Correspondence-free local-to-global liver deformation correction via implicit neural representation and biomechanical...

In image-guided laparoscopic liver surgery, correcting organ deformation using intraoperative point clouds is crucial for mapping preoperative anatomical information to the intraoperative scene, such as tumors and blood vessels. Optimization-based methods, especially finite-element-model (FEM) based methods avoid non-physical deformations and thus achieve higher accuracy, but they rely on iterative correspondence search. This process not only demands substantial computational resources but also may make the methods vulnerable to noisy and occluded intraoperative point clouds.

We present a novel correspondence-free local-to-global deformation correction framework to improve the FEM-based baselines, that removes the reliance on iterative correspondence search, and achieves more robust and efficient deformation correction. Firstly, we coarsely estimate the visible region and estimate local deformation using an implicit neural representation. Subsequently, the estimated local deformation is treated as boundary conditions and known correspondences, which are propagated throughout the entire organ via a force-driven optimization process, obviating the need for iterative correspondence searching.

We validated our method on two benchmark datasets and an additional real-world laparoscopic dataset, and compared it with several open-source methods. On the two benchmark datasets, our method achieved mean registration errors of 1.02 mm and 3.98 mm, outperforming or remaining comparable to state-of-the-art approaches. In terms of efficiency, our framework achieved average speedups of $16.25\times$ and $5.37\times$ over the CPU and GPU implementations of BCF-FEM, respectively.

Our proposed framework, including a novel local-to-global deformation correction strategy and an implicit neural representation, replaces the commonly used iterative correspondence searching and advances more efficient and robust deformation correction without compromising accuracy. Our code will be released at Github .