  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-field-based 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. Our code is available at:
https://github.com/J-F-Cheng/G-FARS-3DPartGrouping.
