Y. Bar Shalom and T. E. Fortmann. Tracking and Data Association. Academic-Press, Boston, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(i.e. N parameters less) while there is another global scale indetermination in this equation (37) when considering the quantities ( jjSjj jjsjj ; jjqjj) as detailed in the previous paragraph. These quantities are therefore defined by [9 N ] 3 (N Gamma 1) Gamma [N ] Gamma [1] = 11 N Gamma 4 parameters. Now this representation is sufficient since : ffl All S matrices and s vectors can be generated from fS i Gamma1;i ; s i Gamma1;i g i=1: N (i.e. S matrices and s vectors between consecutive frames) though the relations, easily obtained from equation (21) ....

....builded as followed. We consider : a) The F matrix defined between view 0 and 1. 14 (b) Qs representations between other pairs of consecutive frames. c) The relative scale factor between the F matrix and other Q matrices. We obtain a representation of [7] 11 (N Gamma 1) Gamma 1] [1], that is 11 N Gamma 1 parameters, as expected. This is strictly equivalent to the representation proposed in figure 4, because we have established a one toone correspondence between Q matrices and q vectors, s vectors and S matrices, except in the first pair of frames, where only the S matrix, ....

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Y. Bar Shalom and T. E. Fortmann. Tracking and Data Association. Academic-Press, Boston, 1988.

....The presence of background clutter, self occlusions, and complex dynamics during figure tracking results in a state space density function (pdf) which is multi modal. Multiple hypothesis tracking (MHT) is a classical approach to representing multimodal distributions with Kalman filters [11]. It has been used with great effectiveness in radar tracking systems, for example. This method maintains a bank of Kalman filters, where each filter corresponds to a specific hypothesis about the target set. In the usual approach, each hypothesis correspond to a postulated association between the ....

....sequence. Bottom row: the singlehypothesis tracker fails to handle the self occlusion caused by Fred Astaire s legs crossing. in [24, 25] An early survey of these techniques can be found in [26] Recently, Rasmussen and Hager [27] used the joint probabilistic data association filter (JPDAF) [11] to track multi part objects, such as a face and hand. In contrast to our MHT framework, the JPDAF approach uses a correspondence based framework for generating hypotheses. Each target is influenced by a linear combination of the resulting measurements. 5.1 Comparisons to Classical MHT and Monte ....

Y. Bar-Shalom and T. E. Fortmann, Tracking and Data Association. Academic Press, 1988.

....elbow locations in the local coordinate systems (J 02 , J 20 , J 24 , J 42 ) 42 4 24 2 20 2 02 0 0 4 J R J R J R J R = 3) As shown in Figure 5, joint locations in the local body part coordinate systems are expressed as functions of body part dimensions. In the Kalman filter equations [22]: k k k k k k w x H z u Fx x = 1 (4) the only nonlinear parts of the measurement equation are the relationships between the body part centroids and the chosen state parameters, which are linearized around the predicted state in the extended Kalman filter. For example, to linearize ....

Y. Bar-Shalom, T. E. Fortmann, Tracking and Data Association, Academic Press, 1987

....it could be caused by any existing systems (points) in the filter. This determination is made by checking whether the observed point lies within an elliptical region around each predicted point. This region is the validation region that is standard in many Kalman filter based tracking applications [1]. If the observed point lies in the region it is considered valid and associated with an existing stroke. An observed point which is distant from any predicted point will be considered as the start of a new Kalman system or stroke. For each valid observation, we associate the observed point ....

Bal-shalom, Y. and Fortmann, T. E. Tracking and data association, Acadamic Press, 1988.

....matching to obtain 3D information is necessary. Once 3D (depth) information is available, tracking in scene coordinates can be performed. The error measure is here distance between the fixation point and the object. For the motion estimation a Kalman filter (or an ff Gamma fi tracker) is used [11]. The matching between images may be based on structural features, such as lines, or regions. Alternatively the template matching used for the disparity estimation may be used again. To maintain a low computational complexity we have chosen to use the template matching. The basic architecture for ....

....in a local neighborhood. The Q match term is always in the range [0; 1] A quality confidence measure for the tracking process is the estimate of the covariance for the prediction error. The covariance is closely related to the validation gate that is used in target tracking applications [11]. The variance, oe x;y 2 , along coordinate axes is used as an error measure here. To obtain a normalized error measure a ratio similar to that for the matching process is formed: Q track = oe x;y 2 max error 2 The two confidence measures are combined through a simple multiplication. In ....

