We propose a principled approach for non-isometric landmark-preserving non-rigid shape matching. Our method is based on the functional maps framework, but rather than promoting isometries we focus instead on near-conformal maps that preserve landmarks exactly. We achieve this, first, by introducing a novel landmark-adapted basis using an intrinsic Dirichlet-Steklov eigenproblem. Second, we establish the functional decomposition of conformal maps expressed in this basis. Finally, we formulate a conformally-invariant energy that promotes high-quality landmark-preserving maps, and show how it can be solved via a variant of the recently proposed ZoomOut method that we extend to our setting. Our method is descriptor-free, efficient and robust to significant mesh variability. We evaluate our approach on a range of benchmark datasets and demonstrate state-of-the-art performance on non-isometric benchmarks and near state-of-the-art performance on isometric ones.
翻译:我们提出一个原则性方法,用于非测量地标保存非硬质形状的匹配。我们的方法以功能性地图框架为基础,而不是推广异形图,而是侧重于准确保存地标的近正式地图。我们首先通过使用内在的Drichlet-Steklov egenproblem采用新的地标调整基础来实现这一目标。第二,我们建立了以此为基础表达的符合地图的功能分解功能。最后,我们制定了一种符合异变的能量,促进高质量的地标保存地图,并展示如何通过最近提出的扩展到我们位置的“缩放”方法的变式加以解决。我们的方法是无描述性、高效和强健健健的,以适应显著的网状变异性。我们评估了我们关于一系列基准数据集的方法,并展示了非测量基准和近状态的等度基准的先进性能。