# Vox2Cortex: Fast Explicit Reconstruction of Cortical Surfaces from 3D MRI Scans with Geometric Deep Neural Networks

arXiv: https://arxiv.org/abs/2203.09446 · HTML: https://mlsanity.com/paper/2203.09446/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 63 references that are in the map.
- First posted on arXiv 17 Mar 2022.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [Road Extraction by Deep Residual U-Net](https://mlsanity.com/paper/1711.10684/) (2017)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [FastSurfer -- A fast and accurate deep learning based neuroimaging pipeline](https://mlsanity.com/paper/1910.03866/) (2019)
- [Pixel2Mesh++: Multi-View 3D Mesh Generation via Deformation](https://mlsanity.com/paper/1908.01491/) (2019)
- [Neural Mesh Flow: 3D Manifold Mesh Generation via Diffeomorphic Flows](https://mlsanity.com/paper/2007.10973/) (2020)
- [3DN: 3D Deformation Network](https://mlsanity.com/paper/1903.03322/) (2019)
- [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)
- [DeepCSR: A 3D Deep Learning Approach for Cortical Surface Reconstruction](https://mlsanity.com/paper/2010.11423/) (2020)
- [PialNN: A Fast Deep Learning Framework for Cortical Pial Surface Reconstruction](https://mlsanity.com/paper/2109.03693/) (2021)
- [Whole Heart Mesh Generation For Image-Based Computational Simulations By Learning Free-From Deformations](https://mlsanity.com/paper/2107.10839/) (2021)
- [Recalibrating 3D ConvNets with Project & Excite](https://mlsanity.com/paper/2002.10994/) (2020)

## Built on by (most cited first, 27 of 27)

- [S3M: Scalable Statistical Shape Modeling through Unsupervised Correspondences](https://mlsanity.com/paper/2304.07515/) (2023)
- [NexToU: Efficient Topology-Aware U-Net for Medical Image Segmentation](https://mlsanity.com/paper/2305.15911/) (2023)
- [Diffeomorphic Mesh Deformation via Efficient Optimal Transport for Cortical Surface Reconstruction](https://mlsanity.com/paper/2305.17555/) (2023)
- [Recon-all-clinical: Cortical surface reconstruction and analysis of heterogeneous clinical brain MRI](https://mlsanity.com/paper/2409.03889/) (2024)
- [Cortical analysis of heterogeneous clinical brain MRI scans for large-scale neuroimaging studies](https://mlsanity.com/paper/2305.01827/) (2023)
- [End-to-End 4D Heart Mesh Recovery Across Full-Stack and Sparse Cardiac MRI](https://mlsanity.com/paper/2509.12090/) (2025)
- [DeformCL: Learning Deformable Centerline Representation for Vessel Extraction in 3D Medical Image](https://mlsanity.com/paper/2506.05820/) (2025)
- [Abdominal organ segmentation via deep diffeomorphic mesh deformations](https://mlsanity.com/paper/2306.15515/) (2023)
- [Hybrid-CSR: Coupling Explicit and Implicit Shape Representation for Cortical Surface Reconstruction](https://mlsanity.com/paper/2307.12299/) (2023)
- [From Pixels to Polygons: A Survey of Deep Learning Approaches for Medical Image-to-Mesh Reconstruction](https://mlsanity.com/paper/2505.03599/) (2025)
- [SurfNN: Joint Reconstruction of Multiple Cortical Surfaces from Magnetic Resonance Images](https://mlsanity.com/paper/2303.02922/) (2023)
- [AI-Powered Automated Model Construction for Patient-Specific CFD Simulations of Aortic Flows](https://mlsanity.com/paper/2503.12515/) (2025)
- [From Low Field to High Value: Robust Cortical Mapping from Low-Field MRI](https://mlsanity.com/paper/2505.12228/) (2025)
- [Joint Reconstruction and Parcellation of Cortical Surfaces](https://mlsanity.com/paper/2210.01772/) (2022)
- [Spatial Correspondence between Graph Neural Network-Segmented Images](https://mlsanity.com/paper/2303.06550/) (2023)
- [What You See Is What You Detect: Towards better Object Densification in 3D detection](https://mlsanity.com/paper/2310.17842/) (2023)
- [Reconsider the Template Mesh in Deep Learning-based Mesh Reconstruction](https://mlsanity.com/paper/2505.15285/) (2025)
- [UNSURF: Uncertainty Quantification for Cortical Surface Reconstruction of Clinical Brain MRIs](https://mlsanity.com/paper/2506.00498/) (2025)
- [PrIntMesh: Precise Intersection Surfaces for 3D Organ Mesh Reconstruction](https://mlsanity.com/paper/2511.16186/) (2025)
- [Reconstruction of Cortical Surfaces with Spherical Topology from Infant Brain MRI via Recurrent Deformation Learning](https://mlsanity.com/paper/2312.05986/) (2023)
- [V2C-Long: Longitudinal Cortex Reconstruction with Spatiotemporal Correspondence](https://mlsanity.com/paper/2402.17438/) (2024)
- [Medical Visual Prompting (MVP): A Unified Framework for Versatile and High-Quality Medical Image Segmentation](https://mlsanity.com/paper/2404.01127/) (2024)
- [SimCortex: Collision-free Simultaneous Cortical Surfaces Reconstruction](https://mlsanity.com/paper/2507.06955/) (2025)
- [End-to-End Learning of Multi-Organ Implicit Surfaces from 3D Medical Imaging Data](https://mlsanity.com/paper/2509.12068/) (2025)
- [Template-Based Cortical Surface Reconstruction with Minimal Energy Deformation](https://mlsanity.com/paper/2509.14827/) (2025)
- [Unified Brain Surface and Volume Registration](https://mlsanity.com/paper/2512.19928/) (2025)
- [KidMesh: Computational Mesh Reconstruction for Pediatric Congenital Hydronephrosis Using Deep Neural Networks](https://mlsanity.com/paper/2602.13299/) (2026)

## Abstract (arXiv)

The reconstruction of cortical surfaces from brain magnetic resonance imaging (MRI) scans is essential for quantitative analyses of cortical thickness and sulcal morphology. Although traditional and deep learning-based algorithmic pipelines exist for this purpose, they have two major drawbacks: lengthy runtimes of multiple hours (traditional) or intricate post-processing, such as mesh extraction and topology correction (deep learning-based). In this work, we address both of these issues and propose Vox2Cortex, a deep learning-based algorithm that directly yields topologically correct, three-dimensional meshes of the boundaries of the cortex. Vox2Cortex leverages convolutional and graph convolutional neural networks to deform an initial template to the densely folded geometry of the cortex represented by an input MRI scan. We show in extensive experiments on three brain MRI datasets that our meshes are as accurate as the ones reconstructed by state-of-the-art methods in the field, without the need for time- and resource-intensive post-processing. To accurately reconstruct the tightly folded cortex, we work with meshes containing about 168,000 vertices at test time, scaling deep explicit reconstruction methods to a new level.