kelvinlet deformable registration

In image-guided liver surgery, non-rigid 3D–3D registration between preoperative models and intraoperative point clouds remains challenging due to soft-tissue deformation. This paper proposes a biomechanics-driven registration method without prescribed boundary constraints. Our key contribution is the first direct integration of a finite element model (FEM) into the surface-matching objective function—eliminating prior assumptions on zero-displacement boundaries and external force application points. We further introduce a full-surface distributed soft-spring force model coupled with L² regularization on force-magnitude gradients to enhance robustness and generalizability of deformation estimation. Optimization is efficiently performed via an accelerated proximal gradient algorithm with adaptive step sizing. Evaluated on a custom liver phantom and two public datasets, our method achieves performance competitive with or superior to state-of-the-art learning-based and traditional FEM-regularized approaches. The source code and datasets are publicly available.

To address the low accuracy and physical inconsistency in real-time soft-tissue deformation simulation under multi-manipulator coordination in surgical robotics and medical training, this paper proposes a novel modeling paradigm that integrates Kelvinlet-based physical priors with neural networks. We introduce the analytical Kelvinlet solution—modeling elastic displacement due to point forces in infinite homogeneous media—into neural residual learning and physics-informed regularization, yielding a lightweight, physics-guided model. The method is trained end-to-end on large-scale linear and nonlinear finite element method (FEM) simulation data. Achieving sub-10 ms inference latency, it significantly improves deformation accuracy and mechanical plausibility, successfully reproducing high-fidelity soft-tissue responses during laparoscopic multi-instrument interactions. The framework ensures data efficiency, strict physical consistency, and real-time deployability, establishing a reliable foundation for surgical navigation and virtual reality–based medical training.

Existing non-rigid multimodal medical image registration methods struggle to simultaneously achieve high accuracy, computational efficiency, and effective deformation regularization; moreover, they typically rely on intensity consistency assumptions and require large-scale cross-modal pretraining. Method: We propose the first continuous deformation modeling framework integrating Neural Ordinary Differential Equations (Neural ODEs) with modality-agnostic structural descriptors. Our approach introduces three variants coupling structural/feature descriptors with Local Mutual Information (LMI) to ensure robustness to both large and small deformations, and incorporates diffeomorphic regularization to guarantee topology preservation. Crucially, it eliminates the need for cross-modal pretraining and supports differentiable, instance-wise registration with multi-scale optimization. Results: Evaluated on diverse multi-modality scan datasets, our method consistently outperforms state-of-the-art approaches in both qualitative and quantitative metrics. It exhibits strong robustness to variations in regularization strength and achieves superior computational efficiency—particularly under large-deformation scenarios.

Traditional point-to-point or point-to-plane distance metrics in non-rigid point cloud registration suffer from slow convergence and geometric detail loss. To address this, we propose a symmetric point-to-plane distance metric that jointly enforces positional and normal-based geometric constraints, significantly improving geometric fidelity. Methodologically, we introduce the first symmetric distance formulation for non-rigid registration and integrate it with a deformation-graph-based coarse alignment followed by an alternating optimization scheme within the Majorization-Minimization (MM) framework—balancing robustness, accuracy, and efficiency. Extensive experiments on multiple benchmark datasets demonstrate that our approach achieves state-of-the-art registration accuracy while maintaining high computational efficiency. The source code is publicly available.

Aligning highly deformable object simulations with real-world behavior remains challenging due to the difficulty of estimating underlying physical parameters from sparse, noisy observations. Method: This paper proposes an end-to-end differentiable simulation-rendering closed-loop framework. It integrates differentiable point cloud sampling with differentiable physics simulation (DiffSim) to directly invert physical parameters—such as mass and stiffness—from real point cloud observations. Coupled with differentiable point cloud rendering and neural architecture search, the framework establishes a fully differentiable optimization pathway where gradients flow back to physical parameters. Results: Experiments on diverse soft-body objects demonstrate that the method matches or surpasses manual parameter tuning in accuracy, achieves over 10× faster parameter convergence, and significantly accelerates simulation modeling and deployment for novel tasks.

