On advances in differential-geometric approaches for 2D and 3D shape analyses and activity recognition

摘要: In this paper we summarize recent advances in shape analysis and shape-based activity recognition problems with a focus on techniques that use tools from differential geometry statistics. We start general goals challenges faced analysis, followed by summary of the basic ideas, strengths limitations, applications different mathematical representations used analyses 2D 3D objects. These include point sets, curves, surfaces, level deformable templates, medial representations, other feature-based methods. discuss some common choices Riemannian metrics computational for evaluating geodesic paths distances several these representations. Then, study frameworks statistical modeling variability within classes. Next, turn to models algorithms various perspectives. how human its temporal evolutions videos lead over certain special manifolds. features, parametric non-parametric evolution, appropriate manifold-valued constraints. methods gait-based biometrics, action recognition, video summarization indexing. For reader convenience, also provide short overview relevant statistics manifolds Appendix.