13.3 Graph Matching and Relaxation

13.3.1 Graph Matching Theoretical Issues

Corneil, D.G., and Gotlieb, C.C.,
An Efficient Algorithm for Graph Isomorphism,
JACM(17), No. 1, January 1970, pp. 51-64. Graph Isomorphism. This technique for isomorphism derived two graphs from the input graphs. The original graphs are isomorphic only if the derived graphs are identical. The algorithm, complexity O(N^n ) is more efficient than the early renumbering techniques that were O(N!), because the power is usually no more than 5 (for some special cases, usually it is lower). This technique applies to non-directed graphs and was not extended to bi-directional graphs, except as a part of an O(N!) algorithm. BibRef 7001

Corneil, D.G., and Kirkpatrick, D.G.,
A Theoretical Analysis of Various Heuristics for the Graph Isomorphism Problem,
SIAM_JC(9), 1980, pp. 281-297. BibRef 8000

Shaw, A.C.,
Parsing of Graph-Representable Pictures,
JACM(17), No. 3, July 1970, pp. 453-481. BibRef 7007

Shaw, A.C.[Alan C.],
A Formal Picture Description Scheme as a Basis for Picture Processing Systems,
InfoControl(14), No. 1, January 1969, pp. 9-52. BibRef 6901

Mallgren, W.R., Shaw, A.C.,
Graphical transformations and hierarchic picture structures,
CGIP(8), No. 2, October 1978, pp. 237-258.
WWW Version. 0501
BibRef

Hopcroft, J.E., and Tarjan, R.E.,
Isomorphism of Planar Graphs,
CCComp(131-152). 1972. BibRef 7200

Tarjan, R.E.,
Depth First Search and Linear Graph Algorithms,
SIAM_JC(1), No. 1, 1972, pp 146-160. BibRef 7200

Miller, R.E., and Thather, J.W., (Eds.),
Complexity of Computer Computation,
Indexed as CCComp1972. BibRef 7200

Pfaltz, J.L.,
Graph Structures,
JACM(19), No. 3, July 1972, pp. 411-422. BibRef 7207

Berztiss, A.T.,
A Backtrack Procedure for Isomorphism of Directed Graphs,
JACM(20), No. 3, July, 1973, pp. 365-372. Graph Isomorphism. This algorithm, applied to directed graphs, first transforms the graph representation into a linear string that describes the connections between nodes. These strings start from strings describing each node and combine to form a single string describing the entire graph. From the combination rules a matching string is formed by a tree search procedure that adds one node at a time and retains only those possible strings that match the pattern. This technique proved effective for most real graphs even though it does not escape the possible worst cases. BibRef 7307

Ullmann, J.R.,
A Consistency Technique for Pattern Association,
IT(8), No. 5, September 1962, pp. 74-81. Relaxation, Discrete. Describes a simple hardware implementation, lacks an abstract mathematical formulation -- hardware is easier than software in 1962. BibRef 6209

Ullmann, J.R.,
Distributive Implementation of Relational Operations,
IEE-P(E: 137), No. 4, July 1990, pp. 283-294. Updated version of original paper. BibRef 9007

Ullmann, J.R.,
Parallel Recognition of Idealised Line Characters,
Kybernetic(2), Part 5, June 1965, pp. 221-226. Original discrete relaxation with mathematical fomulation. This paper is available:
PDF Version. Also from the Springer site:
Springer DOI Link It has been made available with kind permission of Springer Science+Business Media, The original publication is available at www.springerlink.com A short version of this paper is available:
PDF Version. BibRef 6506

Ullmann, J.R.,
An Algorithm for Subgraph Isomorphism,
JACM(23), No. 1, January 1976, pp. 31-42. Graph Isomorphism. BibRef 7601

Ullmann, J.R.,
Associating Parts of Patterns,
InfoControl(9), 1966, pp. 583-601. Abstract formulation of discrete relaxation. BibRef 6600

Ullmann, J.R.,
A Use of Continutiy in Character Recognition,
SMC(4), No. 3, May 1974, pp. 294-300. Using binary constraint propogation, can a character be a distorted image of another character. See also Recognition experiments with typed numerals from envelopes in the mail. BibRef 7405

