# Going Off-Grid: Continuous Implicit Neural Representations for 3D Vascular Modeling

arXiv: https://arxiv.org/abs/2207.14663 · HTML: https://mlsanity.com/paper/2207.14663/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 36 references that are in the map.
- First posted on arXiv 29 Jul 2022.

## Builds on (most cited first, 9 of 9)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [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)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [MetaSDF: Meta-learning Signed Distance Functions](https://mlsanity.com/paper/2006.09662/) (2020)
- [Deep learning for cardiac image segmentation: A review](https://mlsanity.com/paper/1911.03723/) (2019)
- [Deep Learning-Based Carotid Artery Vessel Wall Segmentation in Black-Blood MRI Using Anatomical Priors](https://mlsanity.com/paper/2112.01137/) (2021)

## Built on by (most cited first, 16 of 16)

- [VesselVAE: Recursive Variational Autoencoders for 3D Blood Vessel Synthesis](https://mlsanity.com/paper/2307.03592/) (2023)
- [Shape of my heart: Cardiac models through learned signed distance functions](https://mlsanity.com/paper/2308.16568/) (2023)
- [Implicit neural representations for unsupervised super-resolution and denoising of 4D flow MRI](https://mlsanity.com/paper/2302.12835/) (2023)
- [Implicit Neural Representations for Modeling of Abdominal Aortic Aneurysm Progression](https://mlsanity.com/paper/2303.01069/) (2023)
- [TiAVox: Time-aware Attenuation Voxels for Sparse-view 4D DSA Reconstruction](https://mlsanity.com/paper/2309.02318/) (2023)
- [TrIND: Representing Anatomical Trees by Denoising Diffusion of Implicit Neural Fields](https://mlsanity.com/paper/2403.08974/) (2024)
- [VesselSDF: Distance Field Priors for Vascular Network Reconstruction](https://mlsanity.com/paper/2506.16556/) (2025)
- [SIRE: scale-invariant, rotation-equivariant estimation of artery orientations using graph neural networks](https://mlsanity.com/paper/2311.05400/) (2023)
- [Global Control for Local SO(3)-Equivariant Scale-Invariant Vessel Segmentation](https://mlsanity.com/paper/2403.15314/) (2024)
- [Enhancing Dynamic CT Image Reconstruction with Neural Fields and Optical Flow](https://mlsanity.com/paper/2406.01299/) (2024)
- [Generating visual explanations from deep networks using implicit neural representations](https://mlsanity.com/paper/2501.11784/) (2025)
- [Unsupervised Anomaly Detection on Implicit Shape representations for Sarcopenia Detection](https://mlsanity.com/paper/2502.09088/) (2025)
- [Wall Shear Stress Estimation in Abdominal Aortic Aneurysms: Towards Generalisable Neural Surrogate Models](https://mlsanity.com/paper/2507.22817/) (2025)
- [Compact Implicit Neural Representations for Plane Wave Images](https://mlsanity.com/paper/2409.11370/) (2024)
- [Recursive Variational Autoencoders for 3D Blood Vessel Generative Modeling](https://mlsanity.com/paper/2506.14914/) (2025)
- [Fighting MRI Anisotropy: Learning Multiple Cardiac Shapes From a Single Implicit Neural Representation](https://mlsanity.com/paper/2602.11436/) (2026)

## Abstract (arXiv)

Personalised 3D vascular models are valuable for diagnosis, prognosis and treatment planning in patients with cardiovascular disease. Traditionally, such models have been constructed with explicit representations such as meshes and voxel masks, or implicit representations such as radial basis functions or atomic (tubular) shapes. Here, we propose to represent surfaces by the zero level set of their signed distance function (SDF) in a differentiable implicit neural representation (INR). This allows us to model complex vascular structures with a representation that is implicit, continuous, light-weight, and easy to integrate with deep learning algorithms. We here demonstrate the potential of this approach with three practical examples. First, we obtain an accurate and watertight surface for an abdominal aortic aneurysm (AAA) from CT images and show robust fitting from as little as 200 points on the surface. Second, we simultaneously fit nested vessel walls in a single INR without intersections. Third, we show how 3D models of individual arteries can be smoothly blended into a single watertight surface. Our results show that INRs are a flexible representation with potential for minimally interactive annotation and manipulation of complex vascular structures.