Point Set Registration: Coherent Point Drift

The coherent point drift (CPD) algorithm is a powerful approach for point set registration. However, it suffers from a serious problem-there is a weight parameter w that reflects the assumption about the amount of noise and number of outliers in the Gaussian mixture model, and its value has an influence on the point set registration performance In the original CPD algorithm, the value of w is set manually, and hence an improper value will lead to poor registration results. To solve this problem, a fully automatic algorithm for the selection of an optimal weight parameter is proposed using a hybrid optimization scheme that combines the genetic algorithm with the Nelder-Mead simplex method. The experiments show that the refined CPD algorithm is more effective and extends the original CPD algorithm in its methodology and applications.

Remote sensing image registration is a key component in many computer vision tasks since it can improve the understanding of information among multisensor images through fusing. After feature detection, the image registration is converted into a point set registration problem. The coherent point drift (CPD) algorithm is regarded as a powerful approach for point set registration. However, for junction set, a serious problem arises when using this algorithm—the structural information of the junction is not included in the Gaussian mixture model. To solve this problem, we present an enhanced coherent point drift (ECPD) algorithm. According to the inherent characteristic of junction, we propose the definition of local structural consistency which measures the similarity between two junctions. Furthermore, we introduce local structural consistency as a part of GMM components’ posterior probabilities to achieve more accurate registration results. The experiments of remote sensing image registration show that the ECPD algorithm is more robust to noises and outliers than CPD and outperforms current state-of-the-art methods.

A fast point cloud registration algorithm is proposed for the problem that the traditional CPD (Coherent Point Drift) algorithm is time consuming and has poor the registration efficiency. Firstly, the voxel grid method is carried out on the three-dimensional bounding box of the cloud space, and the point in the whole voxel are expressed by the voxel centers, and the down-sampling operation of the cloud is completed to reduce the amount of the calculated data. Then, the Gaussian mixture model is established for the obtained point cloud to compute the values of negative log-likelihood functions. Finally, we use the EM algorithm to iterate to solve the closed parameters by minimizing negative logarithmic likelihood function. The rotation matrix and translation vector are obtained to match two points clouds. The experimental results show that the proposed method can greatly improve the registration speed while maintaining the original registration accuracy.

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.

The Coherent Point Drift (CPD) algorithm which based on Gauss Mixture Model is a robust point set registration algorithm. However, the selection of robustness weight which used to describe the noise may directly affect the point set registration efficiency. For resolving the problem, this paper presents a CPD registration algorithm which based on distance threshold constraint. Before the point set registration, the inaccurate template point set by resampling become the initial point set of point set matching, in order to eliminate some points that the distance to target point set is too close and too far in the inaccurate template point set, and set the weights of robustness as . In the simulation experiments, we make two group experiments: the first group is the registration of the inaccurate template point set and the accurate target point set, while the second group is the registration of the accurate template point set and the accurate target point set. The results of comparison show that our method can solve the problem of selection for the weight. And it improves the speed and precision of the original CPD registration.

We propose a new point set registration method, Global-Local Topology Preservation (GLTP), which can cope with complex non-rigid transformations including highly articulated deformation. The registration is formulated as a Maximum Likelihood (ML) estimation problem with two topologically complementary constraints. The first is the previous Coherent Point Drift (CPD) that encodes a global topology constraint by moving one point set coherently to align with the second set. The second, which is inspired by the idea of Local Linear Embedding (LLE), is introduced to handle highly articulated non-rigid deformation while sustaining the local structure. Without any pre-segmentation, the newly introduced LLE constraint is particularly useful and effective when there are multiple non-coherent and nonrigid local deformations (i.e, the CPD assumption may be violated). We have derived the EM algorithm for the ML optimization constrained with both CPD and LLE terms, leading to the new GLTP algorithm. Experimental results on 2D and 3D examples show its accuracy and robustness in the presence of outliers and noise, especially in the case of highly-articulated non-rigid transformation.

Coherent Point Drift (CPD) is one of the popular robust point cloud registration algorithms in recent years. However, the algorithm uses fast Gaussian transformation to calculate the matrix-vector product, resulting in slower overall registration efficiency. We propose an improved coherent point drift (ICPD) algorithm, which introduces faster Gaussian lattice filtering to calculate the above product and uses the global squared iterative method to reduce the number of iterations of the CPD algorithm. In addition, the outlier w is not accurately expressed in CPD. We propose an iterative outlier formula to solve this problem. Experiments show that the improved algorithm is about two orders of magnitude faster than the CPD algorithm, 1-2 times faster than the ICP algorithm, and shows superior performance in environments with different noise and outlier distributions.

