# Boundary Constraint-free Biomechanical Model-Based Surface Matching for Intraoperative Liver Deformation Correction

arXiv: https://arxiv.org/abs/2403.09964 · HTML: https://mlsanity.com/paper/2403.09964/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 53 references that are in the map.
- First posted on arXiv 15 Mar 2024.

## Builds on (most cited first, 7 of 7)

- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [A Survey of Non-Rigid 3D Registration](https://mlsanity.com/paper/2203.07858/) (2022)
- [Non-Rigid Volume to Surface Registration using a Data-Driven Biomechanical Model](https://mlsanity.com/paper/2005.14695/) (2020)
- [Learning Feature Descriptors for Pre- and Intra-operative Point Cloud Matching for Laparoscopic Liver Registration](https://mlsanity.com/paper/2211.03688/) (2022)
- [Deformable Models for Surgical Simulation: A Survey](https://mlsanity.com/paper/1909.03363/) (2019)
- [An Optimal Control Problem for Elastic Registration and Force Estimation in Augmented Surgery](https://mlsanity.com/paper/2206.10931/) (2022)
- [Comparing Regularized Kelvinlet Functions and the Finite Element Method for Registration of Medical Images to Sparse Organ Data](https://mlsanity.com/paper/2306.05509/) (2023)

## Built on by (most cited first, 12 of 12)

- [A Review on Organ Deformation Modeling Approaches for Reliable Surgical Navigation using Augmented Reality](https://mlsanity.com/paper/2408.02713/) (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)
- [Toward Reliable AR-Guided Surgical Navigation: Interactive Deformation Modeling with Data-Driven Biomechanics and Prompts](https://mlsanity.com/paper/2506.08048/) (2025)
- [SemICP: Semantic Non-Rigid Point Cloud Registration with Elastic Energy Regularization](https://mlsanity.com/paper/2503.00972/) (2025)
- [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)
- [Online camera-pose-free stereo endoscopic tissue deformation recovery with tissue-invariant vision-biomechanics consistency](https://mlsanity.com/paper/2506.19388/) (2025)
- [PIVOTS: Aligning unseen Structures using Preoperative to Intraoperative Volume-To-Surface Registration for Liver Navigation](https://mlsanity.com/paper/2507.20337/) (2025)
- [ARport: An Augmented Reality System for Markerless Image-Guided Port Placement in Robotic Surgery](https://mlsanity.com/paper/2602.14153/) (2026)
- [arg-VU: Affordance Reasoning with Physics-Aware 3D Geometry for Visual Understanding in Robotic Surgery](https://mlsanity.com/paper/2603.26814/) (2026)
- [MeiBRD: Meta-Learning Intraoperative Biomechanical Residual Deformation](https://mlsanity.com/paper/2606.17379/) (2026)
- [BridgeMatch: Conditional Transport Bridges in Matching Matrix Space for 3D Deformable Registration](https://mlsanity.com/paper/2609.11472/) (2026)

## Abstract (arXiv)

In image-guided liver surgery, 3D-3D non-rigid registration methods play a crucial role in estimating the mapping between the preoperative model and the intraoperative surface represented as point clouds, addressing the challenge of tissue deformation. Typically, these methods incorporate a biomechanical model, represented as a finite element model (FEM), into the strain energy term to regularize a surface matching term. We propose a 3D-3D non-rigid registration method that incorporates a modified FEM into the surface matching term. The modified FEM alleviates the need to specify boundary conditions, which is achieved by modifying the stiffness matrix of a FEM and using diagonal loading for stabilization. As a result, the modified surface matching term does not require the specification of boundary conditions or an additional strain energy term to regularize the surface matching term. Optimization is achieved through an accelerated gradient algorithm, further enhanced by our proposed method for determining the optimal step size. We evaluated our method and compared it to several state-of-the-art methods across various datasets. Our straightforward and effective approach consistently outperformed or achieved comparable performance to the state-of-the-art methods. Our code and datasets are available at https://github.com/zixinyang9109/BCF-FEM.