论文标题
通过具有里程碑标记的基础上的功能图匹配的非等法形状匹配
Non-Isometric Shape Matching via Functional Maps on Landmark-Adapted Bases
论文作者
论文摘要
我们提出了一种原则上的方法，用于非标志性地标的非刚性形状匹配。我们的方法基于功能地图框架，但是我们没有促进异构体，而是专注于近乎符号的图，这些图可准确地保留地标。首先，我们使用固有的dirichlet-steklov本本特本特本特本特本特征来实现这一目标。其次，我们建立了在此基础上表达的保形图的功能分解。最后，我们制定了一种形式不变的能量，该能量促进了高质量的具有里程碑式的保留地图，并展示了如何通过最近扩展到设置的最近提出的Zoomout方法的变体来解决它。我们的方法是无描述符，有效且可靠的，可显着网格变异性。我们在一系列基准数据集上评估了我们的方法，并在非等法基准方面表现出最先进的性能，以及在等轴测图中的最新性能。
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.