Ullmann, J.R.,
Subset Methods for Recognising Distorted Patterns,
SMC(7), No. 3, March 1977, pp. 180-191. Non-binary constraint propogation, not all boundaries need to be closed. BibRef 7703

Ullmann, J.R.,
Pattern Recognition Using Degenerate Reference Data,
PRAI-76(508-528). Distorted patterns compared to reference patterns. Non-binary propogation. BibRef 7600

Berge, C.,
Graphs and Hypergraphs,
North HollandAmsterdam, 1973. BibRef 7300

Bron, C., and Kerbosch, J.,
Algorithm 457: Finding All Cliques in an Undirected Graph (H),
CACM(16), 1973. BibRef 7300

Osteen, R., and Tou, J.T.,
A Clique-Directed Algorithm Based on Neighborhoods in Graphs,
CIS(2), No. 4, December 1973, pp. 257-268. BibRef 7312

van Scoy, F.L.,
The Parallel Recognition of Classes of Graphs,
TC(29), 1980, pp. 563-570. BibRef 8000

Ghahraman, D.E., Wong, A.K.C., Au, T.,
Graph Optimal Monomorphism Algorithm,
SMC(10), April 1980, pp. 181-188. BibRef 8004

Ghahraman, D.E., Wong, A.K.C., Au, T.,
Graph Monomorphism Algorithms,
SMC(10), 1980, pp. 189-196. BibRef 8000

Wong, A.K.C., and Ghahraman, D.E.,
Random Graphs: Structural-Contextual Dichotomy,
PAMI(2), No. 4, July 1980, pp. 341-348. BibRef 8007

Wong, A.K.C., You, M.,
Entropy and Distance of Random Graphs with Application to Structural pattern Recognition,
PAMI(7), No. 5, September 1985, pp. 599-609. BibRef 8509
Earlier: A2, A1:
An Algorithm for Graph Optimal Isomorphism,
ICPR84(316-319). BibRef

Bhat, K.V.S.,
Refined Vertex Codes and Vertex Partitioning Methodology for Graph Isomorphism Testing,
SMC(10), 1980, pp. 610-615. BibRef 8000

Forgy, C.L.,
Rete: A Fast Algorithm for the Many Pattern/Many Object Pattern Match Problem,
AI(19), No. 1, September 1982, pp. 17-37.
WWW Version. Precompute the network to make matching fast. Intended for production rule matching. BibRef 8209

Fowler, G., Haralick, R.M., Gray, F.G., Feustel, C., and Grinstead, C.,
Efficient Graph Automorphism by Vertex Partitioning,
AI(21), No. 1-2, March 1983, pp. 245-269.
HTML Version. BibRef 8303

Mehlhorn, K.,
Data Structure and Algorithms 2: Graphs Algorithms and NP-Completeness,
Springer-Verlag1984. BibRef 8400 Book BibRef

Quinn, M.J., Deo, N.,
Parallel Graph Algorithms,
Surveys(16), No. 3, September 1984, pp. 319-348. Survey, Graph Matching. BibRef 8409

Nyo, H.L., Suk, M.,
A Polynomial Time Algorithm for Subpattern Matching,
PIEEE(74), 1986, pp. 375-377. BibRef 8600

Galil, Z.,
Efficient Algorithms for Finding Maximum Matching in Graphs,
Surveys(18), No. 1, March 1986, pp. 23-38. See also String Matching in Real Time. BibRef 8603

Thathachar, M.A.L., and Sastry, P.S.,
Relaxation Labeling with Learning Automata,
PAMI(8), No. 2, March 1986, pp. 256-268. BibRef 8603

Davies, E.R.,
The Minimal Match Graph and its Use to Speed Identification of Maximal Cliques,
SP(22), 1991, pp. 329-343. BibRef 9100

Davies, E.R.,
Alternative to Abstract Graph Matching for Locating Objects from Their Salient Features,
IVC(9), No. 4, August 1991, pp. 252-261.
WWW Version. BibRef 9108

Simic, P.,
Constrained Nets for Graph matching and Other Quadratic Assignment Problems,
NeurComp(3), 1991, pp. 268-291. BibRef 9100

