Points of interest linear attention network for real-time non-rigid liver volume to surface registration.

BACKGROUND: In laparoscopic liver surgery, accurately predicting the displacement of key intrahepatic anatomical structures is crucial for informing the doctor's intraoperative decision-making. However, due to the constrained surgical perspective, only a partial surface of the liver is typically visible. Consequently, the utilization of non-rigid volume to surface registration methods becomes essential. But traditional registration methods lack the necessary accuracy and cannot meet real-time requirements. PURPOSE: To achieve high-precision liver registration with only partial surface information and estimate the displacement of internal liver tissues in real-time. METHODS: We propose a novel neural network architecture tailored for real-time non-rigid liver volume to surface registration. The network utilizes a voxel-based method, integrating sparse convolution with the newly proposed points of interest (POI) linear attention module. POI linear attention module specifically calculates attention on the previously extracted POI. Additionally, we identified the most suitable normalization method RMSINorm. RESULTS: We evaluated our proposed network and other networks on a dataset generated from real liver models and two real datasets. Our method achieves an average error of 4.23 mm and a mean frame rate of 65.4 fps in the generation dataset. It also achieves an average error of 8.29 mm in the human breathing motion dataset. CONCLUSIONS: Our network outperforms CNN-based networks and other attention networks in terms of accuracy and inference speed.

MRI non-rigid registration with tumor contraction correction for ablative margin assessment after microwave ablation of hepatocellular carcinomas.

Objective. This study aims to develop and assess a tumor contraction model, enhancing the precision of ablative margin (AM) evaluation after microwave ablation (MWA) treatment for hepatocellular carcinomas (HCCs).Approach. We utilize a probabilistic method called the coherent point drift algorithm to align pre-and post-ablation MRI images. Subsequently, a nonlinear regression method quantifies local tumor contraction induced by MWA, utilizing data from 47 HCC with viable ablated tumors in post-ablation MRI. After automatic non-rigid registration, correction for tumor contraction involves contracting the 3D contour of the warped tumor towards its center in all orientations.Main results. We evaluate the performance of our proposed method on 30 HCC patients who underwent MWA. The Dice similarity coefficient between the post-ablation liver and the warped pre-ablation livers is found to be 0.95 ± 0.01, with a mean corresponding distance between the corresponding landmarks measured at 3.25 ± 0.62 mm. Additionally, we conduct a comparative analysis of clinical outcomes assessed through MRI over a 3 month follow-up period, noting that the AM, as evaluated by our proposed method, accurately detects residual tumor after MWA.Significance. Our proposed method showcases a high level of accuracy in MRI liver registration and AM assessment following ablation treatment. It introduces a potentially approach for predicting incomplete ablations and gauging treatment success.

HCS-Net: Multi-level deformation strategy combined with quadruple attention for image registration.

BACKGROUND AND OBJECTIVE: Non-rigid image registration plays a significant role in computer-aided diagnosis and surgical navigation for brain diseases. Registration methods that utilize convolutional neural networks (CNNs) have shown excellent accuracy when applied to brain magnetic resonance images (MRI). However, CNNs have limitations in understanding long-range spatial relationships in images, which makes it challenging to incorporate contextual information. And in intricate image registration tasks, it is difficult to achieve a satisfactory dense prediction field, resulting in poor registration performance. METHODS: This paper proposes a multi-level deformable unsupervised registration model that combines Transformer and CNN to achieve non-rigid registration of brain MRI. Firstly, utilizing a dual encoder structure to establish the dependency relationship between the global features of two images and to merge features of varying scales, as well as to preserve the relative spatial position information of feature maps at different scales. Then the proposed multi-level deformation strategy utilizes different deformable fields of varying resolutions generated by the decoding structure to progressively deform the moving image. Ultimately, the proposed quadruple attention module is incorporated into the decoding structure to merge feature information from various directions and emphasize the spatial features in the dominant channels. RESULTS: The experimental results on multiple brain MR datasets demonstrate that the promising network could provide accurate registration and is comparable to state-of-the-art methods. CONCLUSION: The proposed registration model can generate superior deformable fields and achieve more precise registration effects, enhancing the auxiliary role of medical image registration in various fields and advancing the development of computer-aided diagnosis, surgical navigation, and related domains.

