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Preface of Special Issue on “Graph-based Processing for Pattern Recognition”
Pattern Recognition ∎ (∎∎∎∎) ∎∎∎–∎∎∎
Contents lists available at ScienceDirect
Pattern Recognition journal homepage: www.elsevier.com/locate/pr
Editorial
Preface of Special Issue on “Graph-based Processing for Pattern Recognition”
In the recent years the interest on pattern recognition within a graph theory framework has been growing and many innovative contributions have been done. New structural and graph models, as well as new structural criteria, like belief-propagation, specific graphs under the constellation approach, graph kernels, graph cuts, dominant set, and graph pyramids have been used to solve a plethora of pattern recognition, image analysis, and computer vision problems nowadays. Furthermore, the application of graphs to pattern recognition problems in other fields like computational topology and bioinformatics is getting growing attention in the community. In the light of this and with the intention of presenting the most recent scientific works it appears evident to present a collection of the works in this special issue. Topics of interest in this research area include the following: graph matching, graph based image segmentation, irregular (graph) pyramids, graph representation of shapes, graph learning and clustering, kernel methods for graphs, graph-cut methods, and graphs in computational topology and bioinformatics. This special issue gathers the best contributions from the 9th IAPR-TC15 Workshop on Graph-based Representation for Pattern Recognition (GbR 2013), held in Vienna, May 15–17, 2013. For more than 15 years GbR provides a forum for researchers from the fields of Pattern Recognition, Image Analysis, and Computer Vision who build their works on the basis of Graph Theory. The Technical Committee 15 (TC15) of the International Association for Pattern Recognition (IAPR) was created in 1996 and thereafter encourages elaboration of graph-based research works, stays as integral partner in organizing the biennial GbR workshops, sponsors related special sessions at conferences, and promotes special issues in journals. The edition GbR2013 was not an exception. The scope of the papers varies from theoretical contributions to applications, from discovering new properties of a single graph (graph edit distance, MaxCut, graph characteristics derived from Schrödinger equation) to developing algorithms for sets of graphs, maximum subgraph problem, and graph matching. A great interest was shown to the problems of graph kernels and topology. Overall, this special issue is a subselection of the 24 papers accepted for the GbR workshop. Their extended version went through the standard reviewing process of the Pattern Recognition Journal. The papers of this special issue can be partitioned into following rough categories:
overview [2] and novel insights [1] into Graph matching; different usages of graph-edit distance [5,8]; kernel methods [7,4]; http://dx.doi.org/10.1016/j.patcog.2014.08.018 0031-3203/& 2014 Elsevier Ltd. All rights reserved.
graph centrality [6] and generalized median surface in 3D [3]; and topological issues with the persistent bar code [9]. The author of [2], Mario Vento, was among the founders of TC15 some 16 years ago. He was one of the two IAPR distinguished speakers at the GbR2013. His paper interprets the last 40 years of research on graphs by considering how, why and when they have been used in Pattern Recognition. This paper divides the history of graphs in Pattern Recognition into three main periods (pure, impure and extreme), although these periods are not separable through clear boundaries. Nevertheless, the author points out trends and identifies the attempt to bridge the gap between structural and statistical PR as the major driving force behind changes across these three periods. This paper is useful to readers who are interested in understanding research trends on graphs in PR. The paper entitled “On the complexity of submap isomorphism and maximum common submap problems” [1] is a theoretical work and studies the complexity issues of submap isomorphism and maximum common submap problem. In particular, it is proved that these two problems are NP complete and NP hard. The paper [5] entitled “Efficient subgraph matching using topological node feature constraints” presents techniques for practically reducing the computational cost of subgraph isomorphism detection. This is done by the creation, strengthening, and effective use of topological node features. Fischer et al. present in their paper [8] a quadratic time approximation of graph edit distance based on Hausdorff distance. Graph edit distance allows us to do error-tolerant graph matching on all types of graphs. Unfortunately, in practice it can only be applied on small graphs due to its exponential time complexity. The proposed Hausdorff edit distance (HED) overcomes these time complexity issues with only a minor loss in accuracy. Fischer et al. show the promising potential of HED in experimental evaluations on various classification and recognition problems. The paper [7] presents a graph kernel which uses the quantum Jensen–Shannon divergence to measure the similarity of graph density matrices. Graph kernels form a class of methods for comparing structured data, which appear in many different applied fields. Analysis of structured data is thus a difficult and important task. The authors use the quantum Jensen–Shannon divergence as a means of measuring the information theoretic dissimilarity of graphs and thus develop a novel graph kernel. Gaüzère et al. propose in the paper [4] several extensions of the treelet kernel for chemoinformatics problems. The treelet kernel tries to take into account chemically relevant characteristics like pattern weighting, contribution of non-isomorphic sub-structures, stereoisomerism and cyclic information. Using different chemoinformatics datasets, the authors show that using the proposed treelet kernel the prediction results get better.
