用少数量方块抽象3D形状，提升结构理解与建模精度

The abstraction of 3D objects with simple geometric primitives like cuboids allows to infer structural information from complex geometry. It is important for 3D shape understanding, structural analysis and geometric modeling. We introduce a novel fine-to-coarse unsupervised learning approach to abstract collections of 3D shapes. Our architectural design allows us to reduce the number of primitives from hundreds (fine reconstruction) to only a few (coarse abstraction) during training. This allows our network to optimize the reconstruction error and adhere to a user-specified number of primitives per shape while simultaneously learning a consistent structure across the whole collection of data. We achieve this through our abstraction loss formulation which increasingly penalizes redundant primitives. Furthermore, we introduce a reconstruction loss formulation to account not only for surface approximation but also volume preservation. Combining both contributions allows us to represent 3D shapes more precisely with fewer cuboid primitives than previous work. We evaluate our method on collections of man-made and humanoid shapes comparing with previous state-of-the-art learning methods on commonly used benchmarks. Our results confirm an improvement over previous cuboid-based shape abstraction techniques. Furthermore, we demonstrate our cuboid abstraction in downstream tasks like clustering, retrieval, and partial symmetry detection.