Globally-Coordinated Locally-Linear Modeling of Multi-Dimensional Data

This thesis considers the problem of modeling and analysis of continuous, locally-linear, multi-dimensional spatio-temporal data. Our work extends the previously reported theoretical work on the global coordination model to temporal analysis of continuous, multi-dimensional data. We have developed algorithms for time-varying data analysis and used them in full-scale, real-world applications. The applications demonstrated in this thesis include tracking, synthesis, recognitions and retrieval of dynamic objects based on their shape, appearance and motion. The proposed approach in this thesis has advantages over existing approaches to analyzing complex spatio-temporal data. Experiments show that the new modeling features of our approach improve the performance of existing approaches in many applications. In object tracking, our approach is the first one to track nonlinear appearance variations by using low-dimensional representation of the appearance change in globally-coordinated linear subspaces. In dynamic texture synthesis, we are able to model non-stationary dynamic textures, which cannot be handled by any of the existing approaches. In human motion synthesis, we show that realistic synthesis can be performed without using specific transition points, or key frames