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Y. Bar-Shalom & T. Fortmann, Tracking and Data Association, Boston: Academic Press, 1988

....the minimum variance Bayes estimate of the state variables of a linear system model. It is the optimum in a least squares sense of a linear system with additive Gaussian noise in both the process and the measurement. In addition, it is the optimal linear filter for all other noise distributions [91, 92]. The standard Kalman filter assumes a linear system model as well as a linear measurement model. The linear system model is described by #x k =# k 1 #x k 1 # w k 1 (2.39) where #x k is the state at sample k; #x k 1 and # w k 1 , respectively, are the states and process noise at sample k ....

....also shown in each figure. This matrix in the linear Kalman filter is the predicted error covariance and depends only on the initial conditions and noise models. In the nonlinear EKF, the covariance matrix depends on the measurements and does not necessarily represent the actual error covariance [92]. In these tests, the covariance matrix values correspond, generally, closely to the actual error values for the dual quaternion method while large di#erences are present for the point method. Specific anomalies are present in the quaternion variables. Near the end of the time sequence, the dual ....

Y. Bar-Shalom and T. E. Fortmann, Tracking and Data Association,AcademicPress Inc., Orlando, Florida, 1988.

....given the present. While DBNs are useful models for a system whose overall composition is fixed, they are inadequate, as defined above, for the task of tracking scenes where the relations between individuals change constantly, there is uncertainty about the identity of the individuals involved [7], and the set of individuals varies over time as objects enter and leave the scene [20] In [16, 29, 30] a new relational probabilistic language was introduced, which extends the Bayesian network language with additional features representing objects and the relations between them. Each object ....

Y. Bar-Shalom and T. E. Fortmann. Tracking and Data Association. Academic Press, 1988.

....the images and the SIFT features found. They introduce inaccuracy in both the landmarks position as well as the least squares estimation of the robot position. We would like to know how reliable the estimates are, so we incorporate covariance into the SIFT database. We employ a Kalman Filter [1] to update the position of each landmark. A 3x3 covariance matrix is associated with each SIFT landmark in the database. When a match is found in the current frame, the current covariance matrix for the landmark will be combined with the covariance matrix in the database so far, and the 3D ....

Y. Bar-Shalom and T.E. Fortmann. Tracking and Data Association. Academic Press, Boston, 1988.

....for the fact that the measurements used in the filter might originate from a source other than the target of interest. The Kalman Filter is an optimal system state estimator particularly used when the noise affects both the measurements and the parameters characterizing the system state (see [49], 26] 41] With Kalman Filtering we can track system s parameters flattening noise contributions. 3.6 Dynamic Event s Model In order to provide a high level description of an image sequence, we need a description of events as they are occurring in the scene. For this purpose we have to ....

Y.Bar-Shalom and T.E.Fortmann. Tracking and data association. 1991.

....In the first, a single user walked along a triangular path on the floor while being tracked by the color stereo system. The estimated and ground truth trajectories are given in Figure 4. We filtering the estimated coordinates with a constant acceleration Kalman filter (Sec. 2. 7 in [3]) to improve the smoothness of the trajectory. These results demonstrate good qualitative agreement with the actual motion, particularly for distances within fourteen feet of the kiosk. The larger errors along the arc from A to B are due to the decreased size of the target at this distance, and ....

Y. Bar-Shalom and T. E. Fortmann. Tracking and Data Association. Academic Press, 1988.

....data to properly associate with an object being tracked and therefore to base the estimation process on. In previous work [14] we adapted to vision two existing data association methods: the Probabilistic Data Association Filter (PDAF) and the Joint Probabilistic Data Association Filter (JPDAF) [1]. Our implementations of the PDAF and JPDAF improved tracking performance over standard nearest neighbor versions of the the Kalman filter for certain classes of visual disturbances: agile single targets with transient distractions and multiple similar (but not overlapping) targets, respectively. ....

....of the tracked object s salient parameters, or state, and let I t = I t , I t 1 , be the sequence of images observed so far. Under the Bayesian paradigm, a MAP tracker estimates a state that maximizes p(X t I t ) Applying Bayes theorem and rearranging yields the following expression [1]: p(X t I t ) k t p(I t X t )p(X t I t 1 ) 1) Here p(X t I t 1 ) which summarizes prior knowledge about X t , is a prediction based on the previous state estimate and knowledge of the object s dynamics. Asserting that object dynamics are such that states form a Markov chain ....

