Non-rigid Point Set Registration Research Articles

A novel model-based welding trajectory planning method for identical structural workpieces

Welding robots have been widely used with the development of manufacturing industry. At present, welding trajectory planning and programming of welding robots are performed separately for similar (structural) workpieces with different dimensions or deformations. Besides, the welding torch pose planning using conventional robot programming methods is time-consuming for workpieces with complex welding trajectories. To realize automatic planning of the welding torch pose for similar workpieces and improve the programming efficiency of welding robots, we propose a novel model-based welding trajectory planning method for welding robots. We create a basic model (point set) containing information on welding seam trajectory planning for similar workpieces. The welding seam trajectory extraction of similar workpieces is achieved by the non-rigid point set registration of the feature point cloud of similar workpieces with the basic model. Then, the welding torch pose planning is implemented by the geometric projection method of the local point cloud of the welding seam trajectory. Finally, the results of offline experiments and online experiments demonstrate the effectiveness of the proposed method.

Non-rigid point set registration based on Gaussian mixture model with integrated feature divergence

PurposeThis paper aims to propose a robust method for non-rigid point set registration, using the Gaussian mixture model and accommodating non-rigid transformations. The posterior probabilities of the mixture model are determined through the proposed integrated feature divergence.Design/methodology/approachThe method involves an alternating two-step framework, comprising correspondence estimation and subsequent transformation updating. For correspondence estimation, integrated feature divergences including both global and local features, are coupled with deterministic annealing to address the non-convexity problem of registration. For transformation updating, the expectation-maximization iteration scheme is introduced to iteratively refine correspondence and transformation estimation until convergence.FindingsThe experiments confirm that the proposed registration approach exhibits remarkable robustness on deformation, noise, outliers and occlusion for both 2D and 3D point clouds. Furthermore, the proposed method outperforms existing analogous algorithms in terms of time complexity. Application of stabilizing and securing intermodal containers loaded on ships is performed. The results demonstrate that the proposed registration framework exhibits excellent adaptability for real-scan point clouds, and achieves comparatively superior alignments in a shorter time.Originality/valueThe integrated feature divergence, involving both global and local information of points, is proven to be an effective indicator for measuring the reliability of point correspondences. This inclusion prevents premature convergence, resulting in more robust registration results for our proposed method. Simultaneously, the total operating time is reduced due to a lower number of iterations.

Non-Rigid Point Set Registration Based on Gaussian Mixture Model

Non-Rigid Point Set Registration Based on Gaussian Mixture Model

Correction: Rotation robust non-rigid point set registration with Bayesian student’s t mixture model

Correction: Rotation robust non-rigid point set registration with Bayesian student’s t mixture model

Non-rigid point set registration: recent trends and challenges

Non-rigid point set registration: recent trends and challenges

Non-rigid point set registration based on local neighborhood information support

Non-rigid point set registration is a crucial task and an unsolved problem in the field of computer vision. One commonly used method for solving the problem is based on the Gaussian mixture model (GMM). In this method, the point set registration is formalized as a probability density estimation problem. Most GMM-based methods achieve registration by maintaining global and local structures of points. However, the previous methods did not filter the neighborhood information in the local structure, and the quality of local neighborhood information directly affects the accuracy of registration. Therefore, extracting effective local neighborhood information is still a challenge. We propose a novel point set registration method based on GMM by extracting local neighborhood information. The two point sets X and Y are regarded as the centroids of GMM and data points produced by GMM, respectively. Our method computes initial correspondences by comparing the feature descriptors of point sets, and the initial correspondences are updated by considering the neighborhood information. Our method then uses the Expectation–Maximization method to solve the GMM. In the experimental results, the efficiency and advantages of our method relative to the current methods are verified by applying five commonly used datasets.

Rotation robust non-rigid point set registration with Bayesian student’s t mixture model

Rotation robust non-rigid point set registration with Bayesian student’s t mixture model

GP-Aligner: Unsupervised Groupwise Nonrigid Point Set Registration Based on Optimizable Group Latent Descriptor

In this paper, we propose a novel unsupervised method named GP-Aligner to address the problem of groupwise non-rigid point set registration. Compared to previous non-learning-based approaches, the proposed method gains competitive advantages by leveraging deep neural networks to effectively and efficiently align a large number of highly deformed 3D shapes with superior performance. Unlike most learning-based methods that use an explicit feature encoding network to extract per-shape features and their correlations, our model leverages a model-free learnable latent descriptor to characterize shape correlations among groups. More specifically, for a given group we first define an optimizable Group Latent Descriptor (GLD) to characterize the relationship among a group of point sets. Each GLD is randomly initialized from a Gaussian distribution and then concatenated with the coordinates of each point of the associated point sets in the group. A neural network-based decoder network is further constructed to predict the coherent flow fields to optimally deform the input groups of shapes to the aligned ones. During the optimization process, GP-Aligner jointly updates all GLDs and weight parameters of the decoder network towards the minimization of an unsupervised groupwise alignment loss. After optimization, for each group, our model coherently drives each point set towards a mean position (shape) without specifying one as the target. GP-Aligner does not require large-scale training data for network training, and it can directly align groups of point sets in a one-stage optimization process. GP-Aligner shows both accuracy and computational efficiency improvement in comparison with the state-of-the-art methods for groupwise point set registration. Moreover, GP-Aligner exhibits high efficiency in aligning a large number of groups of real-world 3D shapes.

