Object Segmentation by Shape Matching with Wasserstein Modes

We gradually develop a novel functional for joint variational object segmentation and shape matching. The formulation, based on the Wasserstein distance, allows modelling of local object appearance, statistical shape variations and geometric invariance in a uniform way. For learning of class typical shape variations we adopt a recently presented approach and extend it to support inference of deformations during segmentation of new query images. The resulting way of describing and fitting trained shape variations is in style reminiscent of contour-based variational shape priors, but does not require an intricate conversion between the contour and the region representation of shapes. A wellfounded hierarchical branch-and-bound scheme, based on local adaptive convex relaxation, is presented, that provably finds the global minimum of the functional.