Non-rigid-registration-based positioning and labelling of triaxial OPMs on a flexible cap for wearable magnetoencephalography.

BACKGROUND: Recent advances in highly sensitive miniaturized optically pumped magnetometers (OPMs) have enabled the development of wearable magnetoencephalography (MEG) offering great flexibility in experimental setting. The OPM array for wearable MEG is typically attached to a flexible cap and exhibits a variable spatial layout across different subjects, which imposes challenges concerning the efficient positioning and labelling of OPMs. NEW METHOD: A pair of reflective markers are affixed to each triaxial OPM sensor above its cable to determine its location and sensitive axes. A non-rigid registration of optically digitized marker locations with a pre-labelled template of marker locations is performed to map newly digitized markers to OPMs. RESULTS: The positioning and labelling of 66 OPM sensors could be completed within 35 s. Across ten experiments, all OPMs were accurately labelled, and the mean test-retest errors were 0.48 mm for sensor locations and 0.20 degree for sensitive axes. By combining six OPMs' positions with their respective recordings, magnetic dipoles inside a phantom were located with a mean error of 5.5 mm, and the best fitted dipole for MEG with auditory stimuli presented was located on a subject's primary auditory cortex. COMPARISON WITH EXISTING METHODS: The proposed method reduces the reliance on error-prone and laborious manual operations inherent in existing methods, therefore significantly improving the efficiency of OPM positioning and labelling on a flexible cap. CONCLUSION: We developed a method for the precise and rapid positioning and labelling triaxial OPMs on a flexible cap, thereby facilitating the practical implementation of wearable OPM-MEG.

Inter-pass motion correction for whole-body dynamic PET and parametric imaging.

Whole-body dynamic FDG-PET imaging through continuous-bed-motion (CBM) mode multi-pass acquisition protocol is a promising metabolism measurement. However, inter-pass misalignment originating from body movement could degrade parametric quantification. We aim to apply a non-rigid registration method for inter-pass motion correction in whole-body dynamic PET. 27 subjects underwent a 90-min whole-body FDG CBM PET scan on a Biograph mCT (Siemens Healthineers), acquiring 9 over-the-heart single-bed passes and subsequently 19 CBM passes (frames). The inter-pass motion correction was executed using non-rigid image registration with multi-resolution, B-spline free-form deformations. The parametric images were then generated by Patlak analysis. The overlaid Patlak slope Ki and y-intercept Vb images were visualized to qualitatively evaluate motion impact and correction effect. The normalized weighted mean squared Patlak fitting errors (NFE) were compared in the whole body, head, and hypermetabolic regions of interest (ROI). In Ki images, ROI statistics were collected and malignancy discrimination capacity was estimated by the area under the receiver operating characteristic curve (AUC). After the inter-pass motion correction was applied, the spatial misalignment appearance between Ki and Vb images was successfully reduced. Voxel-wise normalized fitting error maps showed global error reduction after motion correction. The NFE in the whole body (p = 0.0013), head (p = 0.0021), and ROIs (p = 0.0377) significantly decreased. The visual performance of each hypermetabolic ROI in Ki images was enhanced, while 3.59% and 3.67% average absolute percentage changes were observed in mean and maximum Ki values, respectively, across all evaluated ROIs. The estimated mean Ki values had substantial changes with motion correction (p = 0.0021). The AUC of both mean Ki and maximum Ki after motion correction increased, possibly suggesting the potential of enhancing oncological discrimination capacity through inter-pass motion correction.

Enabling supra-aortic vessels inclusion in statistical shape models of the aorta: a novel non-rigid registration method.

