An Invariant Representation for Matching Trajectories across Uncalibrated Video Streams

We introduce a view-point invariant representation of moving object trajectories that can be used in video database applications. It is assumed that trajectories lie on a surface that can be locally approximated with a plane. Raw trajectory data is first locally approximated with a cubic spline via least squares fitting. For each sampled point of the obtained curve, a projective invariant feature is computed using a small number of points in its neighborhood. The resulting sequence of invariant features computed along the entire trajectory forms the view invariant descriptor of the trajectory itself. Time parametrization has been exploited to compute cross ratios without ambiguity due to point ordering. Similarity between descriptors of different trajectories is measured with a distance that takes into account the statistical properties of the cross ratio, and its symmetry with respect to the point at infinity. In experiments, an overall correct classification rate of about 95% has been obtained on a dataset of 58 trajectories of players in soccer video, and an overall correct classification rate of about 80% has been obtained on matching partial segments of trajectories collected from two overlapping views of outdoor scenes with moving people and cars.

3D Trajectory Recovery for Tracking Multiple Objects and Trajectory Guided Recognition of Actions

A mechanism is proposed that integrates low-level (image processing), mid-level (recursive 3D trajectory estimation), and high-level (action recognition) processes. It is assumed that the system observes multiple moving objects via a single, uncalibrated video camera. A novel extended Kalman filter formulation is used in estimating the relative 3D motion trajectories up to a scale factor. The recursive estimation process provides a prediction and error measure that is exploited in higher-level stages of action recognition. Conversely, higher-level mechanisms provide feedback that allows the system to reliably segment and maintain the tracking of moving objects before, during, and after occlusion. The 3D trajectory, occlusion, and segmentation information are utilized in extracting stabilized views of the moving object. Trajectory-guided recognition (TGR) is proposed as a new and efficient method for adaptive classification of action. The TGR approach is demonstrated using "motion history images" that are then recognized via a mixture of Gaussian classifier. The system was tested in recognizing various dynamic human outdoor activities; e.g., running, walking, roller blading, and cycling. Experiments with synthetic data sets are used to evaluate stability of the trajectory estimator with respect to noise.

Trajectory Guided Tracking and Recognition of Actions

A combined 2D, 3D approach is presented that allows for robust tracking of moving people and recognition of actions. It is assumed that the system observes multiple moving objects via a single, uncalibrated video camera. Low-level features are often insufficient for detection, segmentation, and tracking of non-rigid moving objects. Therefore, an improved mechanism is proposed that integrates low-level (image processing), mid-level (recursive 3D trajectory estimation), and high-level (action recognition) processes. A novel extended Kalman filter formulation is used in estimating the relative 3D motion trajectories up to a scale factor. The recursive estimation process provides a prediction and error measure that is exploited in higher-level stages of action recognition. Conversely, higher-level mechanisms provide feedback that allows the system to reliably segment and maintain the tracking of moving objects before, during, and after occlusion. The 3D trajectory, occlusion, and segmentation information are utilized in extracting stabilized views of the moving object that are then used as input to action recognition modules. Trajectory-guided recognition (TGR) is proposed as a new and efficient method for adaptive classification of action. The TGR approach is demonstrated using "motion history images" that are then recognized via a mixture-of-Gaussians classifier. The system was tested in recognizing various dynamic human outdoor activities: running, walking, roller blading, and cycling. Experiments with real and synthetic data sets are used to evaluate stability of the trajectory estimator with respect to noise.