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.

翻译：实现形状的紧致边界框同时保证完全覆盖，是高效几何操作与无监督语义部件检测的关键任务。然而，现有方法难以同时达成完全覆盖与紧致性。基于神经网络的方法因目标函数的不可微性而不适用于此类目标，而经典迭代搜索方法则受限于初始化的敏感性。我们提出一种新颖框架，通过过分割、迭代合并与精炼，为三维形状寻找一组紧致边界框。实验表明，利用有效的搜索方法与适当的目标函数是生成兼具两种属性的边界框的核心。首先，采用现有预分割方法对形状进行分割以获得过分割结果；随后，通过层次化合并过程，结合我们提出的紧致性感知合并与终止准则进行合并。为克服初始化敏感性，我们在马尔可夫决策过程（MDP）框架中定义边界框参数的精炼动作，并引入促进更广泛探索的软奖励函数。最后，进一步利用基于蒙特卡洛树搜索（MCTS）的多动作空间探索优化精炼步骤。通过对多样化三维形状的细致评估，我们证明了该方法在不依赖任何训练数据或监督的前提下，能够实现完全覆盖、紧致性及合理数量的边界框。因此，该方法可广泛应用于计算机视觉与图形学的各类下游任务。