Non-rigid Point Set Registration Method Research Articles

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.

Non‐rigid point set registration by high‐dimensional representation

Non-rigid point set registration is a key component in many computer vision and pattern recognition tasks. In this study, the authors propose a robust non-rigid point set registration method based on high-dimensional representation. Their central idea is to map the point sets into a high-dimensional space by integrating the relative structure information into the coordinates of points. On the one hand, the point set registration is formulated as the estimation of a mixture of densities in high-dimensional space. On the other hand, the relative distances are used to compute the local features which assign the membership probabilities of the mixture model. The proposed model captures discriminative relative information and enables to preserve both global and local structures of the point set during matching. Extensive experiments on both synthesised and real data demonstrate that the proposed method outperforms the state-of-the-art methods under various types of distortions, especially for the deformation and rotation degradations.

Accurate and Robust Non-rigid Point Set Registration using Student\u2019s-t Mixture Model with Prior Probability Modeling

A new accurate and robust non-rigid point set registration method, named DSMM, is proposed for non-rigid point set registration in the presence of significant amounts of missing correspondences and outliers. The key idea of this algorithm is to consider the relationship between the point sets as random variables and model the prior probabilities via Dirichlet distribution. We assign the various prior probabilities of each point to its correspondences in the Student’s-t mixture model. We later incorporate the local spatial representation of the point sets by representing the posterior probabilities in a linear smoothing filter and get closed-form mixture proportions, leading to a computationally efficient registration algorithm comparing to other Student’s-t mixture model based methods. Finally, by introducing the hidden random variables in the Bayesian framework, we propose a general mixture model family for generalizing the mixture-model-based point set registration, where the existing methods can be considered as members of the proposed family. We evaluate DSMM and other state-of-the-art finite mixture models based point set registration algorithms on both artificial point set and various 2D and 3D point sets, where DSMM demonstrates its statistical accuracy and robustness, outperforming the competing algorithms.

A robust non-rigid point set registration method based on inhomogeneous Gaussian mixture models

In this paper, we propose a novel robust non-rigid point set registration method adopting a new probability model called inhomogeneous Gaussian mixture models (IGMM), where we regard one point set as the centroids of a Gaussian mixture model and the other point set as the data. The IGMM is defined by applying local features and Gaussian mixture models. Considering the local relationship among neighboring points is stable, a neighborhood structural descriptor, named as local shape context, is first presented. On the basis of local descriptors, we can obtain a measure of compatibility between local features in the point sets. Then, the similarity of the local structure of point neighborhoods can be calculated on the basis of the matching scores. Each Gaussian mixture component is assigned a different weight depending on the feature similarity, which differs from the traditional Gaussian mixture model where each Gaussian mixture component has the same weight. The proposed IGMM makes point pairs with more similar features have bigger probability to formulate a match, while in algorithms based on GMMs, all point pairs have the same probability to construct correspondence points. Finally, we support our claims through regularization theory and formulate registration as a likelihood maximization problem, which is solved by updating transformation parameters and outlier ratios using the expectation maximization algorithm. Extensive comparison and evaluation experiments on synthetic point-sets datasets demonstrate that the proposed approach is robust and achieves superior performance in the presence of non-rigid deformation, noise, outliers and occlusion. In addition, a number of experiments on real images reveal that our proposed algorithm is more applicable than state-of-the-art algorithms.

Robust Non-Rigid Point Set Registration Using Spatially Constrained Gaussian Fields.

Estimating transformations from degraded point sets is necessary for many computer vision and pattern recognition applications. In this paper, we propose a robust non-rigid point set registration method based on spatially constrained context-aware Gaussian fields. We first construct a context-aware representation (e.g., shape context) for assignment initialization. Then, we use a graph Laplacian regularized Gaussian fields to estimate the underlying transformation from the likely correspondences. On the one hand, the intrinsic manifold is considered and used to preserve the geometrical structure, and a priori knowledge of the point set is extracted. On the other hand, by using the deterministic annealing, the presented method is extended to a projected high-dimensional feature space, i.e., reproducing kernel Hilbert space through a kernel trick to solve the transformation, in which the local structure is propagated by the coarse-to-fine scaling strategy. In this way, the proposed method gradually recovers much more correct correspondences, and then estimates the transformation parameters accurately and robustly when facing degradations. Experimental results on 2D and 3D synthetic and real data (point sets) demonstrate that the proposed method reaches better performance than the state-of-the-art algorithms.

A robust non-rigid point set registration method based on asymmetric gaussian representation

Point set registration problem confronts with the challenge of large degree of degradations, such as deformation, noise, occlusion and outlier. In this paper, we present a novel robust method for non-rigid point set registration, and it includes four important parts are as follows: First, we used a mixture of asymmetric Gaussian model (MoAG) Kato et al. (2002) [1], a new probability model which can capture spatially asymmetric distributions, to represent each point set. Second, based on the representation of point set by MoAG, we used soft assignment technique to recover the correspondences, and correlation-based method to estimate the transformation parameters between two point sets. Point set registration is formulated as an optimization problem. Third, we solved the optimization problem under regularization theory in a feature space, i.e., Reproducing Kernel Hilbert Space (RKHS). Finally, we chose control points to build a kernel using low-rank kernel matrix approximation. Thus the computational complexity can be reduced down to O(N) approximately. Experimental results on 2D, 3D non-rigid point set, and real image registration demonstrate that our method is robust to a large degree of degradations, and it outperforms several state-of-the-art methods in most tested scenarios.

A robust global and local mixture distance based non-rigid point set registration

We present a robust global and local mixture distance (GLMD) based non-rigid point set registration method which consists of an alternating two-step process: correspondence estimation and transformation updating. We first define two distance features for measuring global and local structural differences between two point sets, respectively. The two distances are then combined to form a GLMD based cost matrix which provides a flexible way to estimate correspondences by minimizing global or local structural differences using a linear assignment solution. To improve the correspondence estimation and enhance the interaction between the two steps, an annealing scheme is designed to gradually change the cost minimization from local to global and the thin plate spline transformation from rigid to non-rigid during registration. We test the performance of our method in contour registration, sequence images and real images, and compare with six state-of-the-art methods where our method shows the best alignments in most scenarios.