cameras  110  and  120  are calibrated to the extent that we know the projection matrices, denoted by P L  and P R , that project from world coordinate vector to image coordinate vector. Furthermore we denote the said images  420  and  430  by I L  and I R  respectively. Given a point (e.g.,  410 ) as a vector in homogenous world coordinates R=(X,Y,Z,W) T  we denote the corresponding homogenous vector representation of that point (e.g.,  410   b  and  410   c ) in the left and right camera image coordinates as r L =(x L ,y L ,w L ) and r R =(x R ,y R ,w R ). The image coordinate points are related to the world coordinate point by r L =P L R and r R =P R R. The x and y coordinates in the images  420  and  430  of r L  and r R  are given by s L =(x L /w L ,y L /w L ) ( 410   b ) and s R =(x R /w R ,y R /w R ) ( 410   c ) according to the theory of projective geometry. 
   Projective geometry states, that we can obtain from the projected locations r L  and r R  of a point R, the corresponding 3D coordinate through triangulation. Most stereo algorithms rely on this principle by finding correspondences between two images and recovering depth through triangulation. However, finding correspondences between views is challenging, especially with wide baseline camera configurations. Simply said, it is very difficult for an apparatus or method to determine the location  410   c  of a point  410  on a person&#39;s hand in an image  430  if given an image  420  and location  410   b.    
   The disclosed method and apparatus circumnavigates this problem in the following way: Given a hypothesized hand location in world coordinates R, the image data is used to measure the confidence in this hypothesis, i.e., the degree to which the image data supports the hypothesis that a hand is indeed present at the 2D locations corresponding to the world coordinate R. To increase the accuracy of the approach, a large number of such hypotheses are maintained and combined to get a statistical measure of the true hand location in world coordinate space. 
   More specifically, given a hand location R and the said projection matrices P L  and P R , we can project R into the left and right image coordinate system and analyze image observations I L [s L ] and I R [s R ] towards determining whether or not a hand is present at location R. The decision of whether or not a hand is present at R given I L [s L ] or I R [s R ] is based on color and motion information extracted from the images that are captured by cameras  110  and  120 . 
   Color Cue 
   Picture elements (pixels) in images captured by the cameras I L  and I R  are assumed to be given by color triplets (Y,U,V). More specifically, a location I L [s] in the image contains three values (Y s ,U s ,V s ) corresponding to the luminance and the two chrominance channels of the camera. 
   The color of the target to be tracked (the users hand in the described preferred embodiment) can be represented by a color histogram H. This histogram can for example be obtained as follows. An image/of the users hand is taken and locations in the image that are occupied by the hand are marked. The pixels at the marked locations s i , namely, I[s i ]=(Y i ,U i ,V i ) are inserted into a three channel histogram, i.e., one histogram H Y  is created from values Y i , a second one H U  is created from values U i  and a third one H V  from values V i  by appropriately inserting these values into histogram bins. Now, given a color image triplet (Y s ,U s ,V s ) at a location s in an image (e.g., I L ) that may or may not be occupied by the hand of the user during tracking, a confidence measure of whether or not a hand is indeed present at that location is given by the function 
                     C   ⁡     (   s   )       =           H   Y     ⁡     [     Y   s     ]       ⁢       H   U     ⁡     [     U   s     ]       ⁢       H   V     ⁡     [     V   s     ]           max   ⁢           ⁢     H   Y     ⁢           ⁢   max   ⁢           ⁢     H   U     ⁢           ⁢   max   ⁢           ⁢     H   V           ,           (   1.1   )               
where H Y [Y s ] corresponds to amount of samples that were inserted into the bin in histogram H Y  that corresponds to the value Y s . The color feature image C(s) takes values between zero and one, where a value of one corresponds to the highest confidence of a hand being present at location s in the image. The color feature images created from the left or right camera image are denoted as C L  and C R  respectively.
 
Motion Cue
 
   In addition to the color information, motion information is utilized for measuring whether or not a hand is present at a certain image location. Two images I L,t  and I L,t−dt  captured consecutively from a camera at time t with a short time interval dt between them (typically 33 ms) are used in the following manner: At an image location s at which motion is supposed to be measured, the color triplets are extracted from each of the two images, denoted as (Y s,t ,U s,t ,V s,t ) and (Y s,t−dt ,U s,t−dt ,V s,t−dt ). If an object moved in the image at the location s, these values will be different from each other. The size of this difference indicates how rapidly, the scene changes at that location. Hence, the function
 
 D ( Y   s,t   ,U   s,t   ,V   s,t   ,Y   s,t−dt   ,U   s,t−dt   ,V   s,t−dt )=√{square root over (( Y   s,t−dt   −Y   s,t ) 2 +( U   s,t−dt   −U   s,t ) 2 +( V   s,t−dt   −V   s,t ) 2 )}{square root over (( Y   s,t−dt   −Y   s,t ) 2 +( U   s,t−dt   −U   s,t ) 2 +( V   s,t−dt   −V   s,t ) 2 )}{square root over (( Y   s,t−dt   −Y   s,t ) 2 +( U   s,t−dt   −U   s,t ) 2 +( V   s,t−dt   −V   s,t ) 2 )}
 
is small or zero, when there is little or no change in the scene and large if there is change, which is an indication for motion. This function is scaled to an interval of zero to one using
 