Statistical Shape Models (SSMs) are well-established tools for assessing the variability of 3D geometry and for broadening a limited set of shapes. They are widely used in medical imaging due to their ability to model complex geometries and their high efficiency as generative models. The principal step behind these techniques is a registration phase, which, in the case of complex geometries, can be a critical issue due to the correspondence problem, as it necessitates the development of correspondence mapping between shapes. The thoracic aorta, with its high level of morphological complexity, poses a multi-scale deformation problem due to the presence of several branch vessels with varying diameters. Moreover, branch vessels exhibit significant variability in shape, making the correspondence optimization even more challenging. Consequently, existing studies have focused on developing SSMs based only on the main body of the aorta, excluding the supra-aortic vessels from the analysis. In this work, we present a novel non-rigid registration algorithm based on optimizing a differentiable distance function through a modified gradient descent approach. This strategy enables the inclusion of custom, domain-specific constraints in the objective function, which act as landmarks during the registration phase. The algorithm's registration performance was tested and compared to an alternative Statistical Shape modeling framework, and subsequently used for the development of a comprehensive SSM of the thoracic aorta, including the supra-aortic vessels. The developed SSM was further evaluated against the alternative framework in terms of generalisation, specificity, and compactness to assess its effectiveness.

SPaM: soft patch matching for non-rigid pointcloud registration.

3d reconstruction of deformable objects in dynamic scenes forms the fundamental basis of many robotic applications. Existing mesh-based approaches compromise registration accuracy, and lose important details due to interpolation and smoothing. Additionally, existing non-rigid registration techniques struggle with unindexed points and disconnected manifolds. We propose a novel non-rigid registration framework for raw, unstructured, deformable point clouds purely based on geometric features. The global non-rigid deformation of an object is formulated as an aggregation of locally rigid transformations. The concept of locality is embodied in soft patches described by geometrical properties based on SHOT descriptor and its neighborhood. By considering the confidence score of pairwise association between soft patches of two scans (not necessarily consecutive), a computed similarity matrix serves as the seed to grow a correspondence graph which leverages rigidity terms defined in As-Rigid-As-Possible for pruning and optimization. Experiments on simulated and publicly available datasets demonstrate the capability of the proposed approach to cope with large deformations blended with numerous missing parts in the scan process.

[Non-rigid registration for medical images based on deformable convolution and multi-scale feature focusing modules].

Non-rigid registration plays an important role in medical image analysis. U-Net has been proven to be a hot research topic in medical image analysis and is widely used in medical image registration. However, existing registration models based on U-Net and its variants lack sufficient learning ability when dealing with complex deformations, and do not fully utilize multi-scale contextual information, resulting insufficient registration accuracy. To address this issue, a non-rigid registration algorithm for X-ray images based on deformable convolution and multi-scale feature focusing module was proposed. First, it used residual deformable convolution to replace the standard convolution of the original U-Net to enhance the expression ability of registration network for image geometric deformations. Then, stride convolution was used to replace the pooling operation of the downsampling operation to alleviate feature loss caused by continuous pooling. In addition, a multi-scale feature focusing module was introduced to the bridging layer in the encoding and decoding structure to improve the network model's ability of integrating global contextual information. Theoretical analysis and experimental results both showed that the proposed registration algorithm could focus on multi-scale contextual information, handle medical images with complex deformations, and improve the registration accuracy. It is suitable for non-rigid registration of chest X-ray images.

Learning feature descriptors for pre- and intra-operative point cloud matching for laparoscopic liver registration.

PURPOSE: In laparoscopic liver surgery, preoperative information can be overlaid onto the intra-operative scene by registering a 3D preoperative model to the intra-operative partial surface reconstructed from the laparoscopic video. To assist with this task, we explore the use of learning-based feature descriptors, which, to our best knowledge, have not been explored for use in laparoscopic liver registration. Furthermore, a dataset to train and evaluate the use of learning-based descriptors does not exist. METHODS: We present the LiverMatch dataset consisting of 16 preoperative models and their simulated intra-operative 3D surfaces. We also propose the LiverMatch network designed for this task, which outputs per-point feature descriptors, visibility scores, and matched points. RESULTS: We compare the proposed LiverMatch network with a network closest to LiverMatch and a histogram-based 3D descriptor on the testing split of the LiverMatch dataset, which includes two unseen preoperative models and 1400 intra-operative surfaces. Results suggest that our LiverMatch network can predict more accurate and dense matches than the other two methods and can be seamlessly integrated with a RANSAC-ICP-based registration algorithm to achieve an accurate initial alignment. CONCLUSION: The use of learning-based feature descriptors in laparoscopic liver registration (LLR) is promising, as it can help achieve an accurate initial rigid alignment, which, in turn, serves as an initialization for subsequent non-rigid registration.