Almohamad, H.A., and Duffuaa, S.O.,
A Linear Programming Approach fo the Weighted Graph Matching Problem,
PAMI(15), No. 5, May 1993, pp. 522-525.
IEEE Abstract.
WWW Version. Linear Programming. BibRef 9305

Seong, D.S., Choi, Y.K., Kim, H.S., Park, K.H.,
An Algorithm For Optimal Isomorphism Between 2 Random Graphs,
PRL(15), No. 4, April 1994, pp. 321-327. BibRef 9404

Jeavons, P.G., Cooper, M.C.,
Tractable Constraints on Ordered Domains,
AI(79), No. 2, January 1996, pp. 327-339.
WWW Version. By ordering the domain it is possible to limit the constraints to pairwise constraints, then get a linear solution. Used in See also Linear-time algorithms for testing the realisability of line drawings of curved objects. BibRef 9601

Pedrycz, W.,
Classification of Relational Patterns as a Decomposition Problem,
PRL(17), No. 1, January 10 1996, pp. 91-99. BibRef 9601

Pedrycz, W.,
Neurocomputations in relational systems,
PAMI(13), No. 3, March 1991, pp. 289-297.
IEEE Abstract.
WWW Version. 0401
BibRef

Shoukry, A., Aboutabl, M.,
Neural-Network Approach for Solving the Maximal Common Subgraph Problem,
SMC-B(26), No. 5, October 1996, pp. 785-790.
IEEE Top Reference. Hopfield network. BibRef 9610

Cucka, P., Netanyahu, N.S., and Rosenfeld, A.,
Learning in Navigation: Goal Finding in Graphs,
PRAI(10), 1996, pp. 429-446. BibRef 9600

Jumarie, G.,
Informational Similarity of Graphs in Syntactic Pattern Recognition,
PRL(15), 1994, pp. 1177-1181. BibRef 9400

Owolabi, O.,
A Graph Canonization Method For Pattern Recognition,
PRL(12), 1991, pp. 701-705. BibRef 9100

Seong, D.S., Kim, H.S., Park, K.H.,
Incremental Clustering of Attributed Graphs,
SMC(23), 1993, pp. 1399-1411. BibRef 9300

Goldman, R.P., Charniak, E.,
A language for construction of belief networks,
PAMI(15), No. 3, March 1993, pp. 196-208.
IEEE Abstract.
WWW Version. 0401
BibRef

Buckley, M., Yang, J.,
Regularized Shortest Path Extraction,
PRL(18), No. 7, July 1997, pp. 621-629. 9711
Shortest path through a graph. BibRef

Barbehenn, M.,
A Note on the Complexity of Dijkstras Algorithm for Graphs with Weighted Vertices,
TC(47), No. 2, February 1998, pp. 263-263. 9803
BibRef

Suganthan, P.N., Yan, H., Teoh, E.K., Mital, D.P.,
Optimal Encoding of Graph Homomorphism Energy Using Fuzzy Information Aggregation Operators,
PR(31), No. 5, May 1998, pp. 623-639.
WWW Version. 9805
BibRef

Wang, J.T.L., Shapiro, B.A., Shasha, D., Zhang, K., and Currey, K.M.,
An Algorithm for Finding the Largest Approximately Common Substructures of Two Trees,
PAMI(20), No. 8, August 1998, pp. 889-895.
IEEE Abstract.
WWW Version. BibRef 9808

Abdulrahim, M.[Mohammad], Misra, M.[Manavendra],
A Graph Isomorphism Algorithm for Object Recognition,
PAA(1), No. 3, 1998, pp. xx-yy. BibRef 9800

Bunke, H.,
Error Correcting Graph Matching: On the Influence of the Underlying Cost Function,
PAMI(21), No. 9, September 1999, pp. 917-922.
IEEE Abstract.
WWW Version. For any cost function, there are an infinite number of others that lead to the same optimal error correcting matching. BibRef 9909

Perlovsky, L.I.,
Conundrum of Combinatorial Complexity,
PAMI(20), No. 6, June 1998, pp. 666-670.
IEEE Abstract.
WWW Version. 9807
BibRef

