# Non-Rigid Volume to Surface Registration using a Data-Driven Biomechanical Model

arXiv: https://arxiv.org/abs/2005.14695 · HTML: https://mlsanity.com/paper/2005.14695/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2020.

## Built on by (most cited first, 17 of 17)

- [Learning Feature Descriptors for Pre- and Intra-operative Point Cloud Matching for Laparoscopic Liver Registration](https://mlsanity.com/paper/2211.03688/) (2022)
- [Boundary Constraint-free Biomechanical Model-Based Surface Matching for Intraoperative Liver Deformation Correction](https://mlsanity.com/paper/2403.09964/) (2024)
- [Non-rigid Medical Image Registration using Physics-informed Neural Networks](https://mlsanity.com/paper/2302.10343/) (2023)
- [Landmark-Free Preoperative-to-Intraoperative Registration in Laparoscopic Liver Resection](https://mlsanity.com/paper/2504.15152/) (2025)
- [A Review on Organ Deformation Modeling Approaches for Reliable Surgical Navigation using Augmented Reality](https://mlsanity.com/paper/2408.02713/) (2024)
- [Deep Learning-based Facial Appearance Simulation Driven by Surgically Planned Craniomaxillofacial Bony Movement](https://mlsanity.com/paper/2210.01685/) (2022)
- [LIBR+: Improving Intraoperative Liver Registration by Learning the Residual of Biomechanics-Based Deformable Registration](https://mlsanity.com/paper/2403.06901/) (2024)
- [LUDO: Low-Latency Understanding of Deformable Objects using Point Cloud Occupancy Functions](https://mlsanity.com/paper/2411.08777/) (2024)
- [Resolving the Ambiguity of Complete-to-Partial Point Cloud Registration for Image-Guided Liver Surgery with Patches-to-Partial Matching](https://mlsanity.com/paper/2412.19328/) (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)
- [Real-time elastic partial shape matching using a neural network-based adjoint method](https://mlsanity.com/paper/2303.09343/) (2023)
- [Evaluation of Intra-operative Patient-specific Methods for Point Cloud Completion for Minimally Invasive Liver Interventions](https://mlsanity.com/paper/2503.11969/) (2025)
- [Toward Patient-specific Partial Point Cloud to Surface Completion for Pre- to Intra-operative Registration in Image-guided Liver Interventions](https://mlsanity.com/paper/2505.19518/) (2025)
- [PIVOTS: Aligning unseen Structures using Preoperative to Intraoperative Volume-To-Surface Registration for Liver Navigation](https://mlsanity.com/paper/2507.20337/) (2025)
- [MeiBRD: Meta-Learning Intraoperative Biomechanical Residual Deformation](https://mlsanity.com/paper/2606.17379/) (2026)
- [Occupancy Network-Guided Autonomous Robotic Partial Nephrectomy](https://mlsanity.com/paper/2609.16186/) (2026)

## Abstract (arXiv)

Non-rigid registration is a key component in soft-tissue navigation. We focus on laparoscopic liver surgery, where we register the organ model obtained from a preoperative CT scan to the intraoperative partial organ surface, reconstructed from the laparoscopic video. This is a challenging task due to sparse and noisy intraoperative data, real-time requirements and many unknowns - such as tissue properties and boundary conditions. Furthermore, establishing correspondences between pre- and intraoperative data can be extremely difficult since the liver usually lacks distinct surface features and the used imaging modalities suffer from very different types of noise. In this work, we train a convolutional neural network to perform both the search for surface correspondences as well as the non-rigid registration in one step. The network is trained on physically accurate biomechanical simulations of randomly generated, deforming organ-like structures. This enables the network to immediately generalize to a new patient organ without the need to re-train. We add various amounts of noise to the intraoperative surfaces during training, making the network robust to noisy intraoperative data. During inference, the network outputs the displacement field which matches the preoperative volume to the partial intraoperative surface. In multiple experiments, we show that the network translates well to real data while maintaining a high inference speed. Our code is made available online.