Comparison Study of Extraction Accuracy of 3D Facial Anatomical Landmarks Based on Non-Rigid Registration of Face Template.

(1) Background: Three-dimensional (3D) facial anatomical landmarks are the premise and foundation of facial morphology analysis. At present, there is no ideal automatic determination method for 3D facial anatomical landmarks. This research aims to realize the automatic determination of 3D facial anatomical landmarks based on the non-rigid registration algorithm developed by our research team and to evaluate its landmark localization accuracy. (2) Methods: A 3D facial scanner, Face Scan, was used to collect 3D facial data of 20 adult males without significant facial deformities. Using the radial basis function optimized non-rigid registration algorithm, TH-OCR, developed by our research team (experimental group: TH group) and the non-rigid registration algorithm, MeshMonk (control group: MM group), a 3D face template constructed in our previous research was deformed and registered to each participant's data. The automatic determination of 3D facial anatomical landmarks was realized according to the index of 32 facial anatomical landmarks determined on the 3D face template. Considering these 32 facial anatomical landmarks manually selected by experts on the 3D facial data as the gold standard, the distance between the automatically determined and the corresponding manually selected facial anatomical landmarks was calculated as the "landmark localization error" to evaluate the effect and feasibility of the automatic determination method (template method). (3) Results: The mean landmark localization error of all facial anatomical landmarks in the TH and MM groups was 2.34 ± 1.76 mm and 2.16 ± 1.97 mm, respectively. The automatic determination of the anatomical landmarks in the middle face was better than that in the upper and lower face in both groups. Further, the automatic determination of anatomical landmarks in the center of the face was better than in the marginal part. (4) Conclusions: In this study, the automatic determination of 3D facial anatomical landmarks was realized based on non-rigid registration algorithms. There is no significant difference in the automatic landmark localization accuracy between the TH-OCR algorithm and the MeshMonk algorithm, and both can meet the needs of oral clinical applications to a certain extent.

Non-rigid registration based on hierarchical deformation of coronary arteries in CCTA images.

In this paper, we propose an accurate and rapid non-rigid registration method between blood vessels in temporal 3D cardiac computed tomography angiography images of the same patient. This method provides auxiliary information that can be utilized in the diagnosis and treatment of coronary artery diseases. The proposed method consists of the following four steps. First, global registration is conducted through rigid registration between the 3D vessel centerlines obtained from temporal 3D cardiac CT angiography images. Second, point matching between the 3D vessel centerlines in the rigid registration results is performed, and the corresponding points are defined. Third, the outliers in the matched corresponding points are removed by using various information such as thickness and gradient of the vessels. Finally, non-rigid registration is conducted for hierarchical local transformation using an energy function. The experiment results show that the average registration error of the proposed method is 0.987 mm, and the average execution time is 2.137 s, indicating that the registration is accurate and rapid. The proposed method that enables rapid and accurate registration by using the information on blood vessel characteristics in temporal CTA images of the same patient.

A Feature-based Affine Registration Method for Capturing Background Lung Tissue Deformation for Ground Glass Nodule Tracking.

