In computer-assisted orthopedic surgery (CAOS), robust and accurate registration of the preoperative full bone model and the intraoperative partial point set is a prerequisite for reliable surgical navigation, yet remains highly challenging due to partial overlap, noise, and outliers. We propose the Overlap-Guided Bidirectional Hybrid Mixture Registration (OBHMR) framework for robust and accurate partial-to-full registration. First, geometric features (i.e., surface normals) extracted from raw point sets are incorporated in both correspondence estimation and transform computation. Meanwhile, we formulate a hybrid mixture model that jointly represents positions with Gaussian mixtures (GMMs) and normals with von Mises–Fisher (vMF) mixtures across the two generalized point sets. Second, a dual-branch overlap prediction network leverages feature similarity and geometric structure to provide accurate point-wise overlap scores that guide hybrid-mixture construction under partial overlap. Third, a correspondence module integrates rotation-invariant features, multi-level self-attention, and clustering-based refinement to enhance reliability under noise and misalignment. Finally, a bidirectional objective jointly aligns source-to-target and target-to-source mixtures, explicitly accounting for discrepancies induced by noise and outliers in both the preoperative and intraoperative point sets to achieve robust optimization. Extensive experiments on 1,399 femur and 1,301 hip models demonstrate superior performance over state-of-the-art methods across overlap ratios from 5% to 70%, under both isotropic and anisotropic noise and outlier ratios up to 100%, achieving errors as low as 1.27° rotation and 1.18 mm translation at 50% overlap with 2.5mm noise. Additional tests on liver and ModelNet40 confirm strong generalization across medical and non-medical data. Ablation studies further validate the contributions of normals, overlap estimation, and the bidirectional formulation.

Biomechanical modelling of soft tissue provides a method for constraining medical image registration, such that the estimated spatial transformation is considered biophysically plausible. Existing methods either directly optimize the loss function containing the biomechanical-constrained regularization term over deformations, which takes much computational time, or are trained using biomechanically plausible data generated via finite element simulation, which is cumbersome. This work first instantiates the recently-proposed physics-informed neural networks (PINNs) to 3D elastic models that are used to establish the partial differential equations (PDEs) representing physics laws of biomechanical constraints to be satisfied. The registration algorithm that aligns point sets considering PINN-imposed biomechanics (i.e., the forward problem) is then formulated. In addition, the inverse problem and its algorithm of physical parameter (i.e., material property) estimation along with the registration are also formulated and developed. We carefully compare linear and nonlinear elasticity theories' capabilities in solving both tasks of forward registration and inverse physical parameter identification under PINNs respectively. Furthermore, two specific network configurations that leverage one common branch or two individual branches to predict deformation vectors and biomechanical states are also constructed and compared. The proposed PINNs-based registration approaches have been extensively evaluated with three experiments, that is single and multiple patient MRI-US registration using clinical MRI-US pairs, and registration using pairs of undeformed MR images from clinical cases of prostate cancer biopsy and deformed counterparts with finite-element-computed ground-truth deformation. Results demonstrate that the proposed methods achieve state-of-the-art performances compared to biomechanical-model-based and learning-based registration approaches, and the biomechanical constraints of soft tissues have been successfully warranted after registration. The codes are available at https://github.com/ZheMin-1992/Registration_PINNs.

