# Automatic Landmark Detection and Registration of Brain Cortical Surfaces via Quasi-Conformal Geometry and Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2208.07010 · HTML: https://mlsanity.com/paper/2208.07010/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 85 references that are in the map.
- First posted on arXiv 15 Aug 2022.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [Learning shape correspondence with anisotropic convolutional neural networks](https://mlsanity.com/paper/1605.06437/) (2016)
- [FPConv: Learning Local Flattening for Point Convolution](https://mlsanity.com/paper/2002.10701/) (2020)
- [Spherical U-Net on Cortical Surfaces: Methods and Applications](https://mlsanity.com/paper/1904.00906/) (2019)
- [Vertex-Frequency Analysis on Graphs](https://mlsanity.com/paper/1307.5708/) (2013)
- [Landmark and Intensity Based Registration with Large Deformations via Quasi-conformal Maps](https://mlsanity.com/paper/1310.1710/) (2013)
- [TEMPO: Feature-Endowed Teichm"uller Extremal Mappings of Point Clouds](https://mlsanity.com/paper/1511.06624/) (2015)
- [Fast Disk Conformal Parameterization of Simply-connected Open Surfaces](https://mlsanity.com/paper/1408.6974/) (2014)
- [Cortical surface registration using unsupervised learning](https://mlsanity.com/paper/2004.04617/) (2020)
- [Robust Spatial Filtering with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1703.00792/) (2017)
- [Geometric Convolutional Neural Network for Analyzing Surface-Based Neuroimaging Data](https://mlsanity.com/paper/1708.00587/) (2017)
- [Shape analysis via inconsistent surface registration](https://mlsanity.com/paper/2003.01357/) (2020)
- [Parallelizable global conformal parameterization of simply-connected surfaces via partial welding](https://mlsanity.com/paper/1903.12359/) (2019)
- [Tooth morphometry using quasi-conformal theory](https://mlsanity.com/paper/1901.01651/) (2019)
- [A Linear Formulation for Disk Conformal Parameterization of Simply-Connected Open Surfaces](https://mlsanity.com/paper/1508.00396/) (2015)
- [Quasi-conformal Geometry based Local Deformation Analysis of Lateral Cephalogram for Childhood OSA Classification](https://mlsanity.com/paper/2006.11408/) (2020)
- [Quasiconformal model with CNN features for large deformation image registration](https://mlsanity.com/paper/2011.00731/) (2020)
- [Efficient conformal parameterization of multiply-connected surfaces using quasi-conformal theory](https://mlsanity.com/paper/2009.08279/) (2020)

## Built on by (most cited first, 5 of 5)

- [A Bi-variant Variational Model for Diffeomorphic Image Registration with Relaxed Jacobian Determinant Constraints](https://mlsanity.com/paper/2308.02393/) (2023)
- [Shape Prior Segmentation Guided by Harmonic Beltrami Signature](https://mlsanity.com/paper/2407.04360/) (2024)
- [Deep Learning-Based Quasi-Conformal Surface Registration for Partial 3D Faces Applied to Facial Recognition](https://mlsanity.com/paper/2405.09880/) (2024)
- [Two-chart Beltrami Optimization for Distortion-Controlled Spherical Bijection with Application to Brain Surface Registration](https://mlsanity.com/paper/2602.01589/) (2026)
- [Harmonic Beltrami Signature Network: a Shape Prior Module in Deep Learning Framework](https://mlsanity.com/paper/2603.02907/) (2026)

## Abstract (arXiv)

In medical imaging, surface registration is extensively used for performing systematic comparisons between anatomical structures, with a prime example being the highly convoluted brain cortical surfaces. To obtain a meaningful registration, a common approach is to identify prominent features on the surfaces and establish a low-distortion mapping between them with the feature correspondence encoded as landmark constraints. Prior registration works have primarily focused on using manually labeled landmarks and solving highly nonlinear optimization problems, which are time-consuming and hence hinder practical applications. In this work, we propose a novel framework for the automatic landmark detection and registration of brain cortical surfaces using quasi-conformal geometry and convolutional neural networks. We first develop a landmark detection network (LD-Net) that allows for the automatic extraction of landmark curves given two prescribed starting and ending points based on the surface geometry. We then utilize the detected landmarks and quasi-conformal theory for achieving the surface registration. Specifically, we develop a coefficient prediction network (CP-Net) for predicting the Beltrami coefficients associated with the desired landmark-based registration and a mapping network called the disk Beltrami solver network (DBS-Net) for generating quasi-conformal mappings from the predicted Beltrami coefficients, with the bijectivity guaranteed by quasi-conformal theory. Experimental results are presented to demonstrate the effectiveness of our proposed framework. Altogether, our work paves a new way for surface-based morphometry and medical shape analysis.