Lung nodule tracking assessment relies on cross-sectional measurements of the largest lesion profile depicted in initial and follow-up computed tomography (CT) images. However, apparent changes in nodule size assessed via simple image-based measurements may also be compromised by the effect of the background lung tissue deformation on the GGN between the initial and follow-up images, leading to erroneous conclusions about nodule changes due to disease. To compensate for the lung deformation and enable consistent nodule tracking, here we propose a feature-based affine registration method and study its performance vis-a-vis several other registration methods. We implement and test each registration method using both a lung- and a lesion-centered region of interest on ten patient CT datasets featuring twelve nodules, including both benign and malignant GGO lesions containing pure GGNs, part-solid, or solid nodules. We evaluate each registration method according to the target registration error (TRE) computed across 30 - 50 homologous fiducial landmarks surrounding the lesions and selected by expert radiologists in both the initial and follow-up patient CT images. Our results show that the proposed feature-based affine lesion-centered registration yielded a 1.1 ± 1.2 mm TRE, while a Symmetric Normalization deformable registration yielded a 1.2 ± 1.2 mm TRE, and a least-square fit registration of the 30-50 validation fiducial landmark set yielded a 1.5 ± 1.2 mm TRE. Although the deformable registration yielded a slightly higher registration accuracy than the feature-based affine registration, it is significantly more computationally efficient, eliminates the need for ambiguous segmentation of GGNs featuring ill-defined borders, and reduces the susceptibility of artificial deformations introduced by the deformable registration, which may lead to increased similarity between the registered initial and follow-up images, over-compensating for the background lung tissue deformation, and, in turn, compromising the true disease-induced nodule change assessment. We also assessed the registration qualitatively, by visual inspection of the subtraction images, and conducted a pilot pre-clinical study that showed the proposed feature-based lesion-centered affine registration effectively compensates for the background lung tissue deformation between the initial and follow-up images and also serves as a reliable baseline registration method prior to assessing lung nodule changes due to disease.

Suitability of propagated contours for adaptive replanning for head and neck radiotherapy.

PURPOSE: Adaptive radiotherapy relies on rapid recontouring for replanning. Contour propagation offers workflow efficiencies, but the impact of using unedited propagated OAR contours directly during re-optimisation is unclear. METHODS: Plans for ten head and neck patients were created on the planning CT scan. OAR contours for the spinal cord, brainstem, parotids and larynx were then propagated to five shading-corrected CBCTs equally spaced throughout treatment using five commercial packages. Two reference contours were created on the CBCTs by (1) a clinician and (2) a geometric consensus from the propagated contours. Treatment plans were re-optimised on each CBCT for each set of contours, and the DVH statistic differences to the reference contours were calculated. The spread of DVH statistic differences between the 5th and 95th percentiles was quantified. RESULTS: The spread of DVH statistic differences was 3.7 Gy compared to the clinician contour and 3.3 Gy compared to the consensus contour for the brainstem (and PRV) and 2.4 Gy and 2 Gy for the spinal cord (and PRV), across all 5 auto-contouring solutions. The parotids and larynx showed differences of 3.7 Gy compared to the clinician and 0.9 Gy to the consensus contour, with the larger difference for the clinician possibly caused by uncertainty in the clinician standard due to poor image quality on the CBCTs. CONCLUSIONS: Propagated OAR contours can be used safely for adaptive radiotherapy replanning, however, where organ doses are close to clinical tolerance then the contours should be reviewed for accuracy regardless of the propagation software used.

Motion-aligned 4D-MRI reconstruction using higher degree total variation and locally low-rank regularization.

Four-dimensional magnetic resonance imaging (4D-MRI) is becoming increasingly important in radiotherapy treatment planning for its ability to simultaneously provide 3D structural information and temporal profiles of the examined tissues in a non-ionizing manner. However, the relatively long acquisition time and the resulting motion artifacts severely limit the further application of 4D-MRI. In this paper, we propose a novel motion-aligned reconstruction method based on higher degree total variation and locally low-rank regularization (maHDTV-LLR) to recover 4D MR images from the highly undersampled Fourier coefficients. Specifically, we propose a two-stage reconstruction framework alternating between a motion alignment step and a regularized optimization reconstruction step. Moreover, we incorporate the 3D-HDTV and the locally low-rank penalties into a unified framework to simultaneously exploit the spatial and temporal correlation of the 4D-MRI data. A fast alternating minimization algorithm based on variable splitting is utilized to solve the optimization problem efficiently. The performance of the proposed method is demonstrated in the context of 4D cardiac and abdominal MR images reconstruction with high undersampling factors. Numerical results show that the proposed method enables accelerated 4D-MRI with improved image quality and reduced artifacts.

