Self-supervised Shape Completion via Involution and Implicit Correspondences

3D shape completion is traditionally solved using supervised training or by distribution learning on complete shape examples. Recently self-supervised learning approaches that do not require any complete 3D shape examples have gained more interests. In this paper, we propose a non-adversarial self-supervised approach for the shape completion task. Our first finding is that completion problems can be formulated as an involutory function trivially, which implies a special constraint on the completion function G, such that G(G(X)) = X. Our second constraint on self-supervised shape completion relies on the fact that shape completion becomes easier to solve with correspondences and similarly, completion can simplify the correspondences problem. We formulate a consistency measure in the canonical space in order to supervise the completion function. We efficiently optimize the completion and correspondence modules using "freeze and alternate" strategy. The overall approach performs well for rigid shapes in a category as well as dynamic non-rigid shapes. We ablate our design choices and compare our solution against state-of-the-art methods, showing remarkable accuracy approaching supervised accuracy in some cases.