Point set registration via particle filtering and stochastic dynamics

Research on Student's T-Distribution Point Cloud Registration Algorithm Based on Local Features

LiDAR offers a wide range of uses in autonomous driving, remote sensing, urban planning, and other areas. The laser 3D point cloud acquired by LiDAR typically encounters issues during registration, including laser speckle noise, Gaussian noise, data loss, and data disorder. This work suggests a novel Student's t-distribution point cloud registration algorithm based on the local features of point clouds to address these issues. The approach uses Student's t-distribution mixture model (SMM) to generate the probability distribution of point cloud registration, which can accurately describe the data distribution, in order to tackle the problem of the missing laser 3D point cloud data and data disorder. Owing to the disparity in the point cloud registration task, a full-rank covariance matrix is built based on the local features of the point cloud during the objective function design process. The combined penalty of point-to-point and point-to-plane distance is then added to the objective function adaptively. Simultaneously, by analyzing the imaging characteristics of LiDAR, according to the influence of the laser waveform and detector on the LiDAR imaging, the composite weight coefficient is added to improve the pertinence of the algorithm. Based on the public dataset and the laser 3D point cloud dataset acquired in the laboratory, the experimental findings demonstrate that the proposed algorithm has high practicability and dependability and outperforms the five comparison algorithms in terms of accuracy and robustness.

Point Set Registration for 3D Range Scans Using Fuzzy Cluster-Based Metric and Efficient Global Optimization

This study presents a new point set registration method to align 3D range scans. In our method, fuzzy clusters are utilized to represent a scan, and the registration of two given scans is realized by minimizing a fuzzy weighted sum of the distances between their fuzzy cluster centers. This fuzzy cluster-based metric has a broad basin of convergence and is robust to noise. Moreover, this metric provides analytic gradients, allowing standard gradient-based algorithms to be applied for optimization. Based on this metric, the outlier issues are addressed. In addition, for the first time in rigid point set registration, a registration quality assessment in the absence of ground truth is provided. Furthermore, given specified rotation and translation spaces, we derive the upper and lower bounds of the fuzzy cluster-based metric and develop a branch-and-bound (BnB)-based optimization scheme, which can globally minimize the metric regardless of the initialization. This optimization scheme is performed in an efficient coarse-to-fine fashion: First, fuzzy clustering is applied to describe each of the two given scans by a small number of fuzzy clusters. Then, a global search, which integrates BnB and gradient-based algorithms, is implemented to achieve a coarse alignment for the two scans. During the global search, the registration quality assessment offers a beneficial stop criterion to detect whether a good result is obtained. Afterwards, a relatively large number of points of the two scans are directly taken as the fuzzy cluster centers, and then, the coarse solution is refined to be an exact alignment using the gradient-based local convergence. Compared to existing counterparts, this optimization scheme makes a large improvement in terms of robustness and efficiency by virtue of the fuzzy cluster-based metric and the registration quality assessment. In the experiments, the registration results of several 3D range scan pairs demonstrate the accuracy and effectiveness of the proposed method, as well as its superiority to state-of-the-art registration approaches.

Registration of multi-view point sets under the perspective of expectation-maximization

Multi-view registration plays a critical role in 3D model reconstruction. To solve this problem, most previous methods align point sets by either partially exploring available information or blindly utilizing unnecessary information, which may lead to undesired results or extra computation complexity. Accordingly, we propose a novel solution for the multi-view registration under the perspective of Expectation-Maximization (EM). The proposed method assumes that each data point is generated from one unique Gaussian Mixture Model (GMM), where its corresponding points in other point sets are regarded as Gaussian centroids with equal covariance and membership probabilities. As it is difficult to obtain real corresponding points in the registration problem, they are approximated by the nearest neighbor in each other aligned point sets. Based on this assumption, it is reasonable to define the likelihood function including all rigid transformations, which require to be estimated for multi-view registration. Subsequently, the EM algorithm is derived to estimate rigid transformations with one Gaussian covariance by maximizing the likelihood function. Since the GMM component number is automatically determined by the number of point sets, there is no trade-off between registration accuracy and efficiency in the proposed method. Finally, the proposed method is tested on several benchmark data sets and compared with state-of-the-art algorithms. Experimental results demonstrate its superior performance on the accuracy, efficiency, and robustness for multi-view registration.

