Split, Merge, and Refine: Fitting Tight Bounding Boxes via Over-Segmentation and Iterative Search

Achieving tight bounding boxes of a shape while guaranteeing complete boundness is an essential task for efficient geometric operations and unsupervised semantic part detection. But previous methods fail to achieve both full coverage and tightness. Neural-network-based methods are not suitable for these goals due to the non-differentiability of the objective, while classic iterative search methods suffer from their sensitivity to the initialization. We propose a novel framework for finding a set of tight bounding boxes of a 3D shape via over-segmentation and iterative merging and refinement. Our result shows that utilizing effective search methods with appropriate objectives is the key to producing bounding boxes with both properties. We employ an existing pre-segmentation to split the shape and obtain over-segmentation. Then, we apply hierarchical merging with our novel tightness-aware merging and stopping criteria. To overcome the sensitivity to the initialization, we also define actions to refine the bounding box parameters in an Markov Decision Process (MDP) setup with a soft reward function promoting a wider exploration. Lastly, we further improve the refinement step with Monte Carlo Tree Search (MCTS) based multi-action space exploration. By thoughtful evaluation on diverse 3D shapes, we demonstrate full coverage, tightness, and an adequate number of bounding boxes of our method without requiring any training data or supervision. It thus can be applied to various downstream tasks in computer vision and graphics.