Fundamentals of Three-dimensional Digital Image Processing (eBook)

Introduction.- Models of Images and Image Operations.- Introduction.- Continuous and Digitized Images.- Continuous Images.- Digitized Images.- Three-dimensional Images.- 3D Line Figures and Digitization.- Crosse Section and Projection.- Relations among Images.- Model of Image Operations.- Formulation of Image Operations.- Relations between Image Operators.- Binary Operators between Images.- Composition if Image Operations.- Basic Operators.- Algorithm of Image Operators.- General Form of Image Operations.- Important Types of Algorithms.- Local Processing of 3D Images.- Classification of Local Operations.- General Form.- Classification by Functions of Filters.- Classification by the Form of a Local Function.- Smoothing Filter.- Linear Smoothing Filter.- Median Filter and Order Statistics Filter.- Edge Preserving Smoothing.- Morphology Filter.- Difference Filter.- Significance.- Differentials in Continuous Space.- Derivatives in Digitized Space.- Basic Characteristics of Difference Filter.- Omnidirectionalization.- 1-D Difference Filters and their Combinations.- 3D Laplacian.- 2D Difference Filters and their Combination.- Differential Features of Curved Surface.- Region Growing (Region Merging).- Outline.- Region Expansion.- Geometrical Property of Three-Dimensional Digitized Images.- Neighborhood and Connectivity.- Neighborhood.- Connectivity and Connected Component.- Simplex and Simplicious Decomposition.- Euler Number.- Local Feature of a Connected Component and Topology of a Figure.- Local Patterns and their Characterization.- 2 x 2 x 2 Local Patterns.- 3 x 3 x 3 Local Patterns.- Classification of the Voxel State.- Voxel State and Connectivity Index.- Calculation of Connectivity Index and Connectivity Number.- Basic Ideas.- Calculation of the Connectivity Index.- Calculation of the Connectivity Number.- Calculation of the Euler Number.- Triangulation Method.- Simplex Counting Method.- Algorithm of Deletability Test.- Path.- Distance Function.- Distance Function in Applications.- Improvement in Distance Metric.- Border Surface.- Algorithms of Binary Image Processing.- Introduction.- Labeling of a Connected Component.- Shrinking.- Surface Thinning and Axis Thinning.- Definition.- Requirements to Thinning.- Realization-the Sequential Type.- Examples of Surface/Axis Thinning Algorithms (Sequential Type).- Surface Thinning Algorithm Accompanying the Euclidean Distance Transformation.- Use of One-dimensional List for Auxiliary Information.- Examples of Surface/Axis Thinning Algorithm (Parallel Type).- Experimental Results.- Points in Algorithm Construction.- Distance Transformation and Skeleton.- Definition.- Significance of DT and Skeleton.- Classification of Algorithms.- Example of an Algorithm (1) – Squared Euclidean DT.- Example of Algorithms (2) – Variable Neighborhood DT (Parallel Type).- Supplementary Comments on Algorithms of DT.- Skeleton.- Reverse Distance Transformation.- Example of RDT Algorithms – (i) Euclidean Squared RDT.- Example of RDT Algorithm (ii) Fixed Neighborhood (6, 18, or26-Neighborhood) RDT (Sequential Type).- Extraction of Skeleton.- Distance Transformation of a Line Figure.- Border Surface Following.- Outline.- Examples of Algorithm.- Restoration of a Figure.- Knot and Link.- Outline.- Reduction of a Digital Knot.- Voronoi Division of a Digitized Image.- Algorithms for Processing Connected Components with Grey Values.- Distance Transformation of a Gray-Tone Image.- Definition.- An Example of Algorithm.- Thinning of a Gray-Tone Image.- Basic Idea.- Requirements.- Principles of Thinning.- Examples of Algorithms – (1) Integration of Information concerning Density Values.- Algorithm.- Experimental Results.- Examples of Algorithms – (2) Ridge Line following.- Meanings of a Ridge Lien.- Algorithm.- Experiments.- Visualization of a 3D Gray-Tone Images.- Formulation of Visualization Problem .- Voxel Data and Polygon Model.- Marching Cubes Algorithm.- Cross Section, Surface, and Projection.- Cross Section.- Surface.- Projection.- Idea of Visualization Basing upon Ray Casting (1) – Projection of a Point.- Display of a Point.- Display of Line.- Display of Surface.- Idea of Visualization Based on Ray Casting (2) – Manipulation of Density Values.- Rendering Surface Based on Ray Casting – Surface Rendering.- Calculation of the Brightness of Surface.- Smooth Shading.- Depth Coding.- Ray Tracing.- Photorealistic Rendering and Rendering for Visualization.- Display of Density Values Basing upon Ray Casting – Volume Rendering.- Algorithm of Volume Rendering.- Selection of Parameters.- Front-to-back Algorithm.- Properties of Volume Rendering and Surface Rendering.- Gradient Shading.- References.-