4-D voting for matching, densification and segmentation into motion layers

We present an approach for grouping from motion, based on a 4-D tensor voting computational framework. From sparse point tokens in two frames we recover the dense velocity field, motion boundaries and regions, in a non-iterative process that does not involve initialization or search in a parametric space, and therefore does not suffer from local optima or poor convergence problems. We encode the image position and potential velocity for each token into a 4-D tensor. A voting process then enforces the smoothness of motion while preserving motion discontinuities, selecting the correct velocity for each input point, as the most salient token. By performing an additional dense voting step we infer velocities at every pixel location, which are then used to determine motion boundaries and regions. We demonstrate our contribution with synthetic and real images, by analyzing several difficult cases-opaque and transparent motion, rigid and non-rigid motion.