Miller, D.A.[Douglas A.], Zucker, S.W.[Steven W.],
Cliques, computation, and computational tractability,
PR(33), No. 4, April 2000, pp. 535-542.
WWW Version. 0002
BibRef

Luo, B., Hancock, E.R.,
Structural Graph Matching Using the EM Algorithm and Singular Value Decomposition,
PAMI(23), No. 10, October 2001, pp. 1120-1136.
IEEE Abstract.
WWW Version. 0110
BibRef
Earlier:
Symbolic Graph Matching Using the EM Algorithm and Singular Value Decomposition,
ICPR00(Vol II: 141-144).
IEEE DOI Link
HTML Version. 0009
See also Multiple Line-Template Matching with the EM Algorithm. See also Registering Incomplete Radar Images Using the EM Algorithm. BibRef

Luo, B., Hancock, E.R.,
A robust eigen-decomposition framework for inexact graph-matching,
CIAP01(465-470).
IEEE Top Reference. 0210
BibRef

Carcassoni, M.[Marco], Hancock, E.R.[Edwin R.],
Weighted Graph-Matching Using Modal Clusters,
CAIP01(142 ff.).
HTML Version. 0210
BibRef

Dickinson, S.J.[Sven J.], Pelillo, M.[Marcello], Zabih, R.[Ramin],
Introduction to the Special Section on Graph Algorithms and Computer Vision,
PAMI(23), No. 10, October 2001, pp. 1049-1052.
IEEE Abstract.
WWW Version. 0110
BibRef

Ostergard, P.,
A Fast Algorithm for the Maximum Clique Problem,
DiscAppMath(120), 2002, pp. 197-207. BibRef 0200

Wang, J.T.L.[Jason T.L.], Zhang, K.Z.[Kai-Zhong], Chang, G.[George], Shasha, D.[Dennis],
Finding approximate patterns in undirected acyclic graphs,
PR(35), No. 2, February 2002, pp. 473-483.
WWW Version. 0201
BibRef

Raphael, C.[Christopher],
Coarse-to-Fine Dynamic Programming,
PAMI(23), No. 12, December 2001, pp. 1379-1390.
IEEE Abstract.
WWW Version. 0112
Dynamic Programming. Applied to mine detection. Generalize dynamic programming to hierarchical system. BibRef

Fernandez-Madrigal, J.A.[Juan-Antonio], Gonzalez, J.[Javier],
Multihierarchical Graph Search,
PAMI(24), No. 1, January 2002, pp. 103-113.
IEEE Abstract.
WWW Version. 0201
Applied to path planning. BibRef

de Santo, M., Foggia, P., Sansone, C., Vento, M.,
A large database of graphs and its use for benchmarking graph isomorphism algorithms,
PRL(24), No. 8, May 2003, pp. 1067-1079.
WWW Version. 0304
BibRef

Cordella, L.P., Sansone, C., Tortorella, F., Vento, M.[Mario], Foggia, P.,
Graph Matching: A Fast Algorithm and its Evaluation,
ICPR98(Vol II: 1582-1584).
IEEE DOI Link 9808
BibRef

Cordella, L.P., Foggia, P., Sansone, C., Vento, M.,
A (Sub)Graph Isomorphism Algorithm for Matching Large Graphs,
PAMI(26), No. 10, October 2004, pp. 1367-1372.
IEEE Abstract. 0409
BibRef
Earlier:
Fast Graph Matching for Detecting CAD Image Components,
ICPR00(Vol II: 1034-1037).
IEEE DOI Link
HTML Version. 0009
BibRef
Earlier:
Performance evaluation of the VF graph matching algorithm,
CIAP99(1172-1177).
IEEE DOI Link 9909
BibRef
Earlier:
An Efficient Algorithm for the Inexact Matching of ARG Graphs Using a Contextual Transformational Model,
ICPR96(III: 180-184).
IEEE DOI Link 9608
(Univ. di Napoli, I) Earlier version worked on small and medium sized graphs. This works for large graphs. BibRef

Conte, D.[Donatello], Foggia, P.[Pasquale], Jolion, J.M.[Jean-Michel], Vento, M.[Mario],
A graph-based, multi-resolution algorithm for tracking objects in presence of occlusions,
PR(39), No. 4, April 2006, pp. 562-572.
WWW Version. 0604
Object tracking; Occlusion problem; Graph pyramid; Multi-resolution segmentation BibRef

