Modeling and Estimation of Shape Deformation for Topology-Preserving Object Tracking

In this work we propose a topology-preserving framework for tracking deforming objects in a sequence of video frames. The shape of the object is modeled as obtained through the action of a group of diffeomorphisms on the initial object boundary. We formulate a state-space model for the diffeomorphic deformation of the object and implement a particle filter on this shape space to estimate the state of the shape in each video frame. We use a practical method for sampling diffeomorphic shapes in which we generate deformations via flows of finitely generated vector fields. Based on the observations and the proposed samples we obtain an approximate estimate for the posterior distribution of the shape.