论文标题
功能图计算的结构化正规化
Structured Regularization of Functional Map Computations
论文作者
论文摘要
我们考虑使用功能地图框架的非刚性形状匹配的问题。具体而言，我们分析了一种常用的方法来正规化功能图，该方法包括惩罚未知映射的失败，无法用Laplace-Beltrami操作员在源形状和目标形状上通勤。我们表明，这种方法具有某些不良的基本理论局限性，即使对于平滑环境中的微不足道地图也可能是不确定的。取而代之的是，我们提出了一种通过使用拉普拉斯运算符的分辨率的概念，提出了一种理论上良好的方法，用于正规化功能图。此外，我们提供了天然的单参数正规化家族，可以根据输入形状对的预期近似等轴测图轻松调整。我们在各种形状的对应方案中表明，我们的新颖正则化可以改善估计功能的质量，并最终在常用的完善技术之前和之后最终侧面的对应关系。
We consider the problem of non-rigid shape matching using the functional map framework. Specifically, we analyze a commonly used approach for regularizing functional maps, which consists in penalizing the failure of the unknown map to commute with the Laplace-Beltrami operators on the source and target shapes. We show that this approach has certain undesirable fundamental theoretical limitations, and can be undefined even for trivial maps in the smooth setting. Instead we propose a novel, theoretically well-justified approach for regularizing functional maps, by using the notion of the resolvent of the Laplacian operator. In addition, we provide a natural one-parameter family of regularizers, that can be easily tuned depending on the expected approximate isometry of the input shape pair. We show on a wide range of shape correspondence scenarios that our novel regularization leads to an improvement in the quality of the estimated functional, and ultimately pointwise correspondences before and after commonly-used refinement techniques.