Image Matching from Handcrafted to Deep Features: A Survey

As a fundamental and critical task in various visual applications, image matching can identify then correspond the same or similar structure/content from two or more images. Over the past decades, growing amount and diversity of methods have been proposed for image matching, particularly with the development of deep learning techniques over the recent years. However, it may leave several open questions about which method would be a suitable choice for specific applications with respect to different scenarios and task requirements and how to design better image matching methods with superior performance in accuracy, robustness and efficiency. This encourages us to conduct a comprehensive and systematic review and analysis for those classical and latest techniques. Following the feature-based image matching pipeline, we first introduce feature detection, description, and matching techniques from handcrafted methods to trainable ones and provide an analysis of the development of these methods in theory and practice. Secondly, we briefly introduce several typical image matching-based applications for a comprehensive understanding of the significance of image matching. In addition, we also provide a comprehensive and objective comparison of these classical and latest techniques through extensive experiments on representative datasets. Finally, we conclude with the current status of image matching technologies and deliver insightful discussions and prospects for future works. This survey can serve as a reference for (but not limited to) researchers and engineers in image matching and related fields.

Robust Point Set Registration Using Signature Quadratic Form Distance

Point set registration is a problem with a long history in many pattern recognition tasks. This paper presents a robust point set registration algorithm based on optimizing the distance between two probability distributions. A major problem in point to point algorithms is defining the correspondence between two point sets. This paper follows the idea of some probability-based point set registration methods by representing the point sets as Gaussian mixture models (GMMs). By optimizing the distance between the two GMMs, rigid transformations (rotation and translation) between two point sets can be obtained without having to find a correspondence. Previous studies have used L2, Kullback Leibler, etc. distance to measure similarity between two GMMs; however, these methods have problems with robustness to noise and outliers, especially when the covariance matrix is large, or a local minimum exists. Therefore, in this paper, the signature quadratic form distance is derived to measure the distribution similarity. The contribution of this paper lies in adopting the signature quadratic form distance for the point set registration algorithm. The experimental results show the precision and robustness of this algorithm and demonstrate that it outperforms other state-of-the-art point set registration algorithms regarding factors, such as noise, outliers, missing partial structures, and initial misalignment.

Geometric calibration of a camera and a turntable system using two views

A calibration algorithm for a system comprising a camera and turntable is provided, in which the camera captures three-dimensional point clouds while a target object rotates on the turntable to three-dimensionally scan the entire object. A mathematical approach is used to obtain the geometry between the coordinate systems of the camera and the turntable. As a minimal setup, the camera captures two views of a chessboard calibration pattern placed on the turntable. The coordinate transformation from the camera to the turntable is then calculated through geometric reasoning. First, two camera poses are computed with respect to the chessboard images taken before and after rotation. The direction of the rotation axis of the turntable coordinate system can be calculated without any ambiguity. However, there is one degree of freedom in the choice of the other two directions and one degree of freedom in choosing the location of the origin of the turntable coordinate system. We provide a practical method for these choices. Experimental results with a stereo-vision system and a turntable validate the proposed method.

A Review of Point Set Registration: From Pairwise Registration to Groupwise Registration

This paper presents a comprehensive literature review on point set registration. The state-of-the-art modeling methods and algorithms for point set registration are discussed and summarized. Special attention is paid to methods for pairwise registration and groupwise registration. Some of the most prominent representative methods are selected to conduct qualitative and quantitative experiments. From the experiments we have conducted on 2D and 3D data, CPD-GL pairwise registration algorithm and JRMPC groupwise registration algorithm seem to outperform their rivals both in accuracy and computational complexity. Furthermore, future research directions and avenues in the area are identified.

