Structural matching by discrete relaxation

Wilson, Richard C.; Hancock, Edwin R.

doi:10.1109/34.601251

Cited by 267 publications

(183 citation statements)

References 37 publications

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“…We also compare the results with four alternative algorithms. These are the original discrete relaxation method of Wilson and Hancock [8] which is applied to overlapping supercliques, the quadratic assignment method of Gold and Rangarajan [20], the non-quadratic graduated assignment method of Finch et al [21], and, the singular value decomposition method of Luo and Hancock [7]. In Fig.…”

Section: Sensitivity Studymentioning

confidence: 99%

“…These two methods fail when the graphs being matched contain different numbers of nodes. However, this problem can be overcome by using the apparatus of the EM algorithm [7,8]. More recently, Shokoufandeh et al [9] have shown how graphs can be retrieved efficiently using an indexing mechanism that maps the topological structure of shock-trees into a low-dimensional vector space.…”

Section: Introductionmentioning

confidence: 99%

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Graph matching and clustering using spectral partitions

Qiu

Hancock

2006

Pattern Recognition

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Although inexact graph-matching is a problem of potentially exponential complexity, the problem may be simplified by decomposing the graphs to be matched into smaller subgraphs. If this is done, then the process may cast into a hierarchical framework and hence rendered suitable for parallel computation. In this paper we describe a spectral method which can be used to partition graphs into nonoverlapping subgraphs. In particular, we demonstrate how the Fiedler-vector of the Laplacian matrix can be used to decompose graphs into non-overlapping neighbourhoods that can be used for the purposes of both matching and clustering.

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Section: Sensitivity Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Graph matching and clustering using spectral partitions

Qiu

Hancock

2006

Pattern Recognition

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“…with good color continuity, which can be obtained from either the color segmentation algorithm described above, or any other method such as the one described in [3]. This set of regions is further divided in two subsets.…”

Section: Fusion Of Colour-based Segmentation and Depth From Stereomentioning

confidence: 99%

“…Nevertheless, new developments in approximation algorithms for graph matching have allowed the reduction of this time complexity for sub-optimal solutions (see for example Refs. [3,4]). …”

Section: Introductionmentioning

confidence: 99%

Graph-based representations and techniques for image processing and image analysis

Sanfeliu

Alquézar

Andrade

et al. 2002

Pattern Recognition

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In this paper we will discuss the use of some graph-based representations and techniques for image processing and analysis. Instead of making an extensive review of the graph techniques in this field, we will explain how we are using these techniques in an active vision system for an autonomous mobile robot developed in the Institut de Robòtica i Informàtica Industrial within the project "Active Vision System with Automatic Learning Capacity for Industrial Applications (CICYT TAP98-0473)". Specifically we will discuss the use of graph-based representations and techniques for image segmentation, image perceptual grouping and object recognition. We first present a generalisation of a graph partitioning greedy algorithm for colour image segmentation. Next we describe a novel fusion of colour-based segmentation and depth from stereo that yields a graph representing every object in the scene. Finally we describe a new representation of a set of attributed graphs (AGs), denominated Function Described Graphs (FDGs), a distance measure for matching AGs with FDGs and some applications for robot vision.

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“…In relaxation techniques [24] [25] [10], all locally consistent assignments are made first (short horizon distance). Then the horizon is effectively increased via a constraint propagation that occurs in an iterative fashion.…”

Section: Approximate Techniquesmentioning

confidence: 99%

An algorithm using length-r paths to approximate subgraph isomorphism

DePiero

Krout

2003

Pattern Recognition Letters

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The 'LeRP' algorithm approximates subgraph isomorphism for attributed graphs based on counts of Length-R Paths. The algorithm provides a good approximation to the maximal isomorphic subgraph. The basic approach of the LeRP algorithm differs fundamentally from other methods. When comparing structural similarity LeRP uses a neighborhood of nodes that varies in size dynamically. This approach provides sufficient evidence of similarity to permit LeRP to form a node-to-node mapping and can be computed with polynomial effort in the worst-case. Results from over 32,000 simulated cases are reported. We demonstrate that LeRP does not need a high dynamic range of node and edge coloring to perform well. For example, LeRP can input 50-node and 100-node graphs that contain a common 50-node subgraph, and then compute a matching subgraph having 49.74 +/-0.46 nodes (mean +/-one standard deviation). This takes from 0.4 to 0.5 seconds. In this example, 100 trials were evaluated and graphs had discrete coloring for nodes and edges with a dynamic range of four. Test conditions are varied and include strongly regular graphs as well as Model A.

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Structural matching by discrete relaxation

Cited by 267 publications

References 37 publications

Graph matching and clustering using spectral partitions

Graph matching and clustering using spectral partitions

Graph-based representations and techniques for image processing and image analysis

An algorithm using length-r paths to approximate subgraph isomorphism

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