We present a novel framework for finding a set of tight bounding boxes of a 3D shape via neural-network-based over-segmentation and iterative merging and refinement. Achieving tight bounding boxes of a shape while guaranteeing the 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, and also classic iterative search methods suffer from their sensitivity to the initialization. We demonstrate that the best integration of the learning-based and iterative search methods can achieve the bounding boxes with both properties. We employ an existing unsupervised segmentation network to \textbf{split} the shape and obtain over-segmentation. Then, we apply hierarchical \textbf{merging} with our novel tightness-aware merging and stopping criteria. To overcome the sensitivity to the initialization, we also \textbf{refine} the bounding box parameters in a game setup with a soft reward function promoting a wider exploration. Lastly, we further improve the bounding boxes with a MCTS-based multi-action space exploration. Our experimental results demonstrate the full coverage, tightness, and the adequate number of bounding boxes of our method.

翻译：我们提出了一种新颖框架，用于通过神经网络驱动的过分割与迭代合并及优化，为三维形状找到一组紧密包围盒。在保证完全覆盖的前提下实现形状的紧密包围盒，是高效几何操作和无监督语义部件检测的核心任务，但现有方法无法同时实现完全覆盖与紧密性。由于目标函数不可微，基于神经网络的方法不适合实现这些目标，而传统迭代搜索方法对初始值敏感。我们证明，学习型方法与迭代搜索的最佳结合能够获得兼具两种特性的包围盒。我们采用现有无监督分割网络对形状进行**分割**并获取过分割结果。随后，应用层次化**合并**策略，结合我们提出的紧密度感知合并与停止准则。为克服对初始值的敏感性，我们通过软奖励函数促进更广泛探索，在博弈设置中**优化**包围盒参数。最后，我们基于蒙特卡洛树搜索（MCTS）的多动作空间探索进一步改进包围盒。实验结果表明，我们的方法在完全覆盖、紧密性及包围盒数量合理性方面均表现优异。