Multi-view registration of unordered range scans by fast correspondence propagation of multi-scale descriptors

This paper proposes a global approach for the multi-view registration of unordered range scans. Our method starts with the pair-wise registration, where multi-scale descriptor is selected for feature point and the propagation of feature correspondence is accordingly accelerated. Subsequently, we design an effective rule to judge the reliability of these pair-wise registration results. According to the judgment of reliability, we propose a model fusion method, which can utilize reliable results of pair-wise registration to augment the model shape. Finally, multi-view registration can be achieved by operating the pair-wise registration, reliability judgment, and model fusion alternately. The proposed approach can be applied to scene reconstruction and robot mapping. Experimental results conducted on public datasets show that the proposed approach can automatically achieve multi-view registration of unordered range scans. Compared with other related approaches, the proposed approach has superior performances in accuracy and effectiveness.

Cubature Split Covariance Intersection Filter-based Point Set Registration

Point set registration is a basic but still open problem in numerous computer vision tasks. In general, there are more than one type of error sources for registration, for example, noise, outliers and false initialization may exist simultaneously. These errors could influence the registration independently and dependently. Previous works usually test performance under one of the two types of errors at one time, or they do not perform well under some extreme situations with both of the error sources. This work presents a robust point set registration algorithm under a filtering framework, which aims to be robust under various types of errors simultaneously. The point set registration problem can be cast into a non-linear state space model. We use a split covariance intersection filter (SCIF) to capture the correlation between the state transition and the observation (moving point set). The two above-mentioned types of errors can be represented as dependent and independent parts in the SCIF. The covariance of the two types of errors will be updated every iteration. Meanwhile, the non-linearity of the observation model is approximated by a cubature transformation. First, the recursive cubature split covariance intersection filter is derived based on the non-linear state space model. Then, we use this algorithm to solve the point set registration problem. This algorithm can approximate non-linearity by a third-order term and consider correlations between the process model and the observation model. Compared to other filtering-based methods, this algorithm is more robust and precise. Tests on both public datasets and experiments validate the precision and robustness of this algorithm to outliers and noise. Comparison experiments show that this algorithm outperforms state-of-the-art point set registration algorithms in certain respects.

Fast Descriptors and Correspondence Propagation for Robust Global Point Cloud Registration

In this paper, we present a robust global approach for point cloud registration from uniformly sampled points. Based on eigenvalues and normals computed from multiple scales, we design fast descriptors to extract local structures of these points. The eigenvalue-based descriptor is effective at finding seed matches with low precision using nearest neighbor search. Generally, recovering the transformation from matches with low precision is rather challenging. Therefore, we introduce a mechanism named correspondence propagation to aggregate each seed match into a set of numerous matches. With these sets of matches, multiple transformations between point clouds are computed. A quality function formulated from distance errors is used to identify the best transformation and fulfill a coarse alignment of the point clouds. Finally, we refine the alignment result with the trimmed iterative closest point algorithm. The proposed approach can be applied to register point clouds with significant or limited overlaps and small or large transformations. More encouragingly, it is rather efficient and very robust to noise. A comparison to traditional descriptor-based methods and other global algorithms demonstrates the fine performance of the proposed approach. We also show its promising application in large-scale reconstruction with the scans of two real scenes. In addition, the proposed approach can be used to register low-resolution point clouds captured by Kinect as well.

Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration

The Iterative Closest Point (ICP) algorithm is one of the most widely used methods for point-set registration. However, being based on local iterative optimization, ICP is known to be susceptible to local minima. Its performance critically relies on the quality of the initialization and only local optimality is guaranteed. This paper presents the first globally optimal algorithm, named Go-ICP, for Euclidean (rigid) registration of two 3D point-sets under the L₂ error metric defined in ICP. The Go-ICP method is based on a branch-and-bound scheme that searches the entire 3D motion space SE(3). By exploiting the special structure of SE(3) geometry, we derive novel upper and lower bounds for the registration error function. Local ICP is integrated into the BnB scheme, which speeds up the new method while guaranteeing global optimality. We also discuss extensions, addressing the issue of outlier robustness. The evaluation demonstrates that the proposed method is able to produce reliable registration results regardless of the initialization. Go-ICP can be applied in scenarios where an optimal solution is desirable or where a good initialization is not always available.

