An algorithm using length-r paths to approximate subgraph isomorphism

DePiero, Fred W.; Krout, David W.

doi:10.1016/s0167-8655(02)00186-1

Cited by 12 publications

(12 citation statements)

References 36 publications

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“…In that figure, node 6 cannot be matched to node f because only one of the arcs (6, 4) and (6,5) in the pattern can be matched in the target. The right side of the figure presents two solutions of the matching problem.…”

Section: Approximate Graph Matching and Other Matching Problemsmentioning

confidence: 99%

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Combining Two Structured Domains for Modeling Various Graph Matching Problems

Deville

Dooms

Zampelli

2008

Lecture Notes in Computer Science

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Abstract. Graph pattern matching is a central application in many fields. In various areas, the structure of the pattern can only be approximated and exact matching is then too accurate. We focus here on approximations declared by the user within the pattern (optional nodes and forbidden arcs), covering graph/subgraph mono/isomorphism problems. In this paper, we show how the integration of two domains of computation over countable structures, graphs and maps, can be used for modeling and solving various graph matching problems from the simple graph isomorphism to approximate graph matching. To achieve this, we extend map variables allowing the domain and range to be non-fixed and constrained. We describe how such extended maps are designed then realized on top of finite domain and finite set variables with specific propagators. We show how a single monomorphism constraint is sufficient to model and solve those multiples graph matching problems. Furthermore, our experimental results show that our CP approach is competitive with a state of the art algorithm for subgraph isomorphism.

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Section: Approximate Graph Matching and Other Matching Problemsmentioning

confidence: 99%

“…In a first approach, the matching algorithm may allow part of the pattern to mismatch the target graph (e.g. [4][5][6]). The matching problem can then be stated in a probabilistic framework (see, e.g.…”

Section: Introductionmentioning

confidence: 99%

Combining Two Structured Domains for Modeling Various Graph Matching Problems

Deville

Dooms

Zampelli

2008

Lecture Notes in Computer Science

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“…The LeRP algorithm [4] [11] approximates subgraph isomorphisms by comparing the number of length-r paths in each graph. These are found via A R , where A is the adjacency matrix [7].…”

Section: Approach -Finding Subgraph Isomorphismsmentioning

confidence: 99%

“…The parameter R is actually a weak function of F (see [4]) but was set to a constant in all tests reported herein. If the number of features increased significantly, then additional subsampling would be appropriate to maintain reasonable processing times.…”

Section: Approach -Finding Subgraph Isomorphismsmentioning

confidence: 99%

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Fast landmark-based registration via deterministic and efficient processing, some preliminary results

DePiero

Proceedings. First International Symposium on 3D Data Processing Visualization and Transmission

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AbstractΩ Project sponsored, in part, by the Department of the Navy, Office of Naval Research. Approach Based on Subgraph MatchingThe goal of this research is to pursue a technique that can perform view registration at rates approaching 10 Hz, without any user input for initial estimates. This performance goal is set to match the data rates of range cameras. It is also desired to have a method that computes the rigid transformation (translation plus rotation) in the presence of possible scale changes. Registration at these rates could permit sensor motion to be tracked in realtime. This would permit unconstrained movement of a sensor across a large scene.To achieve fast and deterministic processing, iterative, or random [6] approaches were avoided. Established methods do not typically separate the steps of determining corresponding points and determining the transform. This limits compute speed. In the new approach these steps have been kept separate, and are implemented in a non-iterative fashion. This is an important difference for the new approach. Another difference is that correspondence between the data sets is determined only for select feature points. This improves processing speed, but it does limit accuracy.Correspondence between the data sets is determined via graph matching. Graphs are formed using salient features in each range image. Graph matching is accomplished using the LeRP Algorithm [2] [4]. LeRP approximates a subgraph isomorphism via a deterministic procedure, based on the comparison of length-r paths. The LeRP algorithm yields a set of corresponding locations in the two input range images, from which the absolute orientation may be found via closed-form solution [9].A typical graph appears in Figure 1. The white segments designate an accurately matched subgraph for the scene. Approach -Salient FeaturesGraphs describe the salient features in each range image. For rapid detection, local, well isolated, peaks in the range data were used to form the image features. These are desirable because they are likely to remain in view with small shifts in scene.The significant percentage of black segments shown in Figure 1 demonstrates a lack of stability in feature detection. Stable and invariant feature detection -via fast, efficient, deterministic means -remains the greatest challenge in this new approach. While the lack of stability shown in the figure is undesirable, it was deemed an appropriate tradeoff in terms of processing speed. Other techniques employ more robust local features [10] but require more processing time. The approach taken here was to rely on the LeRP matching algorithm to determine appropriate correspondences, despite noisy features.Some reported techniques use invariant features that involve curvature, moments, or spherical harmonics [18]. These types of features react to jump discontinuities that may occur at a limb [19]. Such feature points were avoided in this new approach. Consider the occurrence of a limb where the line-of-sight of a sensor becomes tangent to a hillside. ...

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Multiplex graph matching matched filters

et al. 2022

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We consider the problem of detecting a noisy induced multiplex template network in a larger multiplex background network. Our approach, which extends the graph matching matched filter framework of Sussman et al. (IEEE Trans Pattern Anal Mach Intell 42(11):2887–2900, 2019) to the multiplex setting, utilizes a multiplex analogue of the classical graph matching problem to use the template as a matched filter for efficiently searching the background for candidate template matches. The effectiveness of our approach is demonstrated both theoretically and empirically, with particular attention paid to the potential benefits of considering multiple channels in the multiplex framework.

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An algorithm using length-r paths to approximate subgraph isomorphism

Cited by 12 publications

References 36 publications

Combining Two Structured Domains for Modeling Various Graph Matching Problems

Combining Two Structured Domains for Modeling Various Graph Matching Problems

Fast landmark-based registration via deterministic and efficient processing, some preliminary results

Multiplex graph matching matched filters

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