2
Editorial / Pattern Recognition ∎ (∎∎∎∎) ∎∎∎–∎∎∎
The paper entitled “Graph-based point drift: Graph centrality on the registration of point-sets” [6] introduces a variant of the point-set registration method Coherent Point Drift by integrating a variety of graph centrality measures popular from social network analysis. They are demonstrated to be a good source of prior information for the registration problem. Wu et al. [3] formulate the generalized median surface problem and use a 3D graph search algorithm to provide an exact solution. The work could be thought of as a generalization of the simpler case of computing the 2D median contour by dynamic programming to 3D median surface. Extending a dynamic programming techniques to 3D is not simple, thus the authors use a graph search to come up with a solution. The authors show its practical usage in parameter space exploration without ground truth, which is a mean to deal with a difficult problem of parameter selection in image segmentation. They show the applicability of their work in artery boundary detection in ultrasound imaging. The paper [9] addresses a very interesting topic: defining an “efficient” filtration. A filtration gives the elements of a simplicial complex (e.g. the triangles, edges and vertices of a triangular network) an order, and there are many possible filtrations for a given simplicial complex. Persistence concepts have been extensively studied recently, but any application directly depends on a filtration, and the choice of this filtration is of crucial importance for the application. This work is motivated by the observation that two different filtrations of the same shape give different information about the shape itself. The authors first introduce a notion of entropy of a filtration and next address the problem of determining a filtration of a simplicial complex satisfying the following conditions: (1) it must be compatible with a given filtration; (2) no two simplices may enter the filtration at the same time; (3) it must have a small entropy. In the name of the GbR2013 organizers we would like to thank the reviewers of this special issue for their competent reviews; the authors of the submitted papers for their works and the abidance
by all deadlines. We also thank the IAPR for sponsoring our workshop and the IAPR distinguished speakers for their excellent contributions. Finally, our thanks go to the Pattern Recognition Journal for giving us the opportunity of guest-editing and the smooth preparation of this special issue. Vienna, August 4, 2014 Walter G. Kropatsch, Nicole M. Artner, Yll Haxhimusa, Xiaoyi Jiang References [1] Christine Solnon, Guillaume Damiand, Colin de la Higuera, Jean-Christophe Janodet, On the complexity of submap isomorphism and maximum common submap problems, Pattern Recognit. (2014), http://dx.doi.org/10.1016/j.patcog.2014.05.019, this issue. [2] Mario Vento, A long trip in the charming world of graphs for Pattern Recognition, Pattern Recognit. (2014), http://dx.doi.org/10.1016/j.patcog.2014. 01.002, this issue. [3] Zhengwang Wu, Xiaoyi Jiang, Nanning Zheng, Yuehu Liu, Dachuan Cheng, Exact solution to median surface problem using 3D graph search and application to parameter space exploration, Pattern Recognit. (2014), http://dx.doi.org/10. 1016/j.patcog.2014.07.019, this issue. [4] Benoit Gaüzère, Pierre-Anthony Grenier, Luc Brun, Didier Villemin, Treelet kernel incorporating cyclic, stereo and inter pattern information in Chemoinformatics, Pattern Recognit. (2014), http://dx.doi.org/10.1016/j.patcog.2014.07. 029, this issue. [5] Nicholas Dahm, Horst Bunke, Terry Caelli, Yongsheng Gao, Efficient subgraph matching using topological node feature constraints, Pattern Recognit. (2014), http://dx.doi.org/10.1016/j.patcog.2014.05.018, this issue. [6] Samuel de Sousa, Walter G. Kropatsch, Graph-based point drift: graph centrality on the registration of point-sets, Pattern Recognit. (2014), http://dx.doi. org/10.1016/j.patcog.2014.06.011, this issue. [7] Lu Bai, Andrea Torsello, Edwin R. Hancock, A quantum Jensen–Shannon graph kernel for unattributed graphs, Pattern Recognit. (2014), http://dx.doi.org/10. 1016/j.patcog.2014.03.028, this issue. [8] Andreas Fischer, Ching Y. Suen, Volkmar Frinken, Kaspar Riesen, Horst Bunke, Approximation of graph edit distance based on Hausdorff matching, Pattern Recognit. (2014), http://dx.doi.org/10.1016/j.patcog.2014.07.015, this issue. [9] Harish Chintakunta, Thanos Gentimis, Rocio Gonzalez-Diaz, Maria-Jose Jimenez, Hamid Krim, An entropy-based persistence barcode, Pattern Recognit. (2014), http://dx.doi.org/10.1016/j.patcog.2014.06.023, this issue.