Estimating Muscle Activity from the Deformation of a Sequential 3D Point Cloud.

Estimation of muscle activity is very important as it can be a cue to assess a person's movements and intentions. If muscle activity states can be obtained through non-contact measurement, through visual measurement systems, for example, muscle activity will provide data support and help for various study fields. In the present paper, we propose a method to predict human muscle activity from skin surface strain. This requires us to obtain a 3D reconstruction model with a high relative accuracy. The problem is that reconstruction errors due to noise on raw data generated in a visual measurement system are inevitable. In particular, the independent noise between each frame on the time series makes it difficult to accurately track the motion. In order to obtain more precise information about the human skin surface, we propose a method that introduces a temporal constraint in the non-rigid registration process. We can achieve more accurate tracking of shape and motion by constraining the point cloud motion over the time series. Using surface strain as input, we build a multilayer perceptron artificial neural network for inferring muscle activity. In the present paper, we investigate simple lower limb movements to train the network. As a result, we successfully achieve the estimation of muscle activity via surface strain.

Augmented reality navigation with ultrasound-assisted point cloud registration for percutaneous ablation of liver tumors.

PURPOSE: We present a novel augmented reality (AR) surgical navigation method with ultrasound-assisted point cloud registration for percutaneous ablation of liver tumors. A preliminary study is carried out to verify its feasibility. METHODS: Two three-dimensional (3D) point clouds of the liver surface are derived from the preoperative images and intraoperative tracked US images, respectively. To compensate for the soft tissue deformation, the point cloud registration between the preoperative images and the liver is performed using the non-rigid iterative closest point (ICP) algorithm. A 3D AR device based on integral videography technology is designed to accurately display naked-eye 3D images for surgical navigation. Based on the above registration, naked-eye 3D images of the liver surface, planning path, entry points, and tumor can be overlaid in situ through our 3D AR device. Finally, the AR-guided targeting accuracy is evaluated through entry point positioning. RESULTS: Experiments on both the liver phantom and in vitro pork liver were conducted. Several entry points on the liver surface were used to evaluate the targeting accuracy. The preliminary validation on the liver phantom showed average entry-point errors (EPEs) of 2.34 ± 0.45 mm, 2.25 ± 0.72 mm, 2.71 ± 0.82 mm, and 2.50 ± 1.11 mm at distinct US point cloud coverage rates of 100%, 75%, 50%, and 25%, respectively. The average EPEs of the deformed pork liver were 4.49 ± 1.88 mm and 5.02 ± 2.03 mm at the coverage rates of 100% and 75%, and the average covered-entry-point errors (CEPEs) were 4.96 ± 2.05 mm and 2.97 ± 1.37 mm at 50% and 25%, respectively. CONCLUSION: Experimental outcomes demonstrate that the proposed AR navigation method based on US-assisted point cloud registration has achieved an acceptable targeting accuracy on the liver surface even in the case of liver deformation.

PatchWarp: Corrections of non-uniform image distortions in two-photon calcium imaging data by patchwork affine transformations.

Complex distortions on calcium imaging often impair image registration accuracy. Here, we developed a registration algorithm, PatchWarp, to robustly correct slow image distortion for calcium imaging data. PatchWarp is a two-step algorithm with rigid and non-rigid image registrations. To correct non-uniform image distortions, it splits the imaging field and estimates the best affine transformation matrix for each of the subfields. The distortion-corrected subfields are stitched together like a patchwork to reconstruct the distortion-corrected imaging field. We show that PatchWarp robustly corrects image distortions of calcium imaging data collected from various cortical areas through glass window or gradient-index (GRIN) lens with a higher accuracy than existing non-rigid algorithms. Furthermore, it provides a fully automated method of registering images from different imaging sessions for longitudinal neural activity analyses. PatchWarp improves the quality of neural activity analyses and is useful as a general approach to correct image distortions in a wide range of disciplines.

Statistical and individual characteristics-based reconstruction for craniomaxillofacial surgery.

