Distributed Signal and Image Processing: Particle Filters, Context Grammars, and Dynamic Games
A novel distributed video and image processing framework is presented in our work. Our work involves a serious of new algorithms in video processing and dynamical games. In the first part of our work, we present a distributed graph-based sequential particle filtering framework for visual tracking from single and multiple collaborative cameras in lossy networks. Many practical visual processing applications require a robust and efficient algorithm to handle occlusions for visual tracking from degraded visual data in camera networks that utilizes limited computational resources. Firstly, distributed graph-based particle filtering for visual tracking from one view is introduced. Specifically, two new distributed approaches: the graph-based sequential particle filtering framework and its hierarchical counterpart are proposed from one camera. We subsequently derive a distributed visual tracking solution from multiple cameras to handle object occlusions in the presence of frame loss by using collaborative particle filters. The proposed approach relies on Markov Properties and partial-order relations to derive a close-form sequential updating scheme on general graphs in lossy networks. The resulting distributed visual tracking technique is therefore robust to occlusion and sensor errors from specific camera views. Furthermore, the computational complexity of the proposed distributed approach from multiple cameras grows linearly with the number of cameras and objects in each camera. The resulting experiments further demonstrate the superiority of our approach to deal with severe occlusions in the presence of frame loss compared with existing methods. In the second part of our work, we propose a novel statistical estimation algorithm to stochastic context-sensitive grammars (SCSGs). First, we show that the SCSGs model can be solved by decomposing it into several causal stochastic context-free grammars (SCFGs) models and each of these SCFGs models can be solved simultaneously using a fully synchronous distributed computing framework. An alternate updating scheme based approximate solution to multiple SCFGs is also provided under the assumption of a realistic sequential computing framework. A series of statistical algorithms are expected to learn SCFGs subsequently. Specific to our case, a hybrid of general Forward-Backward Algorithm, Inside Algorithm and Expectation- Maximization Technique will be used to estimate the parameters for SCFGs. The SCSGs can be then used to represent multiple-trajectory. Experimental results demonstrate the improved performance of our method compared with existing methods for multiple-trajectory classifica- tion. In the third part of our work, we propose a Compressed-Sensing Game Theory (CSGT) framework to solve the Nash equilibria. We demonstrate that the proposed CSGT framework provides a polynomial complexity solution to the Nash Equilibria, thus allowing more general pay-off functions for certain classes of two-player dynamic games. We also provide numerical examples that demonstrate the efficiency of proposed CSGT framework in solving the Nash equilibria for two-player games in comparison to existing algorithms.