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**1 - 3**of**3**### New Approaches to Robust, Point-Based Image Registration

"... We consider various algorithmic solutions to image registration based on the alignment of a set of feature points. We present a number of enhancements to a branch-and-bound algorithm introduced by Mount, Netanyahu, and Le Moigne (Pattern Recognition, Vol. 32, 1999, pp. 17–38), which presented a regi ..."

Abstract
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We consider various algorithmic solutions to image registration based on the alignment of a set of feature points. We present a number of enhancements to a branch-and-bound algorithm introduced by Mount, Netanyahu, and Le Moigne (Pattern Recognition, Vol. 32, 1999, pp. 17–38), which presented a registration algorithm based on the partial Hausdorff distance. Our enhancements include a new distance measure, the discrete Gaussian mismatch, and a number of improvements and extensions to the above search algorithm. Both distance measures are robust to the presence of outliers, that is, data points from either set that do not match any point of the other set. We present experimental studies, which show that the new distance measure considered can provide significant improvements over the partial Hausdorff distance in instances where the number of outliers is not known in advance. These experiments also show that our other algorithmic improvements can offer tangible improvements. We demonstrate the algorithm’s efficacy by considering images involving different sensors and different spectral bands, both in a traditional framework and in a multiresolution framework.

### APPROXIMATION ALGORITHMS FOR POINT PATTERN MATCHING AND SEARCHING

, 2010

"... Point pattern matching is a fundamental problem in computational geometry. For given a reference set and pattern set, the problem is to find a geometric trans-formation applied to the pattern set that minimizes some given distance measure with respect to the reference set. This problem has been heav ..."

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Point pattern matching is a fundamental problem in computational geometry. For given a reference set and pattern set, the problem is to find a geometric trans-formation applied to the pattern set that minimizes some given distance measure with respect to the reference set. This problem has been heavily researched under various distance measures and error models. Point set similarity searching is variation of this problem in which a large database of point sets is given, and the task is to preprocess this database into a data structure so that, given a query point set, it is possible to rapidly find the nearest point set among elements of the database. Here, the term nearest is understood in above sense of pattern matching, where the elements of the database may be transformed to match the given query set. The approach presented here is to compute a low distortion embedding of the pattern matching problem into an (ideally) low dimensional metric space and then apply any standard algorithm for nearest neighbor searching over this metric space. This main focus of this dissertation is on two problems in the area of point pat-