PURPOSE: In craniomaxillofacial (CMF) surgery planning, a preoperative reconstruction of the CMF reference model is crucial for surgical restoration, especially the reconstruction of bilateral defects. Current reconstruction algorithms mainly generate reference models from the image analysis aspect, however, clinical indicators of the CMF reference model mostly consider the distribution of anatomical landmarks. Generating a reference model with optimal clinical evaluation helps promote the feasibility of an algorithm. METHODS: We first build a dataset with 100 normal skull models and then calculate a statistical shape model (SSM) and the distribution of normal cephalometric values, which indicate the statistical features of a population. To further generate personalized reference models, we apply non-rigid registration to align the SSM with the defect skull model. An evaluation standard to select the optimal reference model considers both global performance and anatomical evaluation. Moreover, we develop a landmark detection network to improve the automatic level of the algorithm. RESULTS: The proposed method performs better than methods including Iterative Closest Point and SSM. From a global evaluation aspect, the results show that the RMSE between the reference model and the ground truth is [Formula: see text] mm, the percentage of vertices with error below 2 mm is [Formula: see text]% and the average faces distance is [Formula: see text] mm (better than the state-of-the-art method). From the anatomical evaluation aspect, the target registration error between the landmark pairs is [Formula: see text] mm. In addition, the clinical application confirms that the reference model can meet clinical requirements. CONCLUSION: To the best of our knowledge, we propose the first CMF reconstruction method considering the global performance of reconstruction and anatomically local evaluation from clinical experience. Simulated experiments and clinical cases prove the general applicability and strength of the method.

Non-rigid registration of medical images based on [Formula: see text] non-tensor product B-spline.

In this study, a non-tensor product B-spline algorithm is applied to the search space of the registration process, and a new method of image non-rigid registration is proposed. The tensor product B-spline is a function defined in the two directions of x and y, while the non-tensor product B-spline [Formula: see text] is defined in four directions on the 2-type triangulation. For certain problems, using non-tensor product B-splines to describe the non-rigid deformation of an image can more accurately extract the four-directional information of the image, thereby describing the global or local non-rigid deformation of the image in more directions. Indeed, it provides a method to solve the problem of image deformation in multiple directions. In addition, the region of interest of medical images is irregular, and usually no value exists on the boundary triangle. The value of the basis function of the non-tensor product B-spline on the boundary triangle is only 0. The algorithm process is optimized. The algorithm performs completely automatic non-rigid registration of computed tomography and magnetic resonance imaging images of patients. In particular, this study compares the performance of the proposed algorithm with the tensor product B-spline registration algorithm. The results elucidate that the proposed algorithm clearly improves the accuracy.

LDVoxelMorph: A precise loss function and cascaded architecture for unsupervised diffeomorphic large displacement registration.

PURPOSE: The traditional learning-based non-rigid registration methods for medical images are trained by an invariant smoothness regularization parameter, which cannot satisfy the registration accuracy and diffeomorphic property simultaneously. The diffeomorphic property reflects the credibility of the registration results. METHOD: To improve the diffeomorphic property in 3D medical image registration, we propose a diffeomorphic cascaded network based on the compressed loss (CL), named LDVoxelMorph. The proposed network has several constituent U-Nets and is trained with deep supervision, which uses a different spatial smoothness regularization parameter in each constituent U-Nets for training. This cascade-variant smoothness regularization parameter can maintain the diffeomorphic property in top cascades with large displacement and achieve precise registration in bottom cascades. Besides, we develop the CL as a penalty for the velocity field, which can accurately limit the velocity field that causes the deformation field overlap after the velocity field integration. RESULTS: In our registration experiments, the dice scores of our method were 0.892 ± 0.040 on liver CT datasets SLIVER37 , 0.848 ± 0.044 on liver CT datasets LiTS38 , 0.689 ± 0.014 on brain MRI datasets LPBA38 , and the number of overlapping voxels of deformation field were 325, 159, and 0, respectively. Ablation study shows that the CL improves the diffeomorphic property more effectively than increases. CONCLUSION: Experiment results show that our method can achieve higher registration accuracy assessed by dice scores and overlapping voxels while maintaining the diffeomorphic property for large deformation.