Contents lists available at ScienceDirect
Pattern Recognition journal homepage: www.elsevier.com/locate/pr
Editorial
Preface of Special Issue on “Graph-based Processing for Pattern Recognition”
In the recent years the interest on pattern recognition within a graph theory framework has been growing and many innovative contributions have been done. New structural and graph models, as well as new structural criteria, like belief-propagation, specific graphs under the constellation approach, graph kernels, graph cuts, dominant set, and graph pyramids have been used to solve a plethora of pattern recognition, image analysis, and computer vision problems nowadays. Furthermore, the application of graphs to pattern recognition problems in other fields like computational topology and bioinformatics is getting growing attention in the community. In the light of this and with the intention of presenting the most recent scientific works it appears evident to present a collection of the works in this special issue. Topics of interest in this research area include the following: graph matching, graph based image segmentation, irregular (graph) pyramids, graph representation of shapes, graph learning and clustering, kernel methods for graphs, graph-cut methods, and graphs in computational topology and bioinformatics. This special issue gathers the best contributions from the 9th IAPR-TC15 Workshop on Graph-based Representation for Pattern Recognition (GbR 2013), held in Vienna, May 15–17, 2013. For more than 15 years GbR provides a forum for researchers from the fields of Pattern Recognition, Image Analysis, and Computer Vision who build their works on the basis of Graph Theory. The Technical Committee 15 (TC15) of the International Association for Pattern Recognition (IAPR) was created in 1996 and thereafter encourages elaboration of graph-based research works, stays as integral partner in organizing the biennial GbR workshops, sponsors related special sessions at conferences, and promotes special issues in journals. The edition GbR2013 was not an exception. The scope of the papers varies from theoretical contributions to applications, from discovering new properties of a single graph (graph edit distance, MaxCut, graph characteristics derived from Schrödinger equation) to developing algorithms for sets of graphs, maximum subgraph problem, and graph matching. A great interest was shown to the problems of graph kernels and topology. Overall, this special issue is a subselection of the 24 papers accepted for the GbR workshop. Their extended version went through the standard reviewing process of the Pattern Recognition Journal. The papers of this special issue can be partitioned into following rough categories:
overview [2] and novel insights [1] into Graph matching; different usages of graph-edit distance [5,8]; kernel methods [7,4]; http://dx.doi.org/10.1016/j.patcog.2014.08.018 0031-3203/& 2014 Elsevier Ltd. All rights reserved.
graph centrality [6] and generalized median surface in 3D [3]; and topological issues with the persistent bar code [9]. The author of [2], Mario Vento, was among the founders of TC15 some 16 years ago. He was one of the two IAPR distinguished speakers at the GbR2013. His paper interprets the last 40 years of research on graphs by considering how, why and when they have been used in Pattern Recognition. This paper divides the history of graphs in Pattern Recognition into three main periods (pure, impure and extreme), although these periods are not separable through clear boundaries. Nevertheless, the author points out trends and identifies the attempt to bridge the gap between structural and statistical PR as the major driving force behind changes across these three periods. This paper is useful to readers who are interested in understanding research trends on graphs in PR. The paper entitled “On the complexity of submap isomorphism and maximum common submap problems” [1] is a theoretical work and studies the complexity issues of submap isomorphism and maximum common submap problem. In particular, it is proved that these two problems are NP complete and NP hard. The paper [5] entitled “Efficient subgraph matching using topological node feature constraints” presents techniques for practically reducing the computational cost of subgraph isomorphism detection. This is done by the creation, strengthening, and effective use of topological node features. Fischer et al. present in their paper [8] a quadratic time approximation of graph edit distance based on Hausdorff distance. Graph edit distance allows us to do error-tolerant graph matching on all types of graphs. Unfortunately, in practice it can only be applied on small graphs due to its exponential time complexity. The proposed Hausdorff edit distance (HED) overcomes these time complexity issues with only a minor loss in accuracy. Fischer et al. show the promising potential of HED in experimental evaluations on various classification and recognition problems. The paper [7] presents a graph kernel which uses the quantum Jensen–Shannon divergence to measure the similarity of graph density matrices. Graph kernels form a class of methods for comparing structured data, which appear in many different applied fields. Analysis of structured data is thus a difficult and important task. The authors use the quantum Jensen–Shannon divergence as a means of measuring the information theoretic dissimilarity of graphs and thus develop a novel graph kernel. Gaüzère et al. propose in the paper [4] several extensions of the treelet kernel for chemoinformatics problems. The treelet kernel tries to take into account chemically relevant characteristics like pattern weighting, contribution of non-isomorphic sub-structures, stereoisomerism and cyclic information. Using different chemoinformatics datasets, the authors show that using the proposed treelet kernel the prediction results get better.
