# A Deep-Discrete Learning Framework for Spherical Surface Registration

arXiv: https://arxiv.org/abs/2203.12999 · HTML: https://mlsanity.com/paper/2203.12999/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 30 references that are in the map.
- First posted on arXiv 24 Mar 2022.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [Conditional Random Fields as Recurrent Neural Networks](https://mlsanity.com/paper/1502.03240/) (2015)
- [A Deep Learning Framework for Unsupervised Affine and Deformable Image Registration](https://mlsanity.com/paper/1809.06130/) (2018)
- [Learning Conditional Deformable Templates with Convolutional Networks](https://mlsanity.com/paper/1908.02738/) (2019)
- [CoMIR: Contrastive Multimodal Image Representation for Registration](https://mlsanity.com/paper/2006.06325/) (2020)
- [Closing the Gap between Deep and Conventional Image Registration using Probabilistic Dense Displacement Networks](https://mlsanity.com/paper/1907.10931/) (2019)
- [Spherical U-Net on Cortical Surfaces: Methods and Applications](https://mlsanity.com/paper/1904.00906/) (2019)
- [ProsRegNet: A Deep Learning Framework for Registration of MRI and Histopathology Images of the Prostate](https://mlsanity.com/paper/2012.00991/) (2020)

## Built on by (most cited first, 7 of 7)

- [SUGAR: Spherical Ultrafast Graph Attention Framework for Cortical Surface Registration](https://mlsanity.com/paper/2307.00511/) (2023)
- [NeuroExplainer: Fine-Grained Attention Decoding to Uncover Cortical Development Patterns of Preterm Infants](https://mlsanity.com/paper/2301.00815/) (2023)
- [Unsupervised Multimodal Surface Registration with Geometric Deep Learning](https://mlsanity.com/paper/2311.13022/) (2023)
- [V2C-Long: Longitudinal Cortex Reconstruction with Spatiotemporal Correspondence](https://mlsanity.com/paper/2402.17438/) (2024)
- [GESH-Net: Graph-Enhanced Spherical Harmonic Convolutional Networks for Cortical Surface Registration](https://mlsanity.com/paper/2410.14805/) (2024)
- [NC-Reg : Neural Cortical Maps for Rigid Registration](https://mlsanity.com/paper/2601.19042/) (2026)
- [Two-chart Beltrami Optimization for Distortion-Controlled Spherical Bijection with Application to Brain Surface Registration](https://mlsanity.com/paper/2602.01589/) (2026)

## Abstract (arXiv)

Cortical surface registration is a fundamental tool for neuroimaging analysis that has been shown to improve the alignment of functional regions relative to volumetric approaches. Classically, image registration is performed by optimizing a complex objective similarity function, leading to long run times. This contributes to a convention for aligning all data to a global average reference frame that poorly reflects the underlying cortical heterogeneity. In this paper, we propose a novel unsupervised learning-based framework that converts registration to a multi-label classification problem, where each point in a low-resolution control grid deforms to one of fixed, finite number of endpoints. This is learned using a spherical geometric deep learning architecture, in an end-to-end unsupervised way, with regularization imposed using a deep Conditional Random Field (CRF). Experiments show that our proposed framework performs competitively, in terms of similarity and areal distortion, relative to the most popular classical surface registration algorithms and generates smoother deformations than other learning-based surface registration methods, even in subjects with atypical cortical morphology.