Algorithms to automatically quantify the geometric similarity of anatomical surfaces

TL;DR

This paper introduces new algorithms for automatically measuring the geometric similarity of anatomical surfaces in 3D, eliminating the need for manual landmarking and enabling faster, large-scale morphological comparisons.

Contribution

The authors present landmark-free, polynomial-time algorithms for surface comparison and correspondence, advancing morphological analysis without manual feature marking.

Findings

Algorithms are faster and scalable for large datasets.

High accuracy in comparing primate and human anatomical surfaces.

Eliminates manual landmarking, broadening accessibility.

Abstract

We describe new approaches for distances between pairs of 2-dimensional surfaces (embedded in 3-dimensional space) that use local structures and global information contained in inter-structure geometric relationships. We present algorithms to automatically determine these distances as well as geometric correspondences. This is motivated by the aspiration of students of natural science to understand the continuity of form that unites the diversity of life. At present, scientists using physical traits to study evolutionary relationships among living and extinct animals analyze data extracted from carefully defined anatomical correspondence points (landmarks). Identifying and recording these landmarks is time consuming and can be done accurately only by trained morphologists. This renders these studies inaccessible to non-morphologists, and causes phenomics to lag behind genomics in elucidating evolutionary patterns. Unlike other algorithms presented for morphological correspondences our approach does not require any preliminary marking of special features or landmarks by the user. It also differs from other seminal work in computational geometry in that our algorithms are polynomial in nature and thus faster, making pairwise comparisons feasible for significantly larger numbers of digitized surfaces. We illustrate our approach using three datasets representing teeth and different bones of primates and humans, and show that it leads to highly accurate results.