A Stochastic Approach to Diffeomorphic Point Set Registration with Landmark Constraints

This work presents a deformable point set registration algorithm that seeks an optimal set of radial basis functions to describe the registration. A novel, global optimization approach is introduced composed of simulated annealing with a particle filter based generator function to perform the registration. It is shown how constraints can be incorporated into this framework. A constraint on the deformation is enforced whose role is to ensure physically meaningful fields (i.e., invertible). Further, examples in which landmark constraints serve to guide the registration are shown. Results on 2D and 3D data demonstrate the algorithm's robustness to noise and missing information.

Registration of whole-mount histology and volumetric imaging of the prostate using particle filtering

Registration of histological slices to volumetric imaging of the prostate is an important task that can be used to optimize imaging for cancer detection. Such registration is challenging due to physical changes of the specimen during excision and fixation, and misalignment of the histological slices during preparation and digital scanning. In this work, we consider a multi-slice to volume registration method in which a stack of sparse, unaligned 2-D whole-mount histological slices is registered to a 3-D volumetric imaging of the prostate. We propose a particle filtering framework to contend with the high dimensionality of the search space and multimodal nature of the optimization. Such framework allows modeling of the uncertainty in the pose of the slices and in the imaged information, in order to derive optimal registration parameters in a Bayesian approach. Intensity-, region-, and point-based similarity metrics were incorporated into the registration algorithm to account for different imaging modalities. We demonstrate and evaluate our method on a diverse set of data that includes a synthetic volume, ex vivo and in vivo magnetic resonance imaging, and in vivo ultrasound.

Particle Filters and Occlusion Handling for Rigid 2D-3D Pose Tracking

In this paper, we address the problem of 2D-3D pose estimation. Specifically, we propose an approach to jointly track a rigid object in a 2D image sequence and to estimate its pose (position and orientation) in 3D space. We revisit a joint 2D segmentation/3D pose estimation technique, and then extend the framework by incorporating a particle filter to robustly track the object in a challenging environment, and by developing an occlusion detection and handling scheme to continuously track the object in the presence of occlusions. In particular, we focus on partial occlusions that prevent the tracker from extracting an exact region properties of the object, which plays a pivotal role for region-based tracking methods in maintaining the track. To this end, a dynamical choice of how to invoke the objective functional is performed online based on the degree of dependencies between predictions and measurements of the system in accordance with the degree of occlusion and the variation of the object's pose. This scheme provides the robustness to deal with occlusions of an obstacle with different statistical properties from that of the object of interest. Experimental results demonstrate the practical applicability and robustness of the proposed method in several challenging scenarios.

Deformable image registration for cone-beam CT guided transoral robotic base-of-tongue surgery

Transoral robotic surgery (TORS) offers a minimally invasive approach to resection of base-of-tongue tumors. However, precise localization of the surgical target and adjacent critical structures can be challenged by the highly deformed intraoperative setup. We propose a deformable registration method using intraoperative cone-beam computed tomography (CBCT) to accurately align preoperative CT or MR images with the intraoperative scene. The registration method combines a Gaussian mixture (GM) model followed by a variation of the Demons algorithm. First, following segmentation of the volume of interest (i.e. volume of the tongue extending to the hyoid), a GM model is applied to surface point clouds for rigid initialization (GM rigid) followed by nonrigid deformation (GM nonrigid). Second, the registration is refined using the Demons algorithm applied to distance map transforms of the (GM-registered) preoperative image and intraoperative CBCT. Performance was evaluated in repeat cadaver studies (25 image pairs) in terms of target registration error (TRE), entropy correlation coefficient (ECC) and normalized pointwise mutual information (NPMI). Retraction of the tongue in the TORS operative setup induced gross deformation >30 mm. The mean TRE following the GM rigid, GM nonrigid and Demons steps was 4.6, 2.1 and 1.7 mm, respectively. The respective ECC was 0.57, 0.70 and 0.73, and NPMI was 0.46, 0.57 and 0.60. Registration accuracy was best across the superior aspect of the tongue and in proximity to the hyoid (by virtue of GM registration of surface points on these structures). The Demons step refined registration primarily in deeper portions of the tongue further from the surface and hyoid bone. Since the method does not use image intensities directly, it is suitable to multi-modality registration of preoperative CT or MR with intraoperative CBCT. Extending the 3D image registration to the fusion of image and planning data in stereo-endoscopic video is anticipated to support safer, high-precision base-of-tongue robotic surgery.

