A Mixture Model for Robust Point Matching under Multi-Layer Motion

Abstract

This paper proposes an efficient mixture model for establishing robust point correspondences between two sets of points under multi-layer motion. Our algorithm starts by creating a set of putative correspondences which can contain a number of false correspondences, or outliers, in addition to the true correspondences (inliers). Next we solve for correspondence by interpolating a set of spatial transformations on the putative correspondence set based on a mixture model, which involves estimating a consensus of inlier points whose matching follows a non-parametric geometrical constraint. We formulate this as a maximum a posteriori (MAP) estimation of a Bayesian model with hidden/latent variables indicating whether matches in the putative set are outliers or inliers. We impose non-parametric geometrical constraints on the correspondence, as a prior distribution, in a reproducing kernel Hilbert space (RKHS). MAP estimation is performed by the EM algorithm which by also estimating the variance of the prior model (initialized to a large value) is able to obtain good estimates very quickly (e.g., avoiding many of the local minima inherent in this formulation). We further provide a fast implementation based on sparse approximation which can achieve a significant speed-up without much performance degradation. We illustrate the proposed method on 2D and 3D real images for sparse feature correspondence, as well as a public available dataset for shape matching. The quantitative results demonstrate that our method is robust to non-rigid deformation and multi-layer/large discontinuous motion.

Robust Feature Matching for Remote Sensing Image Registration via Locally Linear Transforming

“…However, for remote sensing image pairs, the difference between the disparities of the point correspondences in local areas are typically quite small; hence, the local structures among neighboring feature points are also very strong and stable. This is particularly beneficial when the images involve nonrigid or discontinuous motions [62]. Therefore, to establish accurate matches, a local geometrical constraint on the point correspondences is desired.…”

Automatic visible and infrared face registration based on silhouette matching and robust transformation estimation

“…The reasons of choosing these two methods lie in twofold: (ii) besides the spatial information of the silhouettes, both the two methods use local shape features such shape context as in our method to help to recover the accurate transformation; (ii) we would like to investigate the necessity of using more complex non-rigid model when the data satisfies or approximately satisfies the rigid model. To have a quantitative evaluation, we compute the recall on all the 100 silhouette pairs of a degradation type as the metric used in [46]. Here the recall, or true positive rate, is defined as the proportion of true positive correspondences between the silhouette point pairs to the ground truth correspondences, and a true positive correspondence is counted when the pair falls within a given accuracy threshold in terms of pairwise distance, e.g., the Euclidean distance between a point in one silhouette and the corresponding point in the other silhouette.…”

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

“…Then, an expectation-maximization (EM) algorithm is applied to perform this ML optimization. Many algorithms were proposed to extend the CPD method [ 1 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 , 88 , 89 , 90 , 91 , 92 ]. These algorithms can be summarized as follows: Selecting a suitable non-rigid transformation function: In the CPD method, only one non-rigid transformation function is considered.…”

“…By automatically adjusting the kernel weights, this method can prune the ineffective kernels and evaluate the importance of each kernel. Considering the multi-layer motion between two sets of points, a robust point set registration using the GMM model was proposed in [ 73 ]. Choosing the distribution of point set: In [ 74 ], the Student’s- t distribution was used to replace the Gaussian distribution for tackling the outliers in the point set registration.…”