In computer-assisted orthopedic surgery (CAOS), accurate point set registration is essential for enhancing surgical accuracy. However, the sparse and low-overlap nature of intraoperative point sets presents significant challenges for reliable registration. To deal with these challenges, we propose a novel registration-after-completion framework, where the intraoperative point set is first completed, after which the two full point sets are registered. Our main contributions include the follows. First, we propose a progressive two-stage strategy to progressively complete the sparse and partial intraoperative point set. Second, considering that 1) intra-operative point set contains noise 2) the point completion process is not perfect, and 3) the resolution of preoperative image is limited, we adopt the bidirectional hybrid mixture models (HMMs) to represent the point set pairs and formulate the probabilistic registration network. In the proposed novel correspondence network where a dual-path cross-attention mechanism is adopted for feature fusion and a clustering mechanism is leveraged for calculating point-to-mixture correspondences. Furthermore, the bidirectional registration mechanism is leveraged to compute the transformation based on estimated correspondences. Third, we have extensively validated the proposed approach on various datasets and bone phantoms. Our experiments on 1399 human femur and 1301 hip models demonstrate that our method achieves state-of-the-art performance across overlap rates from 15% to 35% and at various point counts (i.e., 25, 50, and 100 points) under conditions with less than 50% overlap. Additionally, real phantom experiments on femur and hip models validate the method’s performance in simulated surgical scenarios. Experiments on ModelNet40 further confirmed our method’s effectiveness and generalizability.

In this paper, we propose a novel unsupervised intraoperative liver deformation correction method, called Learning Coherent point drift Network (LCNet), for image-guided liver surgery (IGLS). We first estimate the correspondences between the preoperative and intraoperative point sets in the optimal transport (OT) module by leveraging both original points and extracted features. Afterwards, we compute the point-wise displacement vector by solving the involved matrix equation in the Transformation module, where the point localisation noise is explicitly considered and modeled. Additionally, we present three variants of the proposed approach, i.e., LCNet, LCNet-ED and LCNet-WD, where better registration performances of LCNet against the other two demonstrate the superiority of the utilised Chamfer loss. We have extensively evaluated LCNet on the MedShapeNet dataset consisting of 615 different liver shapes of real patients, and the 3Dircadb dataset comprising 20 liver models of real patients. Extensive experimental results under different deformation and noise magnitudes demonstrate that LCNet outperforms existing state-of-the-art registration algorithms and holds significant application potential in IGLS. For example, when the overlapping ratio between the preoperative and intraoperative point sets is 25%, the deformation magnitude is 8 mm, the maximum point localization noise magnitude is 2 mm and the rotation angle lies in the range of [−45°, 45°], LCNet achieves a root-mean-square error (RMSE) value being 3.21 mm on MedShapeNet dataset, significantly outperforming those of Lepard and RoITr being 5.41 mm (p < 0.001) and 4.90 mm (p < 0.001) respectively.

In this paper, we present a novel curve-to-surface registration method, termed Bi-directional Hybrid Mixture Model Registration based on Dual-constrained Tangent and Normal Vectors (BiHMM-DTN), where two different tangent vectors at the intraoperative point are simultaneously used with the normal vector at the corresponding preoperative point to construct the geometric constraints. While hybrid registration models incorporating tangent and normal vectors (HMM-TN) demonstrate success, their geometric constraints prove inadequate or inappropriate for sparse intraoperative point sets, frequently yielding suboptimal optimization outcomes. By critically revisiting the geometric constraints of HMM-TN, we propose a dual-constraints-based hybrid mixture model registration framework with enhanced intraoperative point set acquisition protocols. To deal with noise and outliers in preoperative and intraoperative point sets—caused by reconstruction inaccuracies and tracking errors, respectively—our approach employs a bi-directional registration mechanism for curve-to-surface registration. We provide rigorous proofs validating the geometric completeness of the dual constraints within this mechanism. The BiHMM-DTN framework is formulated as a maximum likelihood estimation (MLE) problem and optimized using an expectation-maximization (EM) algorithm. Furthermore, to enhance convergence stability and accelerate optimization, the rotation matrix is updated iteratively through successive incremental steps. Extensive experiments on human femur and hip models demonstrate that our method outperforms state-of-the-art approaches, including both traditional optimization and deep learning methods, under various noise and outlier conditions. Furthermore, real-world phantom experiments highlight the potential clinical value of our method for surgical navigation applications. The codes and data are available at https://github.com/sam-zyzhang/BiHMM-DTN.git.

