# SUGAR: Spherical Ultrafast Graph Attention Framework for Cortical Surface Registration

arXiv: https://arxiv.org/abs/2307.00511 · HTML: https://mlsanity.com/paper/2307.00511/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 62 references that are in the map.
- First posted on arXiv 2 Jul 2023.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019)
- [Learning a Probabilistic Model for Diffeomorphic Registration](https://mlsanity.com/paper/1812.07460/) (2018)
- [Spherical U-Net on Cortical Surfaces: Methods and Applications](https://mlsanity.com/paper/1904.00906/) (2019)
- [Aligning individual brains with Fused Unbalanced Gromov-Wasserstein](https://mlsanity.com/paper/2206.09398/) (2022)
- [CortexODE: Learning Cortical Surface Reconstruction by Neural ODEs](https://mlsanity.com/paper/2202.08329/) (2022)
- [Cortical surface registration using unsupervised learning](https://mlsanity.com/paper/2004.04617/) (2020)
- [A Deep-Discrete Learning Framework for Spherical Surface Registration](https://mlsanity.com/paper/2203.12999/) (2022)
- [Learning Continuous Mesh Representation with Spherical Implicit Surface](https://mlsanity.com/paper/2301.04695/) (2023)

## Built on by (most cited first, 4 of 4)

- [Unsupervised Multimodal Surface Registration with Geometric Deep Learning](https://mlsanity.com/paper/2311.13022/) (2023)
- [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 plays a crucial role in aligning cortical functional and anatomical features across individuals. However, conventional registration algorithms are computationally inefficient. Recently, learning-based registration algorithms have emerged as a promising solution, significantly improving processing efficiency. Nonetheless, there remains a gap in the development of a learning-based method that exceeds the state-of-the-art conventional methods simultaneously in computational efficiency, registration accuracy, and distortion control, despite the theoretically greater representational capabilities of deep learning approaches. To address the challenge, we present SUGAR, a unified unsupervised deep-learning framework for both rigid and non-rigid registration. SUGAR incorporates a U-Net-based spherical graph attention network and leverages the Euler angle representation for deformation. In addition to the similarity loss, we introduce fold and multiple distortion losses, to preserve topology and minimize various types of distortions. Furthermore, we propose a data augmentation strategy specifically tailored for spherical surface registration, enhancing the registration performance. Through extensive evaluation involving over 10,000 scans from 7 diverse datasets, we showed that our framework exhibits comparable or superior registration performance in accuracy, distortion, and test-retest reliability compared to conventional and learning-based methods. Additionally, SUGAR achieves remarkable sub-second processing times, offering a notable speed-up of approximately 12,000 times in registering 9,000 subjects from the UK Biobank dataset in just 32 minutes. This combination of high registration performance and accelerated processing time may greatly benefit large-scale neuroimaging studies.