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Table of Contents
Foreword; Preface; Contents; About the Editors; 1 Development of Mathematical Theory in Computer Vision; Abstract; 1.1 Introduction; 1.2 Chapters Included in the Book; 1.3 Conclusion; References; 2 Morphological Image Analysis for Computer Vision Applications; Abstract; 2.1 Introduction; 2.2 Basics of Mathematical Morphology; 2.2.1 Mathematical Morphology as a Set-Theoretic Scheme; 2.2.2 Binary Mathematical Morphology Based on Structuring Elements; 2.2.3 Grayscale Mathematical Morphology Based on Structuring Elements; 2.2.4 Mathematical Morphology as a Lattice-Theoretic Scheme.
2.2.5 Morphologies Based on Connected Filters2.2.6 Morphological Skeleton; 2.3 Skeleton-Based Continuous Binary Morphology; 2.3.1 Skeleton of Binary Image Versus Binary Image of Skeleton; 2.3.2 Continuous Representation of Raster Image Boundary; 2.3.3 Polygonal Figure Skeleton; 2.3.4 Skeleton-Based Continuous Binary Morphologies; 2.4 Morphological Spectrum: Concept and Computation; 2.4.1 Pattern Spectrum and Morphological Spectra; 2.4.2 Thickness Map and Morphological Spectrum with Disk Structuring Elements.
2.4.3 Calculation of Binary Morphological Spectra Based on Continuous Skeletal Representation2.4.4 Calculation of Grayscale Morphological Spectra; 2.5 Morphological Image Analysis (Pyt'ev Morphology); 2.5.1 Image Shape as an Invariant of Image Transforms; 2.5.2 Scene Recognition Based on Image Shape; 2.5.3 Scene Change Detection Based on Image Shape; 2.5.4 Scene Recognition Based on the Shape of Noisy Image; 2.5.5 Morphological Shape Matching; 2.6 Projective Morphologies, Morphological Segmentation and Complexity Analysis; 2.6.1 Projective Morphologies Based on Morphological Decompositions.
2.6.2 Image Segmentation in the Framework of Projective Morphology2.6.3 Shape Regularization and Morphological Filters by Regularization; 2.6.4 Morphological Complexity, Filters, and Spectra by Complexity; 2.7 Conclusion; Acknowledgments; References; 3 Methods for Detecting of Structural Changes in Computer Vision Systems; Abstract; 3.1 Introduction; 3.2 Pixel Structural Similarity Criteria; 3.3 Spectral Criteria of Structural Image Similarity; 3.3.1 Polynomial Transforms; 3.3.2 Discrete Transforms; 3.4 Spectral Image Variation Detection; 3.4.1 Optimal Detection Algorithm.
3.4.2 Quasi-optimal Algorithms3.5 Experimental Research of Structural Similarity Algorithms; 3.5.1 Practical Using of Pixel and Spectral Algorithms in Image Analysis; 3.5.2 Experimental Research of Spectral Statistics D0 and DE; 3.5.3 Experimental Research of MSSIM and MNSSIM1(2) Criteria; 3.6 Conclusion; References; 4 Hierarchical Adaptive KL-Based Transform: Algorithms and Applications; Abstract; 4.1 Introduction; 4.2 Analysis of the Image Transform Methods Based on the KLT; 4.2.1 Karhunen-Loeve Transform for Inter-frame (3D) Processing of a Group of Correlated Images.
2.2.5 Morphologies Based on Connected Filters2.2.6 Morphological Skeleton; 2.3 Skeleton-Based Continuous Binary Morphology; 2.3.1 Skeleton of Binary Image Versus Binary Image of Skeleton; 2.3.2 Continuous Representation of Raster Image Boundary; 2.3.3 Polygonal Figure Skeleton; 2.3.4 Skeleton-Based Continuous Binary Morphologies; 2.4 Morphological Spectrum: Concept and Computation; 2.4.1 Pattern Spectrum and Morphological Spectra; 2.4.2 Thickness Map and Morphological Spectrum with Disk Structuring Elements.
2.4.3 Calculation of Binary Morphological Spectra Based on Continuous Skeletal Representation2.4.4 Calculation of Grayscale Morphological Spectra; 2.5 Morphological Image Analysis (Pyt'ev Morphology); 2.5.1 Image Shape as an Invariant of Image Transforms; 2.5.2 Scene Recognition Based on Image Shape; 2.5.3 Scene Change Detection Based on Image Shape; 2.5.4 Scene Recognition Based on the Shape of Noisy Image; 2.5.5 Morphological Shape Matching; 2.6 Projective Morphologies, Morphological Segmentation and Complexity Analysis; 2.6.1 Projective Morphologies Based on Morphological Decompositions.
2.6.2 Image Segmentation in the Framework of Projective Morphology2.6.3 Shape Regularization and Morphological Filters by Regularization; 2.6.4 Morphological Complexity, Filters, and Spectra by Complexity; 2.7 Conclusion; Acknowledgments; References; 3 Methods for Detecting of Structural Changes in Computer Vision Systems; Abstract; 3.1 Introduction; 3.2 Pixel Structural Similarity Criteria; 3.3 Spectral Criteria of Structural Image Similarity; 3.3.1 Polynomial Transforms; 3.3.2 Discrete Transforms; 3.4 Spectral Image Variation Detection; 3.4.1 Optimal Detection Algorithm.
3.4.2 Quasi-optimal Algorithms3.5 Experimental Research of Structural Similarity Algorithms; 3.5.1 Practical Using of Pixel and Spectral Algorithms in Image Analysis; 3.5.2 Experimental Research of Spectral Statistics D0 and DE; 3.5.3 Experimental Research of MSSIM and MNSSIM1(2) Criteria; 3.6 Conclusion; References; 4 Hierarchical Adaptive KL-Based Transform: Algorithms and Applications; Abstract; 4.1 Introduction; 4.2 Analysis of the Image Transform Methods Based on the KLT; 4.2.1 Karhunen-Loeve Transform for Inter-frame (3D) Processing of a Group of Correlated Images.