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Feature matching, which refers to establishing reliable correspondence between two sets of features (particularly point features), is a critical prerequisite in feature-based registration. In this paper, we propose a flexible and general algorithm, which is called locally linear transforming (LLT), for both rigid and nonrigid feature matching of remote sensing images. We start by creating a set of putative correspondences based on the feature similarity and then focus on removing outliers from the putative set and estimating the transformation as well. We formulate this as a maximum-likelihood estimation of a Bayesian model with hidden/latent variables indicating whether matches in the putative set are outliers or inliers. To ensure the well-posedness of the problem, we develop a local geometrical constraint that can preserve local structures among neighboring feature points, and it is also robust to a large number of outliers. The problem is solved by using the expectation-maximization algorithm (EM), and the closed-form solutions of both rigid and nonrigid transformations are derived in the maximization step. In the nonrigid case, we model the transformation between images in a reproducing kernel Hilbert space (RKHS), and a sparse approximation is applied to the transformation that reduces the method computation complexity to linearithmic. Extensive experiments on real remote sensing images demonstrate accurate results of LLT, which outperforms current state-of-the-art methods, particularly in the case of severe outliers (even up to 80%).

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Seeking reliable correspondences between two feature sets is a fundamental and important task in computer vision. This paper attempts to remove mismatches from given putative image feature correspondences. To achieve the goal, an efficient approach, termed as locality preserving matching (LPM), is designed, the principle of which is to maintain the local neighborhood structures of those potential true matches. We formulate the problem into a mathematical model, and derive a closedform solution with linearithmic time and linear space complexities. More specifically, our method can accomplish the mismatch removal from thousands of putative correspondences in only a few milliseconds. Experiments on various real image pairs for general feature matching, as well as for visual homing and image retrieval demonstrate the generality of our method for handling different types of image deformations, and it is more than two orders of magnitude faster than state-of-the-art methods in the same range of or better accuracy.