Real-time multimodal image registration with partial intraoperative point-set data.

We present Free Point Transformer (FPT) - a deep neural network architecture for non-rigid point-set registration. Consisting of two modules, a global feature extraction module and a point transformation module, FPT does not assume explicit constraints based on point vicinity, thereby overcoming a common requirement of previous learning-based point-set registration methods. FPT is designed to accept unordered and unstructured point-sets with a variable number of points and uses a "model-free" approach without heuristic constraints. Training FPT is flexible and involves minimizing an intuitive unsupervised loss function, but supervised, semi-supervised, and partially- or weakly-supervised training are also supported. This flexibility makes FPT amenable to multimodal image registration problems where the ground-truth deformations are difficult or impossible to measure. In this paper, we demonstrate the application of FPT to non-rigid registration of prostate magnetic resonance (MR) imaging and sparsely-sampled transrectal ultrasound (TRUS) images. The registration errors were 4.71 mm and 4.81 mm for complete TRUS imaging and sparsely-sampled TRUS imaging, respectively. The results indicate superior accuracy to the alternative rigid and non-rigid registration algorithms tested and substantially lower computation time. The rapid inference possible with FPT makes it particularly suitable for applications where real-time registration is beneficial.

Robust and Accurate Nonrigid Point Set Registration Algorithm to Accommodate Anisotropic Positional Localization Error Based on Coherent Point Drift

Nonrigid point set (PS) registration is an outstanding and fundamental problem in the fields of robotics, computer vision, medical image analysis, and image-guided surgery (IGS). The aim of a nonrigid registration problem is to align together two point sets where one has been deformed. The assumption of isotropic localization error is shared in the previous nonrigid registration algorithms. In this article, we have derived and presented a novel nonrigid registration algorithm, where the position localization error (PLE) is generalized to be anisotropic, which means that the error distribution is not the same in different spatial directions. The motivation of considering the anisotropic characteristic is that the PLE is actually different in three spatial directions in real applications of registrations, such as IGS. Mathematically, the difficulty in dealing with the anisotropic error case comes from the change from a standard deviation that is a scalar to a covariance matrix. The formulas for updating the parameters in both expectation and maximization steps are derived. More specifically, in the expectation step, we compute the posterior probabilities that represent the correspondences between points in two PSs. In the maximization step, given the current posteriors, the covariance matrix of the PLE and the nonrigid transformation are updated. To further speed up the proposed algorithm, the low-rank approximation variation of our method is also presented. We have demonstrated through experiments on both general and medical data sets (corrupted with noise) that the proposed algorithm outperforms the state-of-the-art ones in terms of registration accuracy and robustness to noise. More specifically, all the experimental results have passed the statistical tests at the 5% significance level. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article was motivated by solving the problem of nonrigidly registering two point sets where one has been deformed and corrupted with anisotropic noise. Most existing registration methods generally assume the positional error to be the same in all directions, which in fact is not the case in real scenarios. This article presents a new robust method that assumes the positional error to be anisotropic, which is the case in point sets coming from the stereo reconstruction. The nonrigid registration problem is formulated as a maximum-likelihood (ML) problem and solved with the expectation–maximization (EM) technique. We have demonstrated through extensive experiments on both general and medical data sets that the proposed registration algorithm achieves significantly improved accuracy, robustness to noise, and outliers compared with state-of-the-art algorithms. The algorithm is particularly suitable for biomedical applications involving the registration, such as medical imaging and image-guided surgery (IGS).

An Improved Non-Rigid Point Set Registration Algorithm by Preserving Local Topology

An Improved Non-Rigid Point Set Registration Algorithm by Preserving Local Topology

A robust nonrigid point set registration framework based on global and intrinsic topological constraints

The problem of registering nonrigid point sets, with the aim of estimating the correspondences and learning the transformation between two given sets of points, often arises in computer vision tasks. This paper proposes a novel method for performing nonrigid point set registration on data with various types of degradation, in which the registration problem is formulated as a Gaussian mixture model (GMM)-based density estimation problem. Specifically, two complementary constraints are jointly considered for optimization in a GMM probabilistic framework. The first is a thin-plate spline-based regularization constraint that maintains global spatial motion consistency, and the second is a spectral graph-based regularization constraint that preserves the intrinsic structure of a point set. Moreover, the correspondences and the transformation are alternately optimized using the expectation maximization algorithm to obtain a closed-form solution. We first utilize local descriptors to construct the initial correspondences and then estimate the underlying transformation under the GMM-based framework. Experimental results on contour images and real images show the effectiveness and robustness of the proposed method.

