We present an unsupervised data-driven approach for non-rigid shape matching. Shape matching identifies correspondences between two shapes and is a fundamental step in many computer vision and graphics applications. Our approach is designed to be particularly robust when matching shapes digitized using 3D scanners that contain fine geometric detail and suffer from different types of noise including topological noise caused by the coalescence of spatially close surface regions. We build on two strategies. First, using a hierarchical patch based shape representation we match shapes consistently in a coarse to fine manner, allowing for robustness to noise. This multi-scale representation drastically reduces the dimensionality of the problem when matching at the coarsest scale, rendering unsupervised learning feasible. Second, we constrain this hierarchical matching to be reflected in 3D by fitting a patch-wise near-rigid deformation model. Using this constraint, we leverage spatial continuity at different scales to capture global shape properties, resulting in matchings that generalize well to data with different deformations and noise characteristics. Experiments demonstrate that our approach obtains significantly better results on raw 3D scans than state-of-the-art methods, while performing on-par on standard test scenarios.

翻译：我们提出了一种无监督数据驱动的非刚性形状匹配方法。形状匹配旨在识别两个形状之间的对应关系，是许多计算机视觉和图形学应用中的基础步骤。本方法在处理通过三维扫描仪获取的包含精细几何细节且受不同类型噪声（包括由空间邻近表面区域融合引起的拓扑噪声）影响的形状时，展现出特别的鲁棒性。我们基于两种策略构建了该方法：首先，采用基于层次化分块的形状表示，以从粗到细的方式一致地匹配形状，从而增强对噪声的鲁棒性。这种多尺度表示在粗尺度匹配时大幅降低了问题的维度，使得无监督学习成为可行。其次，我们通过拟合分块级别的近刚性形变模型，约束这种层次化匹配在三维空间中得到体现。利用这一约束，我们在不同尺度上利用空间连续性捕获全局形状属性，从而使匹配结果能够良好地泛化到具有不同形变和噪声特性的数据上。实验表明，本方法在处理原始三维扫描数据时显著优于现有最优方法，同时在标准测试场景中达到同等性能水平。