Point set registration is a key problem in many computer vision tasks. The goal of point set registration is to match two sets of points and estimate the transformation parameter that maps one point set to the other. Among the many published registration methods, the recently proposed Coherent Point Drift (CPD) algorithm stands out for its accuracy. In this paper we show that by casting CPD in the Bayesian framework we can obtain even better results. In particular, in case of large translation amount, our proposed mathod has much less number of iterations than CPD without any loss of accuracy. Experimental results confirms the advantages of the proposed method and shows an overall speedup when compared with the CPD method.

Recently, the Coherent Point Drift (CPD) algorithm has become a very popular and efficient method for point set registration. However, this method does not take into consideration the neighborhood structure information of points to find the correspondence and requires a manual assignment of the outlier ratio. Therefore, CPD is not robust for large degrees of degradation. In this paper, an improved method is proposed to overcome the two limitations of CPD. A structure descriptor, such as shape context, is used to perform the auxiliary calculation of the correspondence, and the proportion of each GMM component is adjusted by the similarity. The outlier ratio is formulated in the EM framework so that it can be automatically calculated and optimized iteratively. The experimental results on both synthetic data and real data demonstrate that the proposed method described here is more robust to deformation, noise, occlusion, and outliers than CPD and other state-of-the-art algorithms.

Fully automatic 3-D point cloud registration is a highly challenging task in light detection and ranging (LiDAR) remote sensing. The coherent point drift (CPD) algorithm provides an appropriate solution for point cloud registration because of its high accuracy. However, real application of the traditional CPD algorithm is limited due to its demanding computational complexity. In this letter, we present a novel accelerated CPD (ACPD) algorithm for fast, accurate, and automatic registration of 3-D point clouds. First, a global squared iterative expectation–maximization (gSQUAREM) technique is integrated to the ACPD algorithm. Then, the dual-tree improved fast Gauss transform method is used to further accelerate the Gaussian summation process during the correspondence probability matrix calculation. Experimental results on two real data sets show that the proposed algorithm can perform fast and accurate registration on LiDAR point clouds.

We present a novel algorithm for the registration of multiple temporally related point sets. Although our algorithm is derived in a general setting, our primary motivating application is coronary tree matching in multi-phase cardiac spiral CT. Our algorithm builds upon the fast, outlier-resistant Coherent Point Drift (CPD) algorithm, but incorporates temporal consistency constraints between the point sets, resulting in spatiotemporally smooth displacement fields. We preserve the speed and robustness of the CPD algorithm by using the technique of separable surrogates within an EM (Expectation-Maximization) optimization framework, while still minimizing a global registration cost function employing both spatial and temporal regularization. We demonstrate the superiority of our novel temporally consistent group-wise CPD algorithm over a straightforward pair-wise approach employing the original CPD algorithm, using coronary trees derived from both simulated and real cardiac CT data. In all the tested configurations and datasets, our method presents lower average error between tree landmarks compared to the pairwise method. In the worst case, the difference is around few micrometers but in the better case, our method divides by two the error from the pairwise method. This improvement is especially important for a dataset with numerous outliers. With a fixed set of parameter that has been tuned automatically, our algorithm yields better results than the original CPD algorithm which shows the capacity to register without a priori information on an unknown dataset.

In this paper the problem of pairwise model-to-scene point set registration is considered. Three contributions are made. Firstly, the relations between correspondence-based and some information-theoretic point cloud registration algorithms are formalized. Starting from the observation that the outlier handling of existing methods relies on heuristically determined models, a second contribution is made exploiting aforementioned relations to derive a new robust point set registration algorithm. Representing model and scene point clouds by mixtures of Gaus-sians, the method minimizes their Kullback-Leibler divergence both w.r.t. the registration transformation parameters and w.r.t. the scene's mixture coefficients. This results in an Expectation-Maximization Iterative Closest Point (EM-ICP) approach with a parameter-free outlier model that is optimal in information-theoretical sense. While the current (CUDA) implementation is limited to the rigid registration case, the underlying theory applies to both rigid and non-rigid point set registration. As a by-product of the registration algorithm's theory, a third contribution is made by suggesting a new point cloud Kernel Density Estimation approach which relies on maximizing the resulting distribution's entropy w.r.t. the kernel weights. The rigid registration algorithm is applied to align different patches of the publicly available Stanford Dragon and Stanford Happy Budha range data. The results show good performance regarding accuracy, robustness and convergence range.

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).

A fully automatic surgical registration method for percutaneous abdominal puncture surgical navigation

This paper proposes a non-rigid point set registration method called Structure-Guided Coherent Point Drift (SGCPD). The key idea of our method is to utilize structural information and combine the global and local point registrations together to improve the original Coherent Point Drift (CPD) algorithm. Specifically, given two point sets, we first align them using the CPD method with Localized Operator (CPDLO). Then we divide the target point set into several subsets and apply CPDLO to each subset. Finally, we implement the above two procedures until convergence. In this manner, more detailed information can be well exploited and thus higher registration accuracy can be achieved. Experimental results demonstrate that our method outperforms the original CPD approach on both point registration accuracy and skeleton decomposition accuracy for Chinese characters.