[Article contains additional citation context not shown here]

Y. Bar-Shalom and T. Fortmann. Tracking and Data Association. Academic Press, 1988.

....order to maintain an estimate of it s current state, which typically consists of: ffl Kinematic components (position, velocity, acceleration, etc. ffl Other components (radiated signal strength, spectral characteristics, feature information, etc. ffl Constant or slowly varying parameters [1] These very general definition of tracking is often reduced to the usage of visual sensors and hence images as basis for measurements in the field of computer vision. Furthermore, most efforts are concentrated to obtain the components of the state mentioned in the first item. Most current ....

....conflict (in fact they do in linear control) With a non linear control system (fast movements, high acceleration) the positional error can be reduced, but the target tends to slip. The opposite effect can be achieved by using a linear system. Brown et al. 5] use a ff fi fl filter (see [1]) which is a steady state Kalman filter. To overcome the positional error caused by an approximately 80 ms delay in the system between the prediction of the new position and the actual focusing with the cameras on this position the signal is extrapolated 50 ms into the future by achieving a ....

Y. Bar-Shalom and T. E. Fortmann. Tracking and Data Association. Academic Press, 1988.

....values of delay between left and right signals. Observation likelihood model Cross correlation values are transformed into probabilistic likelihoods by modelling aural clutter (arising from reverberation) as uniformly distributed in space, and imposing mutual exclusivity in data associations [1, 24]. This approach requires that background noise be calibrated, learning a statistical distribution for audio responses in the absence of speech. State space model The audio source is modelled as an object in threedimensional space, sharing a common state space with image processing, and this is ....

Y. Bar-Shalom and T.E. Fortmann. Tracking and Data Association. Academic Press, 1988.

....using this approach are reported in Section 3. In Section 4 we discuss related work and Section 5 concludes. 2. Multi Sensor Fusion When developing an object tracking method, one usually has to deal with track initiation, track update including prediction and data association, and track deletion [1, 3, 4]. This section describes the steps in our system necessary for tracking objects in the RoboCup environment. 1 By reliable we mean that there are usually no incorrect measurements, that is, no false positives, whereas unreliable means that a robot might sense objects that are actually not ....

....and in real game situations we observed usually no more than 4 or 5 possible combinations. Although this geometric method already yields reasonable results in practice, we want to note that the application of a probabilistic method such as joint probabilistic data association filters (JPDAF) [1, 4, 17] might still improve our results. 2.2. Single Object Tracking from Noisy Data Often the task is not to track multiple objects but a single object where observations are both noisy and unreliable. Consider the case of keeping track of the ball in the RoboCup scenario. There can only be one ball ....

Y. Bar-Shalom and T. Fortmann. Tracking and Data Association. Academic Press, 1988.

.... appear when pointing are estimated using the 3D position and orientation of the user s head (from the magnetic tracker) a model of the human motor system and the kinematic constraints related to it, and the camera parameters (calculating the field of view) Furthermore, a first order predictor [2] is used to estimate the position of the hand from the position in the previous image frame. In the following we will, however, describe our algorithm on the entire image for illustrative purpose. Constrain search area Adaptive Thresholding of Intensity Image Increase Saturation Label ....

Yaakov Bar-Shalom and Thomas E. Fortmann. Tracking and Data Association. Academic Press, INC., 1988.

.... appear when pointing are estimated using the 3D position and orientation of the user s head (from the magnetic tracker) a model of the human motor system and the kinematic constraints related to it, and the camera parameters (calculating the field of view) Furthermore, a first order predictor [2] is used to estimate the position of the hand from the position in the previous image frame. In the following we will, however, describe our algorithm on the entire image for illustrative purposes. Constrain search area Adaptive Thresholding of Intensity Image Increase Saturation Label ....

Y. Bar-Shalom and T. E. Fortmann. Tracking and Data Association. Academic Press, INC., 1988.

....could be caused by any existing systems (strokes) in the filter. This determination is made by checking whether the observed point lies within an elliptical region around each predicted point. This region is the validation region that is standard in many Kalman filter based tracking applications [1]. If the observed point lies in the region it is considered valid and associated with an existing stroke. An observed point which is distant from any predicted point will be considered as the start of a new stroke. For each valid observation, we associate the observed point with the closest ....