Medical image registration faces challenges including inter-modal intensity discrepancies, spatial distortions, and modality-specific anatomical variations. To address these, we propose a learnable edge-enhanced registration framework: it integrates learnable edge convolutional kernels—optimized under noise perturbation—into a deep learning registration network to explicitly guide feature learning toward anatomical boundaries and enhance structural awareness; supports both rigid and non-rigid deformation modeling via multi-stage feature matching and deformation field estimation. Through systematic ablation studies involving eight variants, we quantitatively validate the contribution of each component. Evaluated on two public benchmarks under three distinct experimental settings, our method consistently outperforms state-of-the-art approaches, achieving significant improvements in both registration accuracy (e.g., TRE, DICE) and anatomical consistency (e.g., boundary alignment, Jacobian determinant smoothness).

Non-rigid registration of soft-tissue point clouds under large deformations, noise, and outliers remains challenging due to unreliable correspondences and globally implausible deformations when relying solely on local distance metrics. This work proposes DINE, the first framework to incorporate learned global deformation statistical priors into point cloud registration. DINE employs a two-stage optimization strategy: it first pretrains a base model using Chamfer distance and then jointly optimizes the deformation field via maximum a posteriori estimation, integrating either PCA-based Gaussian or normalizing flow priors within the Robust-DefReg and DefTransNet backbones. Experiments demonstrate that DINE reduces Chamfer distance by 27–69% on the DeformedTissue dataset, improves robustness to outliers and Gaussian noise by 66% and 83%, respectively, and achieves performance gains of 59–79% under extreme deformation scenarios in SynBench.

This work addresses the limitations of traditional Coherent Point Drift (CPD) methods in non-rigid point set registration—namely, parameter redundancy, slow convergence, and insufficient stability under large deformations—by introducing a novel approach based on a structured analytical deformation model. Instead of representing displacements via Gaussian kernel-based fields, the method employs a finite-dimensional analytical mapping constructed from a truncated multivariate Taylor expansion. Registration is reformulated as a weighted analytical fitting problem, where soft target points are generated using posterior probabilities from a Gaussian Mixture Model. The number of parameters depends only on spatial dimensionality and expansion order, substantially reducing model complexity. An incremental order-increasing strategy is further incorporated to enhance robustness under large deformations. Experiments demonstrate that the proposed method achieves lower registration errors and faster convergence than standard CPD in both 2D analytical and 3D smooth non-analytical deformation scenarios.

This study addresses the challenges of correspondence ambiguity caused by local geometric similarity and the erroneous exclusion of correct solutions during region matching in non-rigid point cloud registration. To overcome these issues, we propose CoCo-Reg, which decouples regional context from dense matching. Specifically, the method enriches point features via regional patches while preserving the global search space to avoid hard constraints, and optimizes patch similarity through identity-corrected overlap supervision. Experimental results demonstrate that CoCo-Reg reduces the mean correspondence error to 0.0547, achieving a 72.6% improvement over the baseline. Furthermore, the proportion of high-error points decreases significantly from 47.3% to 17.3%, indicating substantial improvements in both registration accuracy and robustness.

This study addresses the fundamental challenge of estimating correspondences between 3D shape instances under non-rigid deformations by providing a systematic review of existing approaches, which it categorizes into three major paradigms: spectral methods based on functional maps, combinatorial methods incorporating discrete constraints, and deformation-based techniques that directly recover global alignment. For the first time, these three lines of work are unified within a coherent framework, clarifying their historical development, respective strengths, and limitations. A key contribution lies in demonstrating the emerging potential of vision foundation models for zero-shot correspondence tasks. The paper further highlights pressing challenges such as local shape matching, identifies current bottlenecks, and outlines promising future directions, thereby offering both a comprehensive theoretical foundation and practical guidance for advancing research in this domain.