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The explosive growth of the internet have accumulated gigantic amount of visual data. Management and retrieval of relevant information from it become a more and more difficult task. Moreover, as security becomes an important issue, there are numerous surveillance cameras all around the world which accumulate terabytes of video data every day. How to intelligently analyze these video data becomes a big challenge. These largely explain the boom of the research on complex motion analysis, the understanding of which would be essential for higher level tasks such as visual recognition and content understanding. This book provides a general framework on complex motion analysis based on probabilistic variational method. It provides a distributed computational paradigm, since each motion component is analyzed individually, with the constraints from the other components being reinforced. It is also a collaborative approach, since it naturally integrates multiple information cues to obtain the optimal solution.