Foggia, P.[Pasquale], Percannella, G.[Gennaro], Sansone, C.[Carlo], Vento, M.[Mario],
Benchmarking graph-based clustering algorithms,
IVC(27), No. 7, 4 June 2009, pp. 979-988.
Elsevier DOI Link
WWW Version. 0904
BibRef
Earlier:
Assessing the Performance of a Graph-Based Clustering Algorithm,
GbRPR07(215-227).
Springer DOI Link 0706
Benchmarking; Graph-based clustering; Cluster detection BibRef

Massaro, A.[Alessio], Pelillo, M.[Marcello],
Matching graphs by pivoting,
PRL(24), No. 8, May 2003, pp. 1099-1106.
WWW Version. 0304
BibRef
Earlier:
A Complementary Pivoting Approach to Graph Matching,
EMMCVPR01(469-479).
Springer DOI Link 0205
BibRef

Luo, B.[Bin], Hancock, E.R.[Edwin R.], Wilson, R.C.[Richard C.],
Eigenspaces For Graphs,
IJIG(2), No. 2, April 2002, pp. 247-268. 0204
BibRef

Luo, B.[Bin], Wilson, R.C.[Richard C.], Hancock, E.R.[Edwin R.],
Spectral embedding of graphs,
PR(36No. 10, October 2003, pp. 2213-2230.
WWW Version. 0308
BibRef
Earlier:
Graph spectral approach for learning view structure,
ICPR02(III: 785-788).
IEEE DOI Link 0211
BibRef

Wilson, R.C., Hancock, E.R.,
Levenshtein distance for graph spectral features,
ICPR04(II: 489-492).
IEEE DOI Link 0409
BibRef

Luo, B.[Bin], Wilson, R.C.[Richard C.], Hancock, E.R.[Edwin R.],
A Spectral Approach to Learning Structural Variations in Graphs,
PR(39), No. 6, June 2006, pp. 1188-1198.
WWW Version. 0604
BibRef
Earlier: CVS03(407 ff).
HTML Version. 0306
BibRef
Earlier:
Learning modes of structural variation in graphs,
ICIP03(II: 37-40).
IEEE Abstract. 0312
BibRef
Earlier:
Spectral Clustering of Graphs,
CAIP03(540-548).
WWW Version. 0311
Generative model; Graph; Covariance matrix; Clustering BibRef

Luo, B.[Bin], Wilson, R.C., Hancock, E.R.,
The independent and principal component of graph spectra,
ICPR02(II: 164-167).
IEEE DOI Link 0211
BibRef

Fu, Z.Y.[Zhou-Yu], Robles-Kelly, A.[Antonio],
An Energy Minimisation Approach to Attributed Graph Regularisation,
EMMCVPR07(71-86).
Springer DOI Link 0708
BibRef

Luo, B.[Bin], Robles-Kelly, A.[Antonio], Torsello, A.[Andrea], Wilson, R.C.[Richard C.], Hancock, E.R.[Edwin R.],
A Probabilistic Framework for Graph Clustering,
CVPR01(I:912-919).
IEEE Abstract. 0110
From set of distances between graphs characterize pairwise affinity. Culuster graphs. BibRef

Qiu, H.J.[Huai-Jun], Hancock, E.R.[Edwin R.],
Graph matching and clustering using spectral partitions,
PR(39), No. 1, January 2006, pp. 22-34.
WWW Version. 0512
BibRef
Earlier:
Spectral Simplification of Graphs,
ECCV04(Vol IV: 114-126).
WWW Version. 0405
BibRef

Qiu, H.J.[Huai-Jun], Hancock, E.R.[Edwin R.],
Graph simplification and matching using commute times,
PR(40), No. 10, October 2007, pp. 2874-2889.
WWW Version. 0707
BibRef
Earlier:
Spanning Trees from the Commute Times of Random Walks on Graphs,
ICIAR06(II: 375-385).
Springer DOI Link 0610
BibRef
And:
Graph Embedding Using Commute Time,
SSPR06(441-449).
Springer DOI Link 0608
BibRef
And:
Graph Matching using Commute Time Spanning Trees,
ICPR06(III: 1224-1227).
WWW Version. 0609
BibRef
And: ICPR06(IV: 955).
WWW Version. 0609
BibRef
And:
Robust Multi-body Motion Tracking Using Commute Time Clustering,
ECCV06(I: 160-173).
Springer DOI Link 0608
Graph-matching; Graph simplification; Commute time; Graph spectrum BibRef

