One of the basic building blocks in any point-based registration scheme involves matching feature points that are extracted from a sensed image to their counterparts in a reference image. This leads to the fundamental problem of point matching: Given two sets of points, find the (affine) transformation that transforms one point set so that its distance from the other point set is minimized. Because of measurement errors and the presence of outlying data points, it is important that the distance measure between the two point sets be robust to these effects. We measure distances using the partial Hausdorff distance. Point matching can be a computationally intensive task, and a number of theoretical and applied approaches have been proposed for solving this problem. In this paper, we present two algorithmic approaches to the point matching problem, in an attempt to reduce its computational complexity, while still providing a guarantee of the quality of the final match. Our first method is an approximation algorithm, which is loosely based on a branch-andbound approach due to Huttenlocher and Rucklidge, (Technical Report 1321, Dept. of Computer Science, Cornell University, Ithaca, 1992; Proc. IEEE Conf. on Computer vision and Pattern Recognition, New York, 1993, pp. 705-706). We show that by varying the approximation error bounds, it is possible to achieve a tradeoff between the quality of the match and the running time of the algorithm. Our second method involves a Monte Carlo method for accelerating the search process used in the first algorithm. This algorithm operates within the framework of a branch-and-bound procedure, but employs point-to-point alignments to accelerate the search. We show that this combination retains many of the strengths of branch-and-bound search, but provides significantly faster search times by exploiting alignments. With high probability, this method succeeds in finding an approximately optimal match. We demonstrate the algorithms' performances on both synthetically generated data points and actual satellite images.

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The problem of image registration. or alignment of two or more images representing the same scene or object, has to be addressed in various disciplines that employ digital imaging. In the area of remote sensing, just like in medical imaging or computer vision. it is necessary to design robust, fast and widely applicable algorithms that would allow automatic registration of images generated by various imaging platforms at the same or different times. and that would provide sub-pixel accuracy. One of the main issues that needs to be addressed when developing a registration algorithm is what type of information should be extracted from the images being registered, to be used in the search for the geometric transformation that best aligns them. The main objective of this paper is to evaluate several wavelet pyramids that may be used both for invariant feature extraction and for representing images at multiple spatial resolutions to accelerate registration. We find that the band-pass wavelets obtained from the Steerable Pyramid due to Simoncelli perform better than two types of low-pass pyramids when the images being registered have relatively small amount of nonlinear radiometric variations between them. Based on these findings, we propose a modification of a gradient-based registration algorithm that has recently been developed for medical data. We test the modified algorithm on several sets of real and synthetic satellite imagery.

Clustering is central to many image processing and remote sensing applications. ISODATA is one of the most popular and widely used clustering methods in geoscience applications, but it can run slowly, particularly with large data sets. We present a more efficient approach to ISODATA clustering, which achieves better running times by storing the points in a kd-tree and through a modification of the way in which the algorithm estimates the dispersion of each cluster. We also present an approximate version of the algorithm which allows the user to further improve the running time, at the expense of lower fidelity in computing the nearest cluster center to each point. We provide both theoretical and empirical justification that our modified approach produces clusterings that are very similar to those produced by the standard ISODATA approach. We also provide empirical studies on both synthetic data and remotely sensed Landsat and MODIS images that show that our approach has significantly lower running times.