We propose a new variational method for the completion of moving shapes through binary video inpainting that works by smoothly recovering the objects into an inpainting hole. We solve it by a simple dynamic shape analysis algorithm based on threshold dynamics. The model takes into account the optical flow and motion occlusions. The resulting inpainting algorithm diffuses the available information along the space and the visible trajectories of the pixels in time. We show its performance with examples from the Sintel dataset, which contains complex object motion and occlusions.