# Neural deformation fields for template-based reconstruction of cortical surfaces from MRI

arXiv: https://arxiv.org/abs/2401.12938 · HTML: https://mlsanity.com/paper/2401.12938/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 56 references that are in the map.
- First posted on arXiv 23 Jan 2024.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [Road Extraction by Deep Residual U-Net](https://mlsanity.com/paper/1711.10684/) (2017)
- [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018)
- [Hypercolumns for Object Segmentation and Fine-grained Localization](https://mlsanity.com/paper/1411.5752/) (2014)
- [FastSurfer -- A fast and accurate deep learning based neuroimaging pipeline](https://mlsanity.com/paper/1910.03866/) (2019)
- [Neural Mesh Flow: 3D Manifold Mesh Generation via Diffeomorphic Flows](https://mlsanity.com/paper/2007.10973/) (2020)
- [Voxel2Mesh: 3D Mesh Model Generation from Volumetric Data](https://mlsanity.com/paper/1912.03681/) (2019)
- [3D Whole Brain Segmentation using Spatially Localized Atlas Network Tiles](https://mlsanity.com/paper/1903.12152/) (2019)
- [A Deep-Learning Approach For Direct Whole-Heart Mesh Reconstruction](https://mlsanity.com/paper/2102.07899/) (2021)
- [QuickNAT: A Fully Convolutional Network for Quick and Accurate Segmentation of Neuroanatomy](https://mlsanity.com/paper/1801.04161/) (2018)
- [GEOMetrics: Exploiting Geometric Structure for Graph-Encoded Objects](https://mlsanity.com/paper/1901.11461/) (2019)
- [Automatic segmentation of MR brain images with a convolutional neural network](https://mlsanity.com/paper/1704.03295/) (2017)
- [DeepNAT: Deep Convolutional Neural Network for Segmenting Neuroanatomy](https://mlsanity.com/paper/1702.08192/) (2017)
- [CortexODE: Learning Cortical Surface Reconstruction by Neural ODEs](https://mlsanity.com/paper/2202.08329/) (2022)
- [PialNN: A Fast Deep Learning Framework for Cortical Pial Surface Reconstruction](https://mlsanity.com/paper/2109.03693/) (2021)
- [CorticalFlow++: Boosting Cortical Surface Reconstruction Accuracy, Regularity, and Interoperability](https://mlsanity.com/paper/2206.06598/) (2022)

## Built on by (most cited first, 14 of 14)

- [From Pixels to Polygons: A Survey of Deep Learning Approaches for Medical Image-to-Mesh Reconstruction](https://mlsanity.com/paper/2505.03599/) (2025)
- [Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunities](https://mlsanity.com/paper/2604.01274/) (2026)
- [MedGS: Gaussian Splatting for Multi-Modal 3D Medical Imaging](https://mlsanity.com/paper/2509.16806/) (2025)
- [Individualized Mapping of Aberrant Cortical Thickness via Stochastic Cortical Self-Reconstruction](https://mlsanity.com/paper/2403.06837/) (2024)
- [A Comprehensive Survey on Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/2503.07097/) (2025)
- [End-to-end Cortical Surface Reconstruction from Clinical Magnetic Resonance Images](https://mlsanity.com/paper/2505.14017/) (2025)
- [Cortex-Grounded Diffusion Models for Brain Image Generation](https://mlsanity.com/paper/2601.19498/) (2026)
- [V2C-Long: Longitudinal Cortex Reconstruction with Spatiotemporal Correspondence](https://mlsanity.com/paper/2402.17438/) (2024)
- [SimCortex: Collision-free Simultaneous Cortical Surfaces Reconstruction](https://mlsanity.com/paper/2507.06955/) (2025)
- [Template-Based Cortical Surface Reconstruction with Minimal Energy Deformation](https://mlsanity.com/paper/2509.14827/) (2025)
- [PAS-Mamba: Phase-Amplitude-Spatial State Space Model for MRI Reconstruction](https://mlsanity.com/paper/2601.14530/) (2026)
- [KidMesh: Computational Mesh Reconstruction for Pediatric Congenital Hydronephrosis Using Deep Neural Networks](https://mlsanity.com/paper/2602.13299/) (2026)
- [High-Fidelity 3D Geometric Reconstruction of Pelvic Organs from MRI: A Hybrid Deep Learning and Iterative Optimization Approach](https://mlsanity.com/paper/2606.17836/) (2026)
- [Uncertainty-Aware Cortical Surface Reconstruction and Spherical Registration for Heterogeneous Brain MRI](https://mlsanity.com/paper/2610.16595/) (2026)

## Abstract (arXiv)

The reconstruction of cortical surfaces is a prerequisite for quantitative analyses of the cerebral cortex in magnetic resonance imaging (MRI). Existing segmentation-based methods separate the surface registration from the surface extraction, which is computationally inefficient and prone to distortions. We introduce Vox2Cortex-Flow (V2C-Flow), a deep mesh-deformation technique that learns a deformation field from a brain template to the cortical surfaces of an MRI scan. To this end, we present a geometric neural network that models the deformation-describing ordinary differential equation in a continuous manner. The network architecture comprises convolutional and graph-convolutional layers, which allows it to work with images and meshes at the same time. V2C-Flow is not only very fast, requiring less than two seconds to infer all four cortical surfaces, but also establishes vertex-wise correspondences to the template during reconstruction. In addition, V2C-Flow is the first approach for cortex reconstruction that models white matter and pial surfaces jointly, therefore avoiding intersections between them. Our comprehensive experiments on internal and external test data demonstrate that V2C-Flow results in cortical surfaces that are state-of-the-art in terms of accuracy. Moreover, we show that the established correspondences are more consistent than in FreeSurfer and that they can directly be utilized for cortex parcellation and group analyses of cortical thickness.