Geolocation Error Estimation and Correction on Long-Term MWRI Data

Due to the limitation of the satellite attitude measurement accuracy and the system servo control error of the payload scanning mechanism, an optimal use of Micro-Wave Radiation Imager (MWRI) observations requires high geolocation accuracy. In the operational system, the MWRI geolocation accuracy reaches 1 pixel, and there still exists room for improvement. In this article, we improve upon the coastline inflection point method (CIM) and propose to assign the accurate correspondence by employing a nonrigid point set registration method. First, the method identifies a set of latent variables to recognize outliers and then applies nonparametric geometric constraints to the correspondence as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> distribution. Second, the maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> (MAP) estimation is applied by the expectation–maximization (EM) algorithm to obtain correct inliers. The comparison with other methods demonstrates that the proposed method can provide more accurate estimation of geolocation bias. In addition, the pixel error and changes in spacecraft attitude with the long-term geolocation data in FY-3C MWRI before and after correction were analyzed during the period from April 1 to August 30, 2018. The results have shown that the geolocation errors are reduced from [0.50, 0.60] pixels to [0.20, 0.33] pixels in the along- and cross-track directions after the attitude correction. In addition, the reduction of the standard deviation shows that the geolocation quality of MWRI is improved.

Non-rigid registration of point clouds using landmarks and stochastic neighbor embedding

Our study presents a probabilistic non-rigid point set registration method to deal with large and uneven deformations. Our method treats the registration as a density estimation problem. In our method, we add two key constraints to enforce landmark correspondences and preserve local neighborhood structure. We assume that the landmarks, which represent the salient points in the point sets, are given or can be detected using keypoint detectors such as scale-invariant feature transform or MeshDOG. By enforcing landmark correspondences, we preserve the overall global shape of the point set with significant deformations. Furthermore, by leveraging stochastic neighbor embedding, we incorporate constraints to preserve local neighborhood structure, which penalizes incoherent transformation within a neighborhood. Our experimental results in both 2D and 3D datasets show that our method outperforms state-of-the-art methods in a large degree of deformations. In particular, quantitative results show that the error is 29% better than the second-best result (from the state-of-the-art methods). Our analysis shows that a relatively small number of landmarks is sufficient to deal with large deformations. Finally, our study shows that our method is computationally comparable to state-of-the-art methods.

Acceleration of Non-Rigid Point Set Registration With Downsampling and Gaussian Process Regression.

Non-rigid point set registration is the process of transforming a shape represented as a point set into a shape matching another shape. In this paper, we propose an acceleration method for solving non-rigid point set registration problems. We accelerate non-rigid registration by dividing it into three steps: i) downsampling of point sets; ii) non-rigid registration of downsampled point sets; and iii) interpolation of shape deformation vectors corresponding to points removed during downsampling. To register downsampled point sets, we use a registration algorithm based on a prior distribution, called motion coherence prior. Using the same prior, we derive an interpolation method interpreted as Gaussian process regression. Through numerical experiments, we demonstrate that our algorithm registers point sets containing over ten million points. We also show that our algorithm reduces computing time more radically than a state-of-the-art acceleration algorithm.

Ultrarobust support vector registration

An iterativeframework based on finding point correspondences and estimating the transformation function is widely adopted for nonrigid point set registration. However, correspondences established based on feature descriptors are likely to be inaccurate. In this paper, we propose a novel transformation model that can learn from such correspondences. The model is built by means of weighted support vector (SV) regression with a quadratic e-insensitive loss and manifold regularization. The loss is insensitive to noise, and the regularization forces the transformation function to preserve the intrinsic geometry of the input data. To assess the confidences of correspondences, we introduce a probabilistic model that is solved using the expectation maximization (EM) algorithm. Then, we input the confidences into the transformation model as instance weights to guide model training. We use the coordinate descent method to solve the transformation model in a reproducing kernel Hilbert space and accelerate its speed by means of sparse approximation. Extensive experiments show that our approach is efficient and outperforms other state-of-the-art methods.

A Robust Nonrigid Point Set Registration Method Based on Collaborative Correspondences.

