# Non-rigid Medical Image Registration using Physics-informed Neural Networks

arXiv: https://arxiv.org/abs/2302.10343 · HTML: https://mlsanity.com/paper/2302.10343/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 21 references that are in the map.
- First posted on arXiv 20 Feb 2023.

## Builds on (most cited first, 10 of 10)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [RPM-Net: Robust Point Matching using Learned Features](https://mlsanity.com/paper/2003.13479/) (2020)
- [Deep Learning in Medical Image Registration: A Survey](https://mlsanity.com/paper/1903.02026/) (2019)
- [Weakly-Supervised Convolutional Neural Networks for Multimodal Image Registration](https://mlsanity.com/paper/1807.03361/) (2018)
- [Generative Myocardial Motion Tracking via Latent Space Exploration with Biomechanics-informed Prior](https://mlsanity.com/paper/2206.03830/) (2022)
- [Non-Rigid Volume to Surface Registration using a Data-Driven Biomechanical Model](https://mlsanity.com/paper/2005.14695/) (2020)
- [Real-time multimodal image registration with partial intraoperative point-set data](https://mlsanity.com/paper/2109.05023/) (2021)
- [Multimodality Biomedical Image Registration using Free Point Transformer Networks](https://mlsanity.com/paper/2008.01885/) (2020)
- [Prostate motion modelling using biomechanically-trained deep neural networks on unstructured nodes](https://mlsanity.com/paper/2007.04972/) (2020)

## Built on by (most cited first, 8 of 8)

- [A Review on Organ Deformation Modeling Approaches for Reliable Surgical Navigation using Augmented Reality](https://mlsanity.com/paper/2408.02713/) (2024)
- [Learning Physics-Inspired Regularization for Medical Image Registration with Hypernetworks](https://mlsanity.com/paper/2311.08239/) (2023)
- [A Narrative Review of Image Processing Techniques Related to Prostate Ultrasound](https://mlsanity.com/paper/2407.00678/) (2024)
- [Biomechanics-informed Non-rigid Medical Image Registration and its Inverse Material Property Estimation with Linear and Nonlinear Elasticity](https://mlsanity.com/paper/2407.03292/) (2024)
- [Toward Reliable AR-Guided Surgical Navigation: Interactive Deformation Modeling with Data-Driven Biomechanics and Prompts](https://mlsanity.com/paper/2506.08048/) (2025)
- [Data-Driven Tissue- and Subject-Specific Elastic Regularization for Medical Image Registration](https://mlsanity.com/paper/2407.04355/) (2024)
- [PINNing Cerebral Blood Flow: Analysis of Perfusion MRI in Infants using Physics-Informed Neural Networks](https://mlsanity.com/paper/2410.19759/) (2024)
- [Salient Region Matching for Fully Automated MR-TRUS Registration](https://mlsanity.com/paper/2501.03510/) (2025)

## Abstract (arXiv)

Biomechanical modelling of soft tissue provides a non-data-driven method for constraining medical image registration, such that the estimated spatial transformation is considered biophysically plausible. This has not only been adopted in real-world clinical applications, such as the MR-to-ultrasound registration for prostate intervention of interest in this work, but also provides an explainable means of understanding the organ motion and spatial correspondence establishment. This work instantiates the recently-proposed physics-informed neural networks (PINNs) to a 3D linear elastic model for modelling prostate motion commonly encountered during transrectal ultrasound guided procedures. To overcome a widely-recognised challenge in generalising PINNs to different subjects, we propose to use PointNet as the nodal-permutation-invariant feature extractor, together with a registration algorithm that aligns point sets and simultaneously takes into account the PINN-imposed biomechanics. The proposed method has been both developed and validated in both patient-specific and multi-patient manner.