Unsupervised recursive deep fitting of 3D primitives to points

The reconstruction of 3D point clouds with high-level geometric primitives is highly desirable due to the compactness and effectiveness of this representation. Nevertheless, correctly fitting 3D point sets with matching primitives is challenging due to the high combinatorial nature of this problem. We introduce a recursive neural network architecture that learns to fit 3D points with geometric primitives in an unsupervised manner. Our core idea is to divide-and-conquer the combinatorial complexity of primitive fitting utilizing recursion layers in our neural network architecture. Through recursion, network layers focus on different shape scales and fit primitives in a coarse-to-fine manner. I.e., early recursion layers solve for coarse regions, fitting large primitives while later layers solve for remaining fine-scale regions, fitting smaller primitives. The network model guarantees a global solution as recursion layers collaborate with each other to minimize an accumulative global loss. We present experiments that validate our approach in terms of accuracy, robustness and performance. We also compare to state-of-the-art to demonstrate our method's advantages.