G-FARS: Gradient-Field-Based Auto-Regressive Sampling for 3D Part Grouping

This paper proposes a novel task named "3D part grouping". Suppose there is a mixed set containing scattered parts from various shapes. This task requires algorithms to find out every possible combination among all the parts. To address this challenge, we propose the so called Gradient Field-based Auto-Regressive Sampling framework (G-FARS) tailored specifically for the 3D part grouping task. In our framework, we design a gradient-field-based selection graph neural network (GNN) to learn the gradients of a log conditional probability density in terms of part selection, where the condition is the given mixed part set. This innovative approach, implemented through the gradient-fieldbased selection GNN, effectively captures complex relationships among all the parts in the input. Upon completion of the training process, our framework becomes capable of autonomously grouping 3D parts by iteratively selecting them from the mixed part set, leveraging the knowledge acquired by the trained gradient-field-based selection GNN.