In this work, we develop a framework for shape analysis using inconsistent surface mapping. Traditional landmark-based geometric morphometr- ics methods suffer from the limited degrees of freedom, while most of the more advanced non-rigid surface mapping methods rely on a strong assumption of the global consistency of two surfaces. From a practical point of view, given two anatomical surfaces with prominent feature landmarks, it is more desirable to have a method that automatically detects the most relevant parts of the two surfaces and finds the optimal landmark-matching alignment between these parts, without assuming any global 1–1 correspondence between the two surfaces. Our method is capable of solving this problem using inconsistent surface registration based on quasi-conformal theory. It further enables us to quantify the dissimilarity of two shapes using quasi-conformal distortion and differences in mean and Gaussian curvatures, thereby providing a natural way for shape classification. Experiments on Platyrrhine molars demonstrate the effectiveness of our method and shed light on the interplay between function and shape in nature.

中文翻译：

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通过不一致的表面配准进行形状分析

在这项工作中，我们开发了一个使用不一致表面映射进行形状分析的框架。传统的基于地标的几何形态测量方法的自由度有限，而大多数更先进的非刚性表面映射方法依赖于两个表面全局一致性的强假设。从实用的角度来看，给定两个具有突出特征标志的解剖表面，更希望有一种方法可以自动检测两个表面中最相关的部分并找到这些部分之间的最佳标志匹配对齐，而无需假设任何两个表面之间的全局 1-1 对应关系。我们的方法能够使用基于准共形理论的不一致表面配准来解决这个问题。它还使我们能够使用准共形失真以及平均曲率和高斯曲率的差异来量化两种形状的不同之处，从而为形状分类提供一种自然的方法。对 Platyrrhine 磨牙的实验证明了我们方法的有效性，并阐明了自然界中功能和形状之间的相互作用。