# Topology-Preserving 3D Image Segmentation Based On Hyperelastic Regularization

arXiv: https://arxiv.org/abs/2103.16768 · HTML: https://mlsanity.com/paper/2103.16768/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 67 references that are in the map.
- First posted on arXiv 31 Mar 2021.

## Builds on (most cited first, 5 of 5)

- [Landmark and Intensity Based Registration with Large Deformations via Quasi-conformal Maps](https://mlsanity.com/paper/1310.1710/) (2013)
- [TEMPO: Feature-Endowed Teichm"uller Extremal Mappings of Point Clouds](https://mlsanity.com/paper/1511.06624/) (2015)
- [Shape analysis via inconsistent surface registration](https://mlsanity.com/paper/2003.01357/) (2020)
- [Tooth morphometry using quasi-conformal theory](https://mlsanity.com/paper/1901.01651/) (2019)
- [A novel variational model for image registration using Gaussian curvature](https://mlsanity.com/paper/1504.07643/) (2015)

## Built on by (most cited first, 13 of 13)

- [A Learning-based Framework for Topology-Preserving Segmentation using Quasiconformal Mappings](https://mlsanity.com/paper/2210.03299/) (2022)
- [Deformation-Invariant Neural Network and Its Applications in Distorted Image Restoration and Analysis](https://mlsanity.com/paper/2310.02641/) (2023)
- [A Deep Learning Framework for Diffeomorphic Mapping Problems via Quasi-conformal Geometry applied to Imaging](https://mlsanity.com/paper/2110.10580/) (2021)
- [Double-well Net for Image Segmentation](https://mlsanity.com/paper/2401.00456/) (2023)
- [Topology-Preserving Segmentation Network: A Deep Learning Segmentation Framework for Connected Component](https://mlsanity.com/paper/2202.13331/) (2022)
- [QIS : Interactive Segmentation via Quasi-Conformal Mappings](https://mlsanity.com/paper/2402.14695/) (2024)
- [Topology-Guaranteed Image Segmentation: Enforcing Connectivity, Genus, and Width Constraints](https://mlsanity.com/paper/2601.11409/) (2026)
- [Shape Prior Segmentation Guided by Harmonic Beltrami Signature](https://mlsanity.com/paper/2407.04360/) (2024)
- [A Registration-Based Star-Shape Segmentation Model and Fast Algorithms](https://mlsanity.com/paper/2508.07721/) (2025)
- [Circular Quasiconformal Deturbulence: Geometry-Based Restoration from Multiple Turbulent Frames](https://mlsanity.com/paper/2504.13432/) (2025)
- [Coupled Reconstruction of 2D Blood Flow and Vessel Geometry from Noisy Images via Physics-Informed Neural Networks and Quasi-Conformal Mapping](https://mlsanity.com/paper/2508.11216/) (2025)
- [Variational Geometry-aware Neural Network based Method for Solving High-dimensional Diffeomorphic Mapping Problems](https://mlsanity.com/paper/2511.01911/) (2025)
- [Continuous-tone Simple Points: An ℓ0-Norm of Cyclic Gradient for Topology-Preserving Data-Driven Image Segmentation](https://mlsanity.com/paper/2604.28159/) (2026)

## Abstract (arXiv)

Image segmentation is to extract meaningful objects from a given image. For degraded images due to occlusions, obscurities or noises, the accuracy of the segmentation result can be severely affected. To alleviate this problem, prior information about the target object is usually introduced. In [10], a topology-preserving registration-based segmentation model was proposed, which is restricted to segment 2D images only. In this paper, we propose a novel 3D topology-preserving registration-based segmentation model with the hyperelastic regularization, which can handle both 2D and 3D images. The existence of the solution of the proposed model is established. We also propose a converging iterative scheme to solve the proposed model. Numerical experiments have been carried out on the synthetic and real images, which demonstrate the effectiveness of our proposed model.