Qiu, H.J.[Huai-Jun], Hancock, E.R.[Edwin R.],
Clustering and Embedding Using Commute Times,
PAMI(29), No. 11, November 2007, pp. 1873-1890.
IEEE DOI Link 0711
BibRef
Earlier:
Commute Times, Discrete Green's Functions and Graph Matching,
CIAP05(454-462).
Springer DOI Link 0509
BibRef
And:
Commute Times for Graph Spectral Clustering,
CAIP05(128).
Springer DOI Link 0509
BibRef

Wilson, R.C.[Richard C.], Hancock, E.R.[Edwin R.], Luo, B.[Bin],
Pattern Vectors from Algebraic Graph Theory,
PAMI(27), No. 7, July 2005, pp. 1112-1124.
IEEE Abstract. 0506
BibRef
Earlier: A2, A3, A1:
Graph Pattern Spaces from Laplacian Spectral Polynomials,
ICIAR04(I: 327-334).
WWW Version. 0409
BibRef
Earlier: A1, A2, Only:
Pattern Spaces from Graph Polynomials,
CIAP03(480-485).
IEEE Abstract. 0310
Embed graphs in pattern space. BibRef

Robles-Kelly, A.[Antonio], Hancock, E.R.[Edwin R.],
A Riemannian approach to graph embedding,
PR(40), No. 3, March 2007, pp. 1042-1056.
WWW Version. 0611
Graph embedding; Riemannian geometry; Combinatorial Laplacian BibRef

Robles-Kelly, A.[Antonio], Hancock, E.R.[Edwin R.],
Graph Matching using Adjacency Matrix Markov Chains,
BMVC01(Session 5: Matching & Retrieval).
HTML Version. University of York 0110
BibRef

Falcao, A.X.[Alexandre X.], Stolfi, J.[Jorge], de Alencar Lotufo, R.[Roberto],
The Image Foresting Transform: Theory, Algorithms, and Applications,
PAMI(26), No. 1, January 2004, pp. 19-29.
IEEE Abstract. 0401
Graph-based design of image processing operators using connectivity. Minimum-cost path forest in a graph. BibRef

van Wyk, B.J.[Barend J.], and van Wyk, M.A.[Michael A.],
A POCS-Based Graph Matching Algorithm,
PAMI(26), No. 11, November 2004, pp. 1526-1530.
IEEE Abstract. 0410
Projections onto Convex Sets. Solve Attributed Graph Matching. BibRef

Wang, H.F.[Hong Fang], Hancock, E.R.[Edwin R.],
Correspondence matching using kernel principal components analysis and label consistency constraints,
PR(39), No. 6, June 2006, pp. 1012-1025.
WWW Version. Non-rigid motion; Correspondence matching; Graph spectral methods; Kernel PCA; Constraints 0604
BibRef
Earlier:
Improving Correspondence Matching Using Label Consistency Constraints,
IbPRIA05(I:235).
Springer DOI Link 0509
BibRef
And:
Kernel Spectral Correspondence Matching Using Label Consistency Constraints,
CIAP05(503-510).
Springer DOI Link 0509
BibRef

Bunke, H.[Horst], Dickinson, P.[Peter], Irniger, C.[Christophe], Kraetzl, M.[Miro],
Recovery of missing information in graph sequences by means of reference pattern matching and decision tree learning,
PR(39), No. 4, April 2006, pp. 573-586.
WWW Version. 0604
Graph sequence analysis; Recovery of missing information; Computer network analysis; Machine learning; Decision tree classifier; Reference pattern matching BibRef

Bunke, H.[Horst], Irniger, C.[Christophe], Neuhaus, M.[Michel],
Graph Matching: Challenges and Potential Solutions,
CIAP05(1-10).
Springer DOI Link 0509
BibRef

