Motion competition: Variational integration of motion segmentation and shape regularization

We present a variational method for the segmentation of piecewise affine flow fields. Compared to other approaches to motion segmentation, we minimize a single energy functional both with respect to the affine motion models in the separate regions and with respect to the shape of the separating contour. In the manner of region competition, the evolution of the segmenting contour is driven by a force which aims at maximizing a homogeneity measure with respect to the estimated motion in the adjoining regions. We compare segmentations obtained for the models of piecewise affine motion, piecewise constant motion, and piecewise constant intensity. For objects which cannot be 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 discontinuous flow field is progressively improved during the gradient descent minimization. By including in the variational method a statistical shape prior, the contour evolution is restricted to a subspace of familiar shapes, such that a robust estimation of irregularly moving shapes becomes feasible.