TearingNet: Point Cloud Autoencoder to Learn Topology-Friendly Representations

Topology matters. Despite the recent success of point cloud processing with geometric deep learning, it remains arduous to capture the complex topologies of point cloud data with a learning model. Given a point cloud dataset containing objects with various genera or scenes with multiple objects, we propose an autoencoder, TearingNet, which tackles the challenging task of representing the point clouds using a fixed-length descriptor. Unlike existing works to deform primitives of genus zero (e.g., a 2D square patch) to an object-level point cloud, we propose a function which tears the primitive during deformation, letting it emulate the topology of a target point cloud. From the torn primitive, we construct a locally-connected graph to further enforce the learned topology via filtering. Moreover, we analyze a widely existing problem which we call point-collapse when processing point clouds with diverse topologies. Correspondingly, we propose a subtractive sculpture strategy to train our TearingNet model. Experimentation finally shows the superiority of our proposal in terms of reconstructing more faithful point clouds as well as generating more topology-friendly representations than benchmarks.