Bunke, H.[Horst], Dickinson, P.[Peter], Kraetzl, M.[Miro],
Theoretical and Algorithmic Framework for Hypergraph Matching,
CIAP05(463-470).
Springer DOI Link 0509
BibRef
And:
Comparison of Two Different Prediction Schemes for the Analysis of Time Series of Graphs,
IbPRIA05(II:99).
Springer DOI Link 0509
BibRef

Huang, R.[Ruihong],
A Schedule-based Pathfinding Algorithm for Transit Networks Using Pattern First Search,
GeoInfo(11), No. 2, June 2007, pp. 269-285.
Springer DOI Link 0709
BibRef

Wen, G.H.[Gui-Hua], Jiang, L.J.[Li-Jun], Wen, J.[Jun],
Using locally estimated geodesic distance to optimize neighborhood graph for isometric data embedding,
PR(41), No. 7, July 2008, pp. 2226-2236.
WWW Version. 0804
BibRef
And: Authors' response: PR(42), No. 5, May 2009, pp. 1014.
Elsevier DOI Link
WWW Version. 0902
Isometric data embedding; Nonlinear neighborhood; Neighborhood graph; Geodesic distance; Manifold learning BibRef

Wen, G.H.[Gui-Hua], Jiang, L.J.[Li-Jun], Wen, J.[Jun],
Local relative transformation with application to isometric embedding,
PRL(30), No. 3, 1 February 2009, pp. 203-211.
Elsevier DOI Link
WWW Version. 0804
Isometric embedding; Cognitive law; Relative transformation; Local relative transformation; Neighborhood graph; Manifold learning BibRef

Zhong, C.M.[Cai-Ming], Miao, D.Q.[Duo-Qian],
A comment on 'Using locally estimated geodesic distance to optimize neighborhood graph for isometric data embedding',
PR(42), No. 5, May 2009, pp. 1012-1013.
Elsevier DOI Link
WWW Version. 0902
Triangle inequality; Geodesic distance; Euclidean distance See also Using locally estimated geodesic distance to optimize neighborhood graph for isometric data embedding. BibRef

Brun, L.[Luc], Escolano, F.[Francisco],
Graph-based Representations Preface,
IVC(27), No. 7, 4 June 2009, pp. 835-836.
Elsevier DOI Link
WWW Version. 0904
BibRef

Bonev, B.[Boyan], Lozano, M.A.[Miguel A.], Escolano, F.[Francisco], Suau, P.[Pablo], Aguilar, W.[Wendy], Saez, J.M., Cazorla, M.A.[Miguel A.],
Region and constellations based categorization of images with unsupervised graph learning,
IVC(27), No. 7, 4 June 2009, pp. 960-978.
Elsevier DOI Link
WWW Version. 0904
Image categorization; Clustering of graphs; EM algorithms BibRef
Earlier: A3, A2, A1, A4, A7, A5, Only:
Constellations and the Unsupervised Learning of Graphs,
GbRPR07(340-350).
Springer DOI Link 0706
BibRef

Escolano, F.[Francisco], Hancock, E.R.[Edwin R.], Lozano, M.A.[Miguel A.],
Birkhoff polytopes, heat kernels and graph complexity,
ICPR08(1-5).
IEEE DOI Link 0812
BibRef

Rota Bulò, S.[Samuel], Torsello, A.[Andrea], Pelillo, M.[Marcello],
A game-theoretic approach to partial clique enumeration,
IVC(27), No. 7, 4 June 2009, pp. 911-922.
Elsevier DOI Link
WWW Version. 0904
BibRef
Earlier:
A Continuous-Based Approach for Partial Clique Enumeration,
GbRPR07(61-70).
Springer DOI Link 0706
Maximal clique enumeration; Maximum clique problem; Evolutionary game theory; Evolutionary stable strategy BibRef

Rota Bulo, S., Albarelli, A., Torsello, A., Pelillo, M.,
A hypergraph-based approach to affine parameters estimation,
ICPR08(1-4).
IEEE DOI Link 0812
BibRef