Bal-shalom, Y. and Fortmann, T. E. Tracking and data association, Acadamic Press, 1988.

....validated on a multisensor diagnostic testbed. Monitoring and diagnosis of hybrid systems are an active research area. Existing approaches to hybrid system monitoring and diagnosis do not address the computational data association problem associated with distributed multi sensor systems [Bar Shalom and Fortmann, 1999] and assume sensor outputhas already been properly assembled to form likelihood functions of system output. Moreover, they assume either no autonomous mode transition or autonomous transition without signal mixing. Lerner et al. 2000] described a Bayesian network approach to tracking ....

Y. Bar-Shalom and T.E. Fortmann. Tracking and Data Association. Academic Press, 1999.

....and a search is performed in its neighborhood for image regions (target candidates) whose distribution is similar to that of the model. In single hypothesis tracking the best match determines the new location estimate, however, more complex strategies also exist to form multiple hypothesis [1]. The exhaustive search in the neighborhood of the predicted target location for the best target candidate is, however, a computationally intensive process. As a solution to this problem we propose a color based tracking method based on the mean shift iterations [4, 5] which works in real time, ....

Y. Bar-Shalom, T. Fortmann, Tracking and Data Association, Academic Press, London, 1988.

....Inference, and therefore learning, is much harder in systems which are nonlinear and or have non Gaussian noise, and one typically has to resort to approximate methods. A popular method for computing P (X t jy 1:t ) online is particle ltering [Doucet et al. 2001] or the extended Kalman lter [Bar Shalom and Fortmann, 1988]; for o ine computation of P (X t jy 1:T ) one can use Gibbs sampling [Gilks et al. 1996] or the extended Kalman smoother [Roweis and Ghahramani, 2001] These inference routines can be used as subroutines for the E step of EM, as before. 3.4 Bayesian estimation EM and gradient ascent both ....

Bar-Shalom, Y. and Fortmann, T. (1988). Tracking and data association. Academic Press.

....the images and the SIFT features found. They introduce inaccuracy in both the landmarks position as well as the least squares estimation of the robot position. We would like to know how reliable the estimates are, so we incorporate covariance into the SIFT database. We employ a Kalman Filter [1] to update the position of each landmark. A 3x3 covariance matrix is associated with each SIFT landmark in the database. When a match is found in the current frame, the current covariance matrix for the landmark will be combined with the covariance matrix in the database so far, and the 3D ....

Y. Bar-Shalom and T.E. Fortmann. Tracking and Data Association. Academic Press, Boston, 1988.

....provide a compact and natural representation for multivariate probability distributions in a wide variety of domains. Recently, there has been a growing interest in domains which contain both discrete and continuous variables, called hybrid domains. Examples of such domains include target tracking [1], where the continuous variables represent the state of one or more targets and the discrete variables might model the maneuver type; visual tracking (e.g. 13] where the continuous variables represent the positions of various body parts of a person and the discrete variables the type of ....

Y. Bar-Shalom and T. E. Fortmann. Tracking and Data Association. Academic Press, 1988.

....Gaussian (CLG) Bayesian networks. In these models, the conditional distribution of the continuous variables given the discrete ones is a multivariate Gaussian. CLG models are popular in a variety of applications, in both static and dynamic settings. Example applications include target tracking [1], where the continuous variables represent the state of one or more targets and the discrete variables might model the maneuver type; visual tracking, e.g. 13] where the continuous variables represent the head, legs, and torso position of a person and the discrete variables the type of ....

....is NP hard for these simple networks, we consider the question of approximate inference. We prove that unless P=NP there does not exist a polynomial time approximate inference algorithm with absolute error smaller than 0:5. The class of networks we consider include Switching Kalman Filters [1, 6] as a special case; thus, we provide the first formal complexity results for this important class of models. The second part of the paper addresses the question of how to perform inference in CLG models in light of our complexity results. The commonly used approach for CLG models is the algorithm ....

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Y. Bar-Shalom and T. E. Fortmann. Tracking and Data Association. Academic Press, 1988.

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Y. Bar-Shalom and T. E. Fortmann. Tracking and Data Association. Academic Press, Boston, San Diego, New York, 1988.

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Y. Bar-Shalom and T. E. Fortmann. Tracking and Data Association. Academic Press, Boston, San Diego, New York, 1988.

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