| Shape has already been a critical feature to many vision applications like object detection, contour tracking and activity recognition. In contrast to singularity based features like edge or texture, a shape is a structured feature with a more explicit geometric definition. The mathematical elegance of shape representation brings in a lot of theoretical analysis of shape space, for instance, the metric, the geodesic path and the statistic in shape space. These theoretical results provide a fundamental support for shape based applications.;Most of the previous shape analyses focused on the point-wise geometry in a shape space, for example, the distance between two arbitrary shapes. However, only a few works elaborated on the dynamics in shape space. In this dissertation, we address the problem of shape dynamics analysis through different levels: (1) the bottom level segmentation in an image; (2) the middle level shape tracking, dimension reduction; and (3) the high level shape dynamic modeling, recognition.;First of all, starting at the bottom level, a shape is observed in an image as a set of edge points. Based on the shearlet transformation, a novel singularity feature estimation is developed to provide a better edge detection algorithm in comparison to the traditional gradient based method in a wavelet domain. Secondly at the middle level, the dynamics of shape is observed as a sequence of shapes. To obtain more accurate shape sequence, the Kalman filter framework is extended to shape manifold as a contour tracking with the proposed edge feature extraction in the shearlet domain. Finally, at the high level, based on the shape tracking result, the shape dynamic is modeled as a piecewise Brownian motion on a shape manifold. The proposed modeling is applied to human activity recognition. More over, given the fact that most of the common human activity such as walking, running and jumping are simple dynamics in terms of the dimensionality. To better represent the simple dynamics in the high dimensional manifold, an invertible dimension reduction technique is developed to effectively represent the shape dynamics in a lower dimensional space. In the lower dimensional space, the shape tracking and visualization are shown to be much more simplified. |
