This paper introduces GenCorres, a novel unsupervised joint shape matching (JSM) approach. The basic idea of GenCorres is to learn a parametric mesh generator to fit an unorganized deformable shape collection while constraining deformations between adjacent synthetic shapes to preserve geometric structures such as local rigidity and local conformality. GenCorres presents three appealing advantages over existing JSM techniques. First, GenCorres performs JSM among a synthetic shape collection whose size is much bigger than the input shapes and fully leverages the data-driven power of JSM. Second, GenCorres unifies consistent shape matching and pairwise matching (i.e., by enforcing deformation priors between adjacent synthetic shapes). Third, the generator provides a concise encoding of consistent shape correspondences. However, learning a mesh generator from an unorganized shape collection is challenging. It requires a good initial fitting to each shape and can easily get trapped by local minimums. GenCorres addresses this issue by learning an implicit generator from the input shapes, which provides intermediate shapes between two arbitrary shapes. We introduce a novel approach for computing correspondences between adjacent implicit surfaces and force the correspondences to preserve geometric structures and be cycle-consistent. Synthetic shapes of the implicit generator then guide initial fittings (i.e., via template-based deformation) for learning the mesh generator. Experimental results show that GenCorres considerably outperforms state-of-the-art JSM techniques on benchmark datasets. The synthetic shapes of GenCorres preserve local geometric features and yield competitive performance gains against state-of-the-art deformable shape generators.

翻译：本文提出GenCorres，一种新颖的无监督联合形状匹配方法。其核心思想是学习一个参数化网格生成器来拟合无组织可变形形状集合，同时约束相邻合成形状间的变形以保持几何结构（如局部刚性与局部共形性）。与现有联合形状匹配技术相比，GenCorres具有三个突出优势：第一，通过生成远大于输入形状规模的合成形状集合执行联合形状匹配，充分挖掘数据驱动能力；第二，通过强制相邻合成形状间的变形先验，统一了一致形状匹配与成对匹配；第三，该生成器提供了一致形状对应关系的简洁编码。然而，从无组织形状集合中学习网格生成器极具挑战性：既需要良好的初始拟合，又极易陷入局部最小值。GenCorres通过从输入形状中学习隐式生成器解决该问题，该生成器可提供任意两个形状间的中间形状。我们提出一种新颖方法计算相邻隐式曲面间的对应关系，并强制这些对应关系保持几何结构且满足循环一致性。隐式生成器合成的形状进而引导用于学习网格生成器的初始拟合（即基于模板的变形）。实验结果表明，GenCorres在基准数据集上显著优于现有联合形状匹配技术。其合成形状既保留了局部几何特征，又在性能上超越现有可变形形状生成器。