                     M   ⁡     (     s   ,   t     )       =     ⅇ       -     1   σ       ⁢     D   ⁡     (       Y     s   ,   t       ,     U     s   ,   t       ,     V     s   ,   t       ,     Y     s   ,     t   -     ⅆ   t           ,     V     s   ,     t   -     ⅆ   t             )             ,           (   1.2   )               
where the value a determines the sensitivity of the motion cue. The motion feature images created from pairs of images of the left or right camera for time t are denoted as M L (s,t) and M R (s,t) respectively.
 
   The final measure of confidence of observing a hand at location s in an image is given by a combination of the color and the motion cue at that location. The proposed method and apparatus is hence tuned towards tracking and locating targets that are moving and have a color according to the target color histogram. However, as illustrated in  FIG. 5  on the example of a moving black rectangle, the color confidence image and the motion confidence image have to be post-processed before they can be utilized. The rectangle is shown as  650  at time t−dt in an image  600  captured by a camera and as  650 B captured at a later time, time t, in an image  610  by the same camera. While the motion cue function M(s,t) ( 630 ) for this target tends to have high responses at the edges  631  and  632  of the target, the color cue function  620  tends to have high responses at the interior of the target  621 . A logical or arithmetic combination of the two cues shown in image  640  only shows a response where both  620  and  630  show a response, i.e., where the cues intersect (at  641 ) if overlaid on top of each other. 
   Therefore, the color and the motion cues are spatially spread out using averaging before they are combined. Given an image  800  with each location in the image containing the value of a cue response, a new image  810  is generated, where a location contains the thresholded average of values in a neighborhood surrounding the location. In  FIG. 7 , location  801  has an associated neighborhood  805   a , location  802  has a neighborhood  805   b  of the same size as  805   a  and location  803  has a neighborhood  805   c  of the same size as  805   a  and  805   b . In the new image  810 , after performing the averaging, location  801  contains a new non-zero value, because its neighborhood  805   a  contains image locations that also have non-zero values. For location  802  in the new image, the new value is zero, because neighborhood  805   b  in image  800  does not contain any non-zero image locations. Finally, location  803  in the new image  810  has a non-zero value, because its neighborhood  805   c  contains only non-zero image locations in image  800 . The amount of spread is determined by the size of the neighborhood. 
   For the example of the rectangle in  FIG. 5 , this amounts to the result illustrated in  FIG. 6 . The spread out color cue image is shown in  700 . The spread out motion cue image is shown in  710 . A combination of the two spread out images now results in an image  720  where a combined response is not only present at some of the edged of the rectangle (as in  641  in  FIG. 5 ) but also contains strong responses in the interior as shown in  720 . 
   If we denote the spread out color cue image with CS(s,t) and the spread out motion cue image as MS(s,t), the final hand location confidence image is obtained via:
 
 CONF ( s,t )= w   c   CS ( s,t )+ w   m   MS ( s,t )+(1− w   c   −w   e ) CS ( s,t ) MS ( s,t )  (1.3)
 
where the factors w c  and w m  weigh the contributions of the motion and color image cues. Here, CONF(s,t) is an image at time t that contains for each location s=(x,y) a measure of the confidence of a hand being present at the world location that projected to the image coordinate s.
 
   Such a confidence image is calculated for each time step for both the right and the left camera.  FIG. 8  illustrates the confidence images  910  and  920  that are captured by the left  110  and right  120  camera of the user&#39;s hand  100 . Given now a location  410  on the users hand that projects to locations  410   b  and  410   c  in the left and right confidence image respectively, the presence of the hand is supported by the fact that both the left and the right confidence images  910  and  920  show a high confidence. In contrast, a location  940  not on the users hand, that projects to locations  940   b  in the left confidence image and to location  940   c  in the right image only shows a high confidence in one of the two cameras. Hence, the confidence of a hand being present at the location  940  is not well supported by the two confidence images as calculated by the image obtained from the two cameras. 
   This combination of confidence images CONF L (s,t) and CONF R (s,t) as obtained by the two cameras is utilized as follows: Given a location R=(X,Y,Z,1) in homogeneous world coordinates that projects to s L  and s R  in the left and right camera image respectively, the overall confidence of a hand being located at R is given by
 
 CONF   LR ( s   L   ,s   R )= CONF   L ( s   L   ,t ) CONF   R ( s   R   ,t ).  (1.4)
 
The confidence function CONF LR (R) has large values for those locations in space R that are occupied by the target object. Furthermore, the function might also have large values at other locations that have a color that is similar to the color of the target object and/or are occupied by a moving object. The confidence function contains useful information because the target object is likely to be the object that leads to the largest and most confident region in space. The disclosed method assumes that the true target location is given as the central location of this assumed confident region and that the uncertainty about the location is given by a measure of the extent of this region.
 