Two-stage point-based registration method between ultrasound and CT imaging of the liver based on ICP and unscented Kalman filter: a phantom study

PURPOSE

In recent years, image-guided liver surgery based on intraoperative ultrasound (US) imaging has become common. Using an efficient point-based registration method to improve both accuracy and computational time for the registration of predeformation computer tomography, liver images with postdeformation US images are important during surgical procedure. Although iterative closest point (ICP) algorithm is widely used in surface-based registration, its performance strongly depends on the presence of noise and initial alignment. A registration technique based on unscented Kalman filter (UKF), which has been proposed recently, can used to overcome the noise and outliers on an incremental basis; however, the technique is associated with computational complexity.

METHODS

To overcome the limitations of ICP and UKF algorithms, we proposed an incremental two-stage registration method based on the combination of ICP and UKF algorithms to update the registration process with the acquired new points from US images. The registration is based on both the vessels and surface information of the liver.

RESULTS

The two-stage method was examined using numerical simulations and phantom data sets. The results of the phantom data set confirmed that the two-stage method outperforms the accuracy of ICP by 23% and reduces the running time of UKF by 60%.

CONCLUSION

The convergence rate, computational speed, and accuracy of the UKF algorithm can be improved using the two-stage method.

Shape Representation and Registration in Vector Implicit Spaces: Adopting a Closed-Form Solution in the Optimization Process

In this paper, a novel method to solve the shape registration problem covering both global and local deformations is proposed. The vector distance function (VDF) is used to represent source and target shapes. The problem is formulated as an energy optimization process by matching the VDFs of the source and target shapes. The minimization process results in estimating the transformation parameters for the global and local deformation cases. Gradient descent optimization handles the computation of scaling, rotation, and translation matrices used to minimize the global differences between source and target shapes. Nonrigid deformations require a large number of parameters which make the use of the gradient descent minimization a very time-consuming process. We propose to compute the local deformation parameters using a closed-form solution as a linear system of equations derived from approximating an objective function. Extensive experimental validations and comparisons performed on generalized 2D shape data demonstrate the robustness and effectiveness of the method.

Filtering in the diffeomorphism group and the registration of point sets

The registration of a pair of point sets as well as the estimation of their pointwise correspondences is a challenging and important task in computer vision. In this paper, we present a method to estimate the diffeomorphic deformation, together with the pointwise correspondences, between a pair of point sets. Many of the registration problems are iteratively solved by estimating the correspondence, locally optimizing certain cost functionals over the rigid or similarity or affine transformation group, then estimating the correspondence again, and so on. This type of approach, however, is well-known to be susceptible to suboptimal local solutions. In this paper, we first adopt the perspective of treating the registration as a posterior estimation optimization problem and solve it accordingly via a particle-filtering framework. Second, within such a framework, the diffeomorphic registration is performed to correct the nonlinear deformation of the points. In doing so, we provide a solution less susceptible to local minima. We provide the experimental results, which include challenging medical data sets where the two point sets differ by 180 (°) rotation as well as local deformations, to highlight the algorithm's capability of robustly finding the more globally optimal solution for the registration task.

Robust Point Set Registration Using Gaussian Mixture Models

In this paper, we present a unified framework for the rigid and nonrigid point set registration problem in the presence of significant amounts of noise and outliers. The key idea of this registration framework is to represent the input point sets using Gaussian mixture models. Then, the problem of point set registration is reformulated as the problem of aligning two Gaussian mixtures such that a statistical discrepancy measure between the two corresponding mixtures is minimized. We show that the popular iterative closest point (ICP) method [1] and several existing point set registration methods [2], [3], [4], [5], [6], [7] in the field are closely related and can be reinterpreted meaningfully in our general framework. Our instantiation of this general framework is based on the the L2 distance between two Gaussian mixtures, which has the closed-form expression and in turn leads to a computationally efficient registration algorithm. The resulting registration algorithm exhibits inherent statistical robustness, has an intuitive interpretation, and is simple to implement. We also provide theoretical and experimental comparisons with other robust methods for point set registration.