Analysis and visualization of dynamic scenes is often constrained by the amount of spatio-temporal information available from the environment. In most scenarios, we have to account for incomplete information and sparse motion data, requiring us to employ interpolation and approximation methods to fill for the missing information. Scattered data interpolation and approximation techniques have been widely used for solving the problem of completing surfaces and images with incomplete input data. We introduce approaches for such data interpolation and approximation from limited sensors, into the domain of analyzing and visualizing dynamic scenes. Data from dynamic scenes is subject to constraints due to the spatial layout of the scene and/or the configurations of video cameras in use. Such constraints include: (1) sparsely available cameras observing the scene, (2) limited field of view provided by the cameras in use, (3) incomplete motion at a specific moment, and (4) varying frame rates due to different exposures and resolutions.;In this thesis, we establish these forms of incompleteness in the scene, as spatio-temporal uncertainties, and propose solutions for resolving the uncertainties by applying scattered data approximation into a spatio-temporal domain.;The main contributions of this research are as follows: First, we provide an efficient framework to visualize large-scale dynamic scenes from distributed static videos. Second, we adopt Radial Basis Function (RBF) interpolation to the spatio-temporal domain to generate global motion tendency. The tendency, represented by a dense flow field, is used to optimally pan and tilt a video camera. Third, we propose a method to represent motion trajectories using stochastic vector fields. Gaussian Process Regression (GPR) is used to generate a dense vector field and the certainty of each vector in the field. The generated stochastic fields are used for recognizing motion patterns under varying frame-rate and incompleteness of the input videos. Fourth, we also show that the stochastic representation of vector field can also be used for modeling global tendency to detect the region of interests in dynamic scenes with camera motion. We evaluate and demonstrate our approaches in several applications for visualizing virtual cities, automating sports broadcasting, and recognizing traffic patterns in surveillance videos.
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