The nonrigid point set registration is one of the bottlenecks and has the wide applications in computer vision, pattern recognition, image fusion, video processing, and so on. In a nonrigid point set registration problem, finding the point-to-point correspondences is challengeable because of the various image degradations. In this paper, a robust method is proposed to accurately determine the correspondences by fusing the two complementary structural features, including the spatial location of a point and the local structure around it. The former is used to define the absolute distance (AD), and the latter is exploited to define the relative distance (RD). The AD-correspondences and the RD-correspondences can be established based on AD and RD, respectively. The neighboring corresponding consistency is employed to assign the confidence for each RD-correspondence. The proposed heuristic method combines the AD-correspondences and the RD-correspondences to determine the corresponding relationship between two point sets, which can significantly improve the corresponding accuracy. Subsequently, the thin plate spline (TPS) is employed as the transformation function. At each step, the closed-form solutions of the affine and nonaffine parts of TPS can be independently and robustly solved. It facilitates to analyze and control the registration process. Experimental results demonstrate that our method can achieve better performance than several existing state-of-the-art methods.

Assessment and application of the coherent point drift algorithm to augmented reality surgical navigation for laparoscopic partial nephrectomy.

The surface-based registration approach to laparoscopic augmented reality (AR) has clear advantages. Nonrigid point-set registration paves the way for surface-based registration. Among current non-rigid point set registration methods, the coherent point drift (CPD) algorithm is rarely used because of two challenges: (1) volumetric deformation is difficult to predict, and (2) registration from intraoperative visible tissue surface to whole anatomical preoperative model is a "part-to-whole" registration that CPD cannot be applied directly to. We preliminarily applied CPD on surgical navigation for laparoscopic partial nephrectomy (LPN). However, it introduces normalization errors and lacks navigation robustness. This paper presents important advances for more effectively applying CPD to LPN surgical navigation while attempting to quantitatively evaluate the accuracy of CPD-based surgical navigation. First, an optimized volumetric deformation (Op-VD) algorithm is proposed to achieve accurate prediction of volume deformation. Then, a projection-based partial selection method is presented to conveniently and robustly apply the CPD to LPN surgical navigation. Finally, kidneys with different deformations in vitro, phantom and in vivo experiments are performed to evaluate the accuracy and effectiveness of our approach. The average root-mean-square error of volume deformation was refined to 0.84 mm. The mean target registration error (TRE) of the surface and inside markers in the in vitro experiments decreased to 1.51 mm and 1.29 mm, respectively. The robustness and precision of CPD-based navigation were validated in phantom and in vivo experiments, and the mean navigation TRE of the phantom experiments was found to be [Formula: see text] mm. Accurate volumetric deformation and robust navigation results can be achieved in AR navigation of LPN by using surface-based registration with CPD. Evaluation results demonstrate the effectiveness of our proposed methods while showing the clinical application potential of CPD. This work has important guiding significance for the application of the CPD in laparoscopic AR.

SCM: Spatially Coherent Matching With Gaussian Field Learning for Nonrigid Point Set Registration.

While point set registration has been studied in many areas of computer vision for decades, registering points encountering different degradations remains a challenging problem. In this article, we introduce a robust point pattern matching method, termed spatially coherent matching (SCM). The SCM algorithm consists of recovering correspondences and learning nonrigid transformations between the given model and scene point sets while preserving the local neighborhood structure. Precisely, the proposed SCM starts with the initial matches that are contaminated by degradations (e.g., deformation, noise, occlusion, rotation, multiview, and outliers), and the main task is to recover the underlying correspondences and learn the nonrigid transformation alternately. Based on unsupervised manifold learning, the challenging problem of point set registration can be formulated by the Gaussian fields criterion under a local preserving constraint, where the neighborhood structure could be preserved in each transforming. Moreover, the nonrigid transformation is modeled in a reproducing kernel Hilbert space, and we use a kernel approximation strategy to boost efficiency. Experimental results demonstrate that the proposed approach robustly rejecting mismatches and registers complex point set pairs containing large degradations.

A Unified Framework for Nonrigid Point Set Registration via Coregularized Least Squares

This paper describes a method for performing nonrigid point set registration on data with different kinds of degradation (deformation, occlusion, noise, and outliers). We formulate the registration problem as a mixture model estimation problem by employing two topologically complementary constraints in a Gaussian mixture model (GMM)-based learning framework. The first constraint is Tikhonov-based regularization, which maintains the overall spatial connectivity by moving the point set collectively and coherently. The second constraint is graph-Laplacian-based regularization embedding, which preserves the intrinsic topological characteristics of the marginal space during registration. Hence, the proposed method is named coregularized least squares (Co-RLS). Our method iteratively estimates the correspondences and nonrigid transformation between two given sets of points. First, the correspondences are established subject to the ordering information of the contour points using feature descriptors, i.e., the shape context. Then, the transformation is recovered by minimizing the Co-RLS function, and the expectation maximization method is used to update the transformation parameters and outlier ratios. Experimental results on various types of synthetic and real data show the superior effectiveness and robustness of the proposed method compared with other state-of-the-art methods.