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：本文介绍一种新型的无监督联合形状匹配（JSM）方法GenCorres。 GenCorres的基本思想是学习一个参数网格生成器来适应无组织可变形形状集，同时限制相邻合成形状之间的变形以保持几何结构，例如局部刚性和局部一致性。 GenCorres相对于现有的JSM技术有三个优点。首先，GenCorres执行的JSM是在一个比输入形状大得多的合成形状集中进行的，并完全利用了JSM的数据驱动能力。 其次，GenCorres统一了一致的形状匹配和成对匹配（即通过在相邻的合成形状之间强制施加变形优先级来实现）。 第三，生成器提供了一种简明的一致性形状对应的编码。但是，从无组织形状集中学习网格生成器是具有挑战性的。它需要对每个形状进行良好的初始拟合，并且很容易被局部最小值卡住。GenCorres通过从输入形状学习隐式生成器来解决这个问题，其在两个任意形状之间提供中间形状。我们引入了一种新的方法来计算相邻隐式曲面之间的对应关系，并强制对应关系保留几何结构并且具有循环一致性。隐式生成器的合成形状随后指导了学习网格生成器的初始配合（即通过基于模板的变形）。实验结果表明，GenCorres在基准数据集上比现有的JSM技术表现出色。 GenCorres的合成形状保留局部几何特征，并产生与现有最先进的可变形形状生成器相比具有竞争性的性能增益。