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 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 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的框架，通过基于神经网络的分割和迭代合并与优化，寻找三维形状的一组紧密包围盒。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基本任务，但先前的方法未能同时实现完全覆盖和紧密性。基于神经网络的方法由于目标函数不可微而不适合这些目标，而经典的迭代搜索方法则因对初始化的敏感性而受限。我们证明，基于学习的方法与迭代搜索方法的最佳结合能够获得兼具两种特性的包围盒。我们采用现有的无监督分割网络对形状进行分割并获得过分割结果。接着，我们应用具有新颖的紧密性感知合并与停止准则的层次化合并方法。为克服对初始化的敏感性，我们还在博弈设定下通过促进更广泛探索的软奖励函数来优化包围盒参数。最后，我们通过基于MCTS的多动作空间搜索进一步改进包围盒。实验结果表明，我们的方法实现了完全覆盖、紧密性以及适当数量的包围盒。