An Application of Point Pattern Matching in Astronautics

Weber, Gerald; Knipping, Lars; Alt, Helmut

doi:10.1006/jsco.1994.1022

Cited by 19 publications

(8 citation statements)

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“…Although the isometric assumption clearly does not hold for a wide baseline, we note that the same pairwise distances were used as features in every algorithm, so we expect this to be a fair comparison. 8 For the experiment with patterns of the same size (30 Â 30), JT has similar performance to GA and PRL when the baseline is increased. For the narrow baseline case, JT slightly outperforms the competing methods.…”

Section: Image Datamentioning

confidence: 93%

“…P OINT pattern matching (or point set matching) is a basic problem in pattern recognition that is fundamental to computer vision (stereo correspondence, image registration and model-based object recognition [3], [4], [5], [6]), astronautics [7], [8], computational chemistry [9], [10] and computational biology [11], [12]. Here, we consider the (possibly noisy) rigid body case, when one pattern differs from a subset of the other by an isometry but position jitter may be present.…”

Section: ç 1 Introductionmentioning

confidence: 99%

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Faster graphical models for point-pattern matching

Caetano

McAuley

2009

Spatial Vis

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It has been shown that isometric matching problems can be solved exactly in polynomial time, by means of a Junction Tree with small maximal clique size. Recently, an iterative algorithm was presented which converges to the same solution an order of magnitude faster. Here, we build on both of these ideas to produce an algorithm with the same asymptotic running time as the iterative solution, but which requires only a single iteration of belief propagation. Thus our algorithm is much faster in practice, while maintaining similar error rates.

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Section: Image Datamentioning

confidence: 93%

Section: ç 1 Introductionmentioning

confidence: 99%

Faster graphical models for point-pattern matching

Caetano

McAuley

2009

Spatial Vis

View full text Add to dashboard Cite

show abstract

“…8 For the experiment with patterns of the same size (30 Â 30), JT has similar performance to GA and PRL when the baseline is increased. For the narrow baseline case, JT slightly outperforms the competing methods.…”

Section: Image Datamentioning

confidence: 93%

“…ðfÞ are nonnegative because DðÁ; ÁÞ is nonnegative (8) and (14). Our purpose is to prove the converse, i.e., that U G kt d ðfÞ ¼ 0 ) U T ðfÞ ¼ 0.…”

Section: Appendix Amentioning

confidence: 99%

Graphical Models and Point Pattern Matching

Caetano

Caelli

Schuurmans

et al. 2006

IEEE Trans. Pattern Anal. Mach. Intell.

118

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Abstract-This paper describes a novel solution to the rigid point pattern matching problem in Euclidean spaces of any dimension. Although we assume rigid motion, jitter is allowed. We present a noniterative, polynomial time algorithm that is guaranteed to find an optimal solution for the noiseless case. First, we model point pattern matching as a weighted graph matching problem, where weights correspond to Euclidean distances between nodes. We then formulate graph matching as a problem of finding a maximum probability configuration in a graphical model. By using graph rigidity arguments, we prove that a sparse graphical model yields equivalent results to the fully connected model in the noiseless case. This allows us to obtain an algorithm that runs in polynomial time and is provably optimal for exact matching between noiseless point sets. For inexact matching, we can still apply the same algorithm to find approximately optimal solutions. Experimental results obtained by our approach show improvements in accuracy over current methods, particularly when matching patterns of different sizes.

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“…More specifically, the Point Set Matching (PSM) problem arises in fields such as astronautics [11], computational biology [1] and computational chemistry [6].…”

Section: Introductionmentioning

confidence: 99%

Efficient Colored Point Set Matching Under Noise

Diéz

Sellarès

Lecture Notes in Computer Science

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Abstract. Let A and B be two colored point sets in R 2 , with |A| ≤ |B|. We propose a process for determining matches, in terms of the bottleneck distance, between A and subsets of B under color preserving rigid motion, assuming that the position of all colored points in both sets contains a certain amount of "noise". The process consists of two main stages: a lossless filtering algorithm and a matching algorithm. The first algorithm determines a number of candidate zones which are regions that contain a subset S of B such that A may match one or more subsets B of S. We use a compressed quadtree to have easy access to the subsets of B related to candidate zones and store geometric information that is used by the lossless filtering algorithm in each quadtree node. The second algorithm solves the colored point set matching problem: we generate all, up to a certain equivalence, possible motions that bring A close to some subset B of every S and seek for a matching between sets A and B . To detect these possible matchings we use a bipartite matching algorithm that uses Skip Quadtrees for neighborhood queries. We have implemented the proposed algorithms and report results that show the efficiency of our approach.

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An Application of Point Pattern Matching in Astronautics

Cited by 19 publications

References 1 publication

Faster graphical models for point-pattern matching

Faster graphical models for point-pattern matching

Graphical Models and Point Pattern Matching

Efficient Colored Point Set Matching Under Noise

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