Contents Chapter 6 Graph Image Language Techniques Supporting Advanced Classification and Cognitive Interpretation of CT Coronary Vessel Visualizations 1 Introduction 2 The Classification problem 3 Stages in the Analysis of CT Images under a Structural Approach Utilising Graph Techniques 4 Parsing Languages Generated by Graph Grammars. 5 Picture Grammars in Classification and Semantic Interpretation of 3D Coronary Vessels Visualisations 5.1 Characteristics of the lmage data 5.2 Preliminary Analysis of 3D Coronary Vascularisation 5.3 Graph-Based Linguistic Formalisms in Spatial Modelling of Coronary Vessels 5.4 Detecting Lesions and Constructing the Syntactic Analyser 6 Conclusions Concerning the Advanced Classification and Cognitive 104 5.5 Selected Results Interpretation of CT Coronary Vessel Visualizations 10 Chapter 7 A Graph Matching Approach to Symmetry Detection and analysis Michael chertok and yosi keller 1 Introduction 113 2 Symmetries and Their Properties 115 2.1 Rotational Symmetry 2.2 Reflectional Symmetry 116 2.3 Interrelations between Rotational and Reflectional Symmetries. 117 2.4 Discussion 3 Previous Work 117 3.1 Previous Work in Symmetry Detection and Analysis 118 3.2 Local features 3.3 Spectral Matching of Sets of Points in R Spectral Symmetry Analysis 4.1 Spectral Symmetry Analysis of Sets in R 4. 1. 1 Perfect Symmetry and Spectral De 4.2 Spectral Symmetry Analysis of Images 4.2. 1 Image Representation by Local Features 125 4.2.2 Symmetry Categorization and Pruning 4.2.3 Computing the Geometrical Properties of the Symmetry..126 5 Experimental Results 127 5.1 Symmetry Analysis of Images... 5.2 Statistical Accuracy Analysis 134Contents IX Chapter 6 Graph Image Language Techniques Supporting Advanced Classification and Cognitive Interpretation of CT Coronary Vessel Visualizations ............ 89 Mirosław Trzupek 1 Introduction ............................................................................................... 89 2 The Classification Problem........................................................................ 92 3 Stages in the Analysis of CT Images under a Structural Approach Utilising Graph Techniques ....................................................................... 93 4 Parsing Languages Generated by Graph Grammars .................................. 95 5 Picture Grammars in Classification and Semantic Interpretation of 3D Coronary Vessels Visualisations ............................................................... 96 5.1 Characteristics of the Image Data ...................................................... 96 5.2 Preliminary Analysis of 3D Coronary Vascularisation Reconstructions.................................................................................. 96 5.3 Graph-Based Linguistic Formalisms in Spatial Modelling of Coronary Vessels ............................................................................... 98 5.4 Detecting Lesions and Constructing the Syntactic Analyser ........... 103 5.5 Selected Results ............................................................................... 104 6 Conclusions Concerning the Advanced Classification and Cognitive Interpretation of CT Coronary Vessel Visualizations............................. 108 References .................................................................................................... 110 Chapter 7 A Graph Matching Approach to Symmetry Detection and Analysis............113 Michael Chertok and Yosi Keller 1 Introduction ..............................................................................................113 2 Symmetries and Their Properties..............................................................115 2.1 Rotational Symmetry ........................................................................115 2.2 Reflectional Symmetry .....................................................................116 2.3 Interrelations between Rotational and Reflectional Symmetries ......117 2.4 Discussion.........................................................................................117 3 Previous Work ..........................................................................................117 3.1 Previous Work in Symmetry Detection and Analysis.......................118 3.2 Local Features...................................................................................121 3.3 Spectral Matching of Sets of Points in Rn .........................................122 4 Spectral Symmetry Analysis.....................................................................123 4.1 Spectral Symmetry Analysis of Sets in Rn .......................................123 4.1.1 Perfect Symmetry and Spectral Degeneracy..........................124 4.2 Spectral Symmetry Analysis of Images ............................................124 4.2.1 Image Representation by Local Features ...............................125 4.2.2 Symmetry Categorization and Pruning ..................................125 4.2.3 Computing the Geometrical Properties of the Symmetry ......126 5 Experimental Results ................................................................................127 5.1 Symmetry Analysis of Images ..........................................................128 5.2 Statistical Accuracy Analysis ...........................................................134