Kokiopoulou, E.[Effrosyni], Frossard, P.[Pascal],
Minimum Distance between Pattern Transformation Manifolds: Algorithm and Applications,
PAMI(31), No. 7, July 2009, pp. 1225-1238.
IEEE DOI Link 0905
BibRef

Kokiopoulou, E.[Effrosyni], Pirillos, S.[Stefanos], Frossard, P.[Pascal],
Graph-based classification for multiple observations of transformed patterns,
ICPR08(1-4).
IEEE DOI Link 0812
BibRef

Gosselin, S.[Stéphane], Damiand, G.[Guillaume], Solnon, C.[Christine],
Signatures of Combinatorial Maps,
IWCIA09(370-382).
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Canonical representation of n-d map. BibRef

Damiand, G.[Guillaume], de la Higuera, C.[Colin], Janodet, J.C.[Jean-Christophe], Samuel, É.[Émilie], Solnon, C.[Christine],
A Polynomial Algorithm for Submap Isomorphism: Application to Searching Patterns in Images,
GbRPR09(102-112).
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Detecting hubs and quasi cliques in scale-free networks,
ICPR08(1-4).
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Coring method for clustering a graph,
ICPR08(1-4).
IEEE DOI Link 0812
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Yaghi, H., Krim, H.,
Probabilistic graph matching by canonical decomposition,
ICIP08(2368-2371).
IEEE DOI Link 0810
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El Ghawalby, H.[Hewayda], Hancock, E.R.[Edwin R.],
Characterizing Graphs Using Spherical Triangles,
IbPRIA09(465-472).
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And:
Graph Regularisation Using Gaussian Curvature,
GbRPR09(233-242).
Springer DOI Link 0905
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Earlier:
Graph Characteristic from the Gauss-Bonnet Theorem,
SSPR08(207-216).
Springer DOI Link 0812
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Earlier:
Measuring Graph Similarity Using Spectral Geometry,
ICIAR08(xx-yy).
Springer DOI Link 0806
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Haxhimusa, Y.[Yll], Kropatsch, W.G.[Walter G.], Pizlo, Z.[Zygmunt], Ion, A.[Adrian], Lehrbaum, A.[Andreas],
Approximating TSP Solution by MST Based Graph Pyramid,
GbRPR07(295-306).
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Travelling saleseman. BibRef

Schellewald, C.[Christian],
A Bound for Non-subgraph Isomorphism,
GbRPR07(71-80).
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Suvonvorn, N.[Nikom], Zavidovique, B.[Bertrand],
A Stable Marriages Algorithm to Optimize Satisfaction and Equity,
ICIAR06(II: 422-433).
Springer DOI Link 0610
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de Piero, F.W.[Fred W.], Carlin, J.K.[John K.],
Structural Matching Via Optimal Basis Graphs,
ICPR06(III: 449-452).
WWW Version. 0609
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de Piero, F.W.,
Structural graph matching with polynomial bounds on memory and on worst-case effort,
ICPR04(III: 379-382).
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Kropatsch, W.G.[Walter G.], Haxhimusa, Y.[Yll],
Grouping of Non-connected Structures by an Irregular Graph Pyramid,
IbPRIA05(II:107).
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Logarithmic Tapering Graph Pyramid,
DAGM02(117 ff.).
HTML Version. 0303
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Giugno, R., Shasha, D.,
GraphGrep: a fast and universal method for querying graphs,
ICPR02(II: 112-115).
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Hlaoui, A., Wang, S.R.[Sheng-Rui],
A new algorithm for inexact graph matching,
ICPR02(IV: 180-183).
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Bunke, H.,
Recent Developments in Graph Matching,
ICPR00(Vol II: 117-124).
IEEE DOI Link
HTML Version. 0009
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Rizzi, S.[Stefano],
A Genetic Approach to Hierarchical Clustering of Euclidean Graphs,
ICPR98(Vol II: 1543-1545).
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Kotzer, T., Cohen, N., Shamir, J.,
Generalized approach to projections onto convex constraint sets,
ICPR94(C:77-81).
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Akinniyi, F.A., and Wong, A.K.C.,
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Chapter on Matching and Recognition Using Volumes, High Level Vision Techniques, Invariants continues in
General Structure and Graph Representation and Matching .