2
Editorial / Pattern Recognition ∎ (∎∎∎∎) ∎∎∎–∎∎∎
The paper entitled “Graph-based point drift: Graph centrality on the registration of point-sets” [6] introduces a variant of the point-set registration method Coherent Point Drift by integrating a variety of graph centrality measures popular from social network analysis. They are demonstrated to be a good source of prior information for the registration problem. Wu et al. [3] formulate the generalized median surface problem and use a 3D graph search algorithm to provide an exact solution. The work could be thought of as a generalization of the simpler case of computing the 2D median contour by dynamic programming to 3D median surface. Extending a dynamic programming techniques to 3D is not simple, thus the authors use a graph search to come up with a solution. The authors show its practical usage in parameter space exploration without ground truth, which is a mean to deal with a difficult problem of parameter selection in image segmentation. They show the applicability of their work in artery boundary detection in ultrasound imaging. The paper [9] addresses a very interesting topic: defining an “efficient” filtration. A filtration gives the elements of a simplicial complex (e.g. the triangles, edges and vertices of a triangular network) an order, and there are many possible filtrations for a given simplicial complex. Persistence concepts have been extensively studied recently, but any application directly depends on a filtration, and the choice of this filtration is of crucial importance for the application. This work is motivated by the observation that two different filtrations of the same shape give different information about the shape itself. The authors first introduce a notion of entropy of a filtration and next address the problem of determining a filtration of a simplicial complex satisfying the following conditions: (1) it must be compatible with a given filtration; (2) no two simplices may enter the filtration at the same time; (3) it must have a small entropy. In the name of the GbR2013 organizers we would like to thank the reviewers of this special issue for their competent reviews; the authors of the submitted papers for their works and the abidance
by all deadlines. We also thank the IAPR for sponsoring our workshop and the IAPR distinguished speakers for their excellent contributions. Finally, our thanks go to the Pattern Recognition Journal for giving us the opportunity of guest-editing and the smooth preparation of this special issue. Vienna, August 4, 2014 Walter G. Kropatsch, Nicole M. Artner, Yll Haxhimusa, Xiaoyi Jiang References [1] Christine Solnon, Guillaume Damiand, Colin de la Higuera, Jean-Christophe Janodet, On the complexity of submap isomorphism and maximum common submap problems, Pattern Recognit. (2014), http://dx.doi.org/10.1016/j.patcog.2014.05.019, this issue. [2] Mario Vento, A long trip in the charming world of graphs for Pattern Recognition, Pattern Recognit. (2014), http://dx.doi.org/10.1016/j.patcog.2014. 01.002, this issue. [3] Zhengwang Wu, Xiaoyi Jiang, Nanning Zheng, Yuehu Liu, Dachuan Cheng, Exact solution to median surface problem using 3D graph search and application to parameter space exploration, Pattern Recognit. (2014), http://dx.doi.org/10. 1016/j.patcog.2014.07.019, this issue. [4] Benoit Gaüzère, Pierre-Anthony Grenier, Luc Brun, Didier Villemin, Treelet kernel incorporating cyclic, stereo and inter pattern information in Chemoinformatics, Pattern Recognit. (2014), http://dx.doi.org/10.1016/j.patcog.2014.07. 029, this issue. [5] Nicholas Dahm, Horst Bunke, Terry Caelli, Yongsheng Gao, Efficient subgraph matching using topological node feature constraints, Pattern Recognit. (2014), http://dx.doi.org/10.1016/j.patcog.2014.05.018, this issue. [6] Samuel de Sousa, Walter G. Kropatsch, Graph-based point drift: graph centrality on the registration of point-sets, Pattern Recognit. (2014), http://dx.doi. org/10.1016/j.patcog.2014.06.011, this issue. [7] Lu Bai, Andrea Torsello, Edwin R. Hancock, A quantum Jensen–Shannon graph kernel for unattributed graphs, Pattern Recognit. (2014), http://dx.doi.org/10. 1016/j.patcog.2014.03.028, this issue. [8] Andreas Fischer, Ching Y. Suen, Volkmar Frinken, Kaspar Riesen, Horst Bunke, Approximation of graph edit distance based on Hausdorff matching, Pattern Recognit. (2014), http://dx.doi.org/10.1016/j.patcog.2014.07.015, this issue. [9] Harish Chintakunta, Thanos Gentimis, Rocio Gonzalez-Diaz, Maria-Jose Jimenez, Hamid Krim, An entropy-based persistence barcode, Pattern Recognit. (2014), http://dx.doi.org/10.1016/j.patcog.2014.06.023, this issue.