  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.