3D point cloud registration is an essential problem in computer vision, robotics, surgical navigation and augmented reality. Accurate registration of partially overlapped intraoperative point clouds (e.g., femoral reconstruction) remains critical yet challenging in orthopedic navigation due to incomplete overlap and dynamic noise. In this study, we propose a partial-to-partial point cloud registration framework based on directional spatial consistency. First, we extract overlapped areas from partially overlapping point clouds and leverage the point registration graph matching module to calculate the hard point matching matrix. Second, we sample nodes from the source point cloud and generate translation-invariant edge vectors (direction/scale-preserving) via their k-nearest neighbors, guided by predicted point correspondences. This bypasses translation ambiguities by encoding spatial consistency through edges, reducing pose estimation to 3DoF alignment (rotation). The loss explicitly couples point-level matches with edge-level geometric constraints for dual optimization. Building upon this framework, we extract reliable overlapping edge representations and prune their similarity matrix by thresholding low-confidence scores, effectively suppressing spurious matches. The proposed edge-aware matching mechanism further exploits the translation invariance of local structures to refine point correspondences with enhanced accuracy. Finally, we introduce a bidirectional registration mechanism to reinforce optimization stability, achieving state-of-the-art performance across benchmarks. Extensive experiments on ModelNet40, ShapeNet, and MedShapeNet validate our method under diverse scenarios: partial-to-partial, unseen categories, partial-to-full, and cross-dataset generalization, surpassing existing methods in registration accuracy. The codes are available at https://github.com/pidan0824/DSCGM.

In this paper, we introduce a novel overlap-based bidirectional point set registration approach, i.e., Overlap-guided Bidirectional Hybrid Mixture Registration (OBHMR), which incorporates geometric information (i.e., normal vectors) in both the correspondence and transformation stages and formulates the optimization objective of registration in a bidirectional manner. More importantly, to address the issue of partial-to-full registration, OBHMR utilises the predicted point-wise overlap score using networks to formulate the overlap-guided Hybrid Mixture Model consisting of the Gaussian Mixture Model (GMM) and Fisher Mixture Model (FMM). OBHMR contains four components: (1) the overlap-guided correspondence network that estimates the correspondence probabilities and calculates the point-wise overlap score; (2) the learning posterior module that estimates the overlap-guided HMM parameters; (3) the transformation module that computes the rigid transformation by formulating the optimisation objective in a bidirectional registration way, given correspondences and overlap-guided HMM parameters. Experiments using 1457 human femur and 1301 human hip models demonstrate significant improvements in partial-to-full registration performance (p < 0.01) under different overlapping ratios, compared to state-of-the-art registration approaches. Furthermore, individual contributions of three modules (i.e., additional normal vectors, overlap score estimation module and the bidirectional mechanism) in OBHMR have been validated in ablation studies. The results demonstrate OBHMR’s capability of tackling the challenging partial-to-full registration problems in computer-assisted orthopedic surgery. The codes are available at https://github.com/Dxinz/DeepOBHMR.

Omnidirectional video enables spherical stimuli with the $360 \times 180^ \circ$ viewing range. Meanwhile, only the viewport region of omnidirectional video can be seen by the observer through head movement (HM), and an even smaller region within the viewport can be clearly perceived through eye movement (EM). Thus, the subjective quality of omnidirectional video may be correlated with HM and EM of human behavior. To fill in the gap between subjective quality and human behavior, this paper proposes a large-scale visual quality assessment (VQA) dataset of omnidirectional video, called VQA-OV, which collects 60 reference sequences and 540 impaired sequences. Our VQA-OV dataset provides not only the subjective quality scores of sequences but also the HM and EM data of subjects. By mining our dataset, we find that the subjective quality of omnidirectional video is indeed related to HM and EM. Hence, we develop a deep learning model, which embeds HM and EM, for objective VQA on omnidirectional video. Experimental results show that our model significantly improves the state-of-the-art performance of VQA on omnidirectional video.