Geometric pattern matching under Euclidean motion

Chew, L. Paul; Goodrich, Michael T.; Huttenlocher, Daniel P.; Kedem, Klara; Kleinberg, Jon; Kravets, Dina

doi:10.1016/0925-7721(95)00047-x

Cited by 112 publications

(81 citation statements)

References 11 publications

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“…Most of the formulations of the point matching problem in computational geometry are not suitable for noisy, cluttered images either because they require exact matches [12], they require 1-1 matches [13,14] or they assume that every point in one set has a close match in the other set in terms of the (standard) Hausdorff distance [15][16][17][18]. Even under these relatively restrictive assumptions, the computational complexity can be quite high.…”

Section: Prior Workmentioning

confidence: 99%

“…Even under these relatively restrictive assumptions, the computational complexity can be quite high. For example, the best-known algorithm for determining the translation and rotation that minimize the Hausdorff distance between sets of sizes m and n runs in O(m n log mn) time [15,16]. This complexity may be unacceptably high for applications involving hundreds or thousands of feature points.…”

Section: Prior Workmentioning

confidence: 99%

See 1 more Smart Citation

Efficient algorithms for robust feature matching

Mount

Netanyahu

Moigne

1999

Pattern Recognition

135

103

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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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Section: Prior Workmentioning

confidence: 99%

Section: Prior Workmentioning

confidence: 99%

Efficient algorithms for robust feature matching

Mount

Netanyahu

Moigne

1999

Pattern Recognition

135

103

View full text Add to dashboard Cite

show abstract

“…Our Results In Section 2 we present an algorithm that solves the Coverage problem between sets of axis-parallel segments in time O(n 3 log 2 n) and the Coverage problem between horizontal segments in time O(n 2 log n) Note that the known algorithms for matching arbitrary sets of line segments are much slower. For example, the best known algorithm for finding a translation that minimizes the Hausdorff Distance between two sets of n segments in the plane runs in time O(n 4 log 2 n) [2,9]. We also show that the that the combinatorial complexity of the Hausdorff matching between segments is Ω(n 4 ), even if all segments are horizontal.…”

Section: Mapping and Orthogonalitymentioning

confidence: 86%

Pattern Matching for Sets of Segments

2004

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In this paper we present algorithms for a number of problems in geometric pattern matching where the input consist of a collections of segments in the plane. Our work consists of two main parts. In the first, we address problems and measures that relate to collections of orthogonal line segments in the plane. Such collections arise naturally from problems in mapping buildings and robot exploration.We propose a new measure of segment similarity called a coverage measure, and present efficient algorithms for maximising this measure between sets of axis-parallel segments under translations. Our algorithms run in time O(n 3 polylog n) in the general case, and run in time O(n 2 polylog n) for the case when all segments are horizontal. In addition, we show that when restricted to translations that are only vertical, the Hausdorff distance between two sets of horizontal segments can be computed in time roughly O(n 3/2 polylog n). These algorithms form significant improvements over the general algorithm of Chew et al. that takes time O(n 4 log 2 n).In the second part of this paper we address the problem of matching polygonal chains. We study the well known Fréchet distance , and present the first algorithm for computing the Fréchet distance under general translations. Our methods also yield algorithms for computing a generalization of the Fréchet distance, and we also present a simple approximation algorithm for the Fréchet distance that runs in time O(n 2 polylog n).

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“…Different computations of the minimum Hausdorff distance have been studied in great depth in the computational geometry literature [12]. We do not seek to minimize δ but rather adopt an acceptable threshold for δ.…”

Section: Identifying Intersection Points From Street Mapsmentioning

confidence: 99%

“…Since the geometric point set matching in two or higher dimensions is a well-studied family of problems with application to different areas such as computer vision, biology, and astronomy [12], [23], we do not intend to invent a novel algorithm to resolve the general point pattern matching problem. Instead, we focus on the datasets we are conflating and particularly design efficient and accurate matching algorithms to discover geospatial point patterns.…”

Section: Enhanced Point Pattern Matching Algorithm: Geoppmmentioning

confidence: 99%

Automatically and Accurately Conflating Raster Maps with Orthoimagery

Chen¹,

Knoblock

Shahabi

2007

Geoinformatica

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Recent growth of geospatial information online has made it possible to access various maps and orthoimagery. Conflating these maps and imagery can create images that combine the visual appeal of imagery with the attribution information from maps. The existing systems require human intervention to conflate maps with imagery. We present a novel approach that utilizes vector datasets as "glue" to automatically conflate street maps with imagery. First, our approach extracts road intersections from imagery and maps as control points. Then, it aligns the two point sets by computing the matched point pattern. Finally, it aligns maps with imagery based on the matched pattern. The experiments show that our approach can conflate various maps with imagery, such that in our experiments on TIGER-maps covering part of St. Louis county, MO, 85.2% of the conflated map roads are within 10.8 m from the actual roads compared to 51.7% for the original and georeferenced TIGER-map roads.

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Geometric pattern matching under Euclidean motion

Cited by 112 publications

References 11 publications

Efficient algorithms for robust feature matching

Efficient algorithms for robust feature matching

Pattern Matching for Sets of Segments

Automatically and Accurately Conflating Raster Maps with Orthoimagery

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