# Shape analysis via inconsistent surface registration

arXiv: https://arxiv.org/abs/2003.01357 · HTML: https://mlsanity.com/paper/2003.01357/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2020.

## Built on by (most cited first, 8 of 8)

- [Topology-Preserving 3D Image Segmentation Based On Hyperelastic Regularization](https://mlsanity.com/paper/2103.16768/) (2021)
- [A unifying framework for n-dimensional quasi-conformal mappings](https://mlsanity.com/paper/2110.10437/) (2021)
- [A Deep Learning Framework for Diffeomorphic Mapping Problems via Quasi-conformal Geometry applied to Imaging](https://mlsanity.com/paper/2110.10580/) (2021)
- [Automatic Landmark Detection and Registration of Brain Cortical Surfaces via Quasi-Conformal Geometry and Convolutional Neural Networks](https://mlsanity.com/paper/2208.07010/) (2022)
- [Harmonic Beltrami Signature: A Novel 2D Shape Representation for Object Classification](https://mlsanity.com/paper/2103.16411/) (2021)
- [Free-Boundary Quasiconformal Maps via a Least-squares Operator in Diffeomorphism Optimization](https://mlsanity.com/paper/2511.11679/) (2025)
- [Adaptive area-preserving parameterization of open and closed anatomical surfaces](https://mlsanity.com/paper/2111.04265/) (2021)
- [Variational Geometry-aware Neural Network based Method for Solving High-dimensional Diffeomorphic Mapping Problems](https://mlsanity.com/paper/2511.01911/) (2025)

## Abstract (arXiv)

In this work, we develop a framework for shape analysis using inconsistent surface mapping. Traditional landmark-based geometric morphometrics 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 those 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.