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 directly deforming predefined primitives of genus zero (e.g., a 2D square patch) to an object-level point cloud, our TearingNet is characterized by a proposed Tearing network module and a Folding network module interacting with each other iteratively. Particularly, the Tearing network module learns the point cloud topology explicitly. By breaking the edges of a primitive graph, it tears the graph into patches or with holes to emulate the topology of a target point cloud, leading to faithful reconstructions. Experimentation shows the superiority of our proposal in terms of reconstructing point clouds as well as generating more topology-friendly representations than benchmarks.
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