Target Location Estimation
 
   As illustrated in  FIG. 11 , the location of the target is estimated over time by maintaining a large number N of location hypotheses H i  ( 1200   a ,  1200   b , . . . ) distributed in viewing volume  400 . In the illustration  FIG. 11 , the value is N=14 but in practice, this number is much larger. Each hypothesis H i  has associated with it a location in space R t   i  ( 1220   a ) and a weight W t   i  ( 1210   a ) that is given by the confidence of that location divided by the sum of the confidences of all hypotheses combined such that their sum is one. The final target location at time t is given by the weighted mean of all location hypotheses 
             TARGETLOC   ⁡     (   t   )       =       ∑     i   =   1     N     ⁢       W   t   i     ⁢       R   t   i     .               
The uncertainty about this location is given by the quantity
 
             UNCERTAIN   ⁡     (   t   )       =           ∑     i   =   1     N     ⁢         W   t   i     ⁡     (       R   t   i     -     TARGETLOC   ⁡     (   t   )         )       2         .           
The more concentrated the hypothesis R t   i  are around the location TARGETLOC(t), the smaller the value UNCERTAIN(t).  FIG. 12  illustrates what the target location  1300  and uncertainty radius  1310  based on the example hypotheses in  FIG. 11 .
 
Target Location Hypothesis Maintenance
 
   The target location hypotheses H i  are generated over time as follows: When the method starts (say at time t=0), and no information from the past is available, the R t   i  at time t=0 are randomly distributed in the interaction volume  400 . For all later times t&gt;0, N new hypotheses are created from the N old hypotheses available from the previous time step t−dt as follows: For the creation of the i-th (i between 1 and N) hypothesis, a number j between 1 and N is randomly drawn such that the probability of drawing a number n is equal to the probability W t−1   n . The location of the new i-th hypothesis is given by the location of the old hypothesis plus a small offset ΔR t   i =(ΔX t   i ,ΔY t   i ,ΔZ t   i ), where each of the three offsets ΔX t   i ,ΔY t   i ,ΔZ t   i  are randomly drawn between two numbers—OFFSET and +OFFSET (−5 mm and +5 mm for the preferred embodiment described here). The weight of the new hypotheses with location R t   i =R t−1   j +ΔR t   i  is given by the confidence function CONF LR (R,t). 
   Calibration 
   The skin color model is obtained by sampling pixels from the users face as detected by the face detector. Alternatively, a generic skin color model that is representative for human skin could be employed. Finally, as illustrated in  FIG. 9 , the camera calibration matrices are obtained by placing a calibration target such as a cube ( 1000 ) with a set of NC calibration points (e.g.,  1010   a ,  1010   b ) with known world coordinates R i   c  in the viewing area. In  FIG. 9 , the calibration cube has N c =8 calibration points. Given images of the calibration target captured by the two cameras  110  and  120 , each calibration point projects to a certain location in that image (e.g.,  1010   a  projects to  1020   a  etc.). Each calibration point R i   c  projects to a location r L,i   C  in the left image and r R,i   C  in the right image. Then, the projections P L  and P R  that project points from the world coordinate system  150  to the left image coordinate system  1030  and the right image coordinate system  1040  can be determined by one with ordinary skill in the art. Using a cube shaped calibration target, the number of points would for example be N c =8. 
   As a summary, the calibration procedure for obtaining the projections for a camera is given in  FIG. 10 . First in step  1100 , the calibration target (such as the cube shown in  FIG. 9 ) is placed in the view of the camera. Then, in step  1110 , a picture of the calibration target is captured with the camera under consideration. In step  1120 , the image locations of the calibration points are determined manually and finally in step  1130 , the projection is determined from the relation between the known calibration points and the image locations obtained in step  1120 . 
   Summary of Target Location Estimation Algorithm 
   The summary of the target location estimation algorithm is shown in  FIG. 13 . When the method is started (step  1400 ) at time t=0, N hypotheses are initially randomly distributed in the viewing volume  400  defined by the two cameras  110  and  120 . Then, for all subsequent times the following procedure is iterated. At a time t it is assumed that images I L,t−dt  and I R,t−dt  from a previous time step t−dt are available. New images I L,t  and I R,t  are captured in step  1410 . Then in step  1415 , based on images I L  and I R , the color feature images C L  and C R  are calculated, and based on the image pairs I L  and I L,t−dt , and I R  and I R,t−dt  the motion feature images M L  and M R  are calculated for time t. In step  1420 , the obtained color and motion feature images are spread out spatially using the procedure previously presented in this disclosure. This yields the spread out color feature images CS L , CS R  and spread out motion feature images MS L  and MS R . In step  1430 , the feature images are combined for each camera, obtaining confidence images CONF L  and CONF R . In step  1440 , N new hypotheses are created from the hypotheses at the previous time step t−dt by randomly selecting previous hypotheses with probability equal to the hypothesis weights. The locations of the newly selected hypotheses are displaced randomly in step  1450 . In step  1460 , a new weight is calculated for each hypothesis using the function CONF LR . The expected target location and target location uncertainties are finally calculated in step  1470  and the algorithm advances to the next time step.