Statistical Analysis on Manifolds and Its Applications to Video Analysis

The analysis and interpretation of video data is an important component of modern vision applications such as biometrics, surveillance, motionsynthesis and web-based user interfaces. A common requirement among these very different applications is the ability to learn statistical models of appearance and motion from a collection of videos, and then use them for recognizing actions or persons in a new video. These applications in video analysis require statistical inference methods to be devised on non-Euclidean spaces or more formally on manifolds. This chapter outlines a broad survey of applications in video analysis that involve manifolds. We develop the required mathematical tools needed to perform statistical inference on manifolds and show their effectiveness in real video-understanding applications.