Statistical shape knowledge in variational motion segmentation

We present a generative approach to model-based motion segmentation by incorporating a statistical shape prior into a novel variational segmentation method. The shape prior statistically encodes a training set of object outlines presented in advance during a training phase. In a region competition manner the proposed variational approach maximizes the homogeneity of the motion vector field estimated on a set of regions, thus evolving the separating discontinuity set. Due to the shape prior, this discontinuity set is not only sensitive to motion boundaries but also favors shapes according to the statistical shape knowledge. In numerical examples we verify several properties of the proposed approach: for objects which cannot be easily discriminated from the background by their appearance, the desired motion segmentation is obtained, although the corresponding segmentation based on image intensities fails. The region-based formulation facilitates convergence of the contour from its initialization over fairly large distances, and the estimated flow field is progressively improved during the gradient descent minimization. Due to the shape prior, partial occlusions of the moving object by 'unfamiliar' objects are ignored, and the evolution of the motion boundary is effectively restricted to the subspace of familiar shapes.