Fundamentals of three-dimensional digital image processing / Junichiro Toriwaki, Hiroyuki Yoshida.

INTRODUCTION
1.1
1.1.1 3D continuous images
1.1.2 3D digitalimages.
1.2 What does "3D image" mean?
1.2.1 Dimensionality of the media and of the subject
1.2.2 Types of 3D images..
1.2.3 Cues for 3D information
1.2.4 Specific examples of 3D images.
1.3 Types and characteristics of 3D image processing .
1.3.1 Examples of 3D image processing
1.3.2 Virtual spaces as 3D digital images
1.3.3 Characteristics of 3D image processing
1.3.4 Objectives in 3D image processing
1.4 The contents of this book..
MODELS OF IMAGES AND IMAGE OPERATIONS
2.1 Introduction
2.2 Continuous and digitized images
2.2.1 Continuous images
2.2.2 Digitized images ..
2.2.3 Three-dimensional images
2.2.4 3D line figures and digitization
2.2.5 Cross section and projection
2.2.6 Relationships among images
2.3 Model of image operations
2.3.1 Formulation of image operations
2.3.2 Relations between image operators
2.3.3 Binary operators between images
2.3.4 Composition of image operations
2.3.5 Basic operators
2.4 Algorithm of image operations
2.4.1 General form of image operations
2.4.2 Important types of algorithms
LOCAL PROCESSING OF 3D IMAGES
3.1 Classification of local operations.
3.1.1 General form
3.1.2 Classification by functions of filters
3.1.3 Classification by the form of a local function
3.2 Smoothing filter
3.2.1 Linear smoothing filter
3.2.2 Median filter and order statistics filter
3.2.3 Edge-preserving smoothing
3.2.4 Morphology filter
3.3 Difference filter
3.3.1 Significance
3.3.2 Differentials in continuous space
3.3.3 Derivatives in digitized space
3.3.4 Basic characteristics of difference filter
3.3.5 Omnidirectionalization .
3.3.6 ID difference filters and their combinations
3.3.7 3D Laplacian ,
3.3.8 2D difference filters and their combination .
3.4 Differential features of a curved surface.
3.5 Region growing (region merging)
3.5.1 Outline
3.5.2 Region expansion.
GEOMETRICAL PROPERTIES OF 3D DIGITIZED
IMAGES
4.1 Neighborhood and connectivity
4.1.1 Neighborhood,
4.1.2 Connectivity and connected component
4.2 Simplex and simplicial decomposition
4.3 Euler numbei
4.4 Local feature of a connected component and topology of a
figure
4.5 Local patterns and their characterization ,
4.5.1 2x2x2 local patterns.
4.5.2 3x3x3 local patterns.
4.5.3 Classification of the voxel state
4.5.4 Voxel state and connectivity inuex
4.6 Calculation of connectivity index and connectivity numoer
4.6.1 Basic ideas
4.6.2 Calculation of the connectivity index
4.6.3 Calculation of the connectivity number
4.7 Calculation of the Euler number
4.7.1 Triangulation method
4.7.2 Simplex counting method
4.8 Algorithm of deletability test
4.9 Path and distance functions
4.9.1 Path
4.9.2 Distance function
4.9.3 Distance function in applications
4.9.4 Improvement in distance metric
4.10 Border surface
ALGORITHM OF BINARY IMAGE PROCESSING
5.1 Introduction
5.2 Labeling of a connected component
5.3 Shrinking.
5.4 Surface thinning and axis thinning
5.4.1 Definition
5.4.2 Requirements of thinning
5.4.3 Realization - the sequential type
5.4.4 Examples of surface/axis thinning algorithms
(sequential type,
5.4.5 Surface thinning algorithm accompanying the
Euclidean distance transformation
5 4 6 Use of a ID list for auxiliary information
5.4.7 Examples of surface/axis thinning algorithm (parallel
type)
5.4.8 Experimental results
5.4.9 Points in algorithm construction
5.5 Distance transformation and skeleton
5.5.1 Definition . , , ^
5 5.2 Significance of DT and skeleton
^ W Classification of algorithms
5 5 4 Example of an algorithm - (1) squared Euclidean DT
5 5^5 Example of algorithms - (2) variable neighborhood
DT (parallel type)
5.5.6 Supplementary comments on algorithms of DT
5.5.7 Skeleton.
5 5 8 Reverse distance transformation
5 5 9 Example of RDT algorithms - (1) Euclidean squared
RDT
c: t: in Fvamnle of RDT algorithm - (2) fixed neighborhood
5 5.11 (E6x-t r1a8c-t,i oonr o2f6 -snkeeilgethobno.rhood) RDT (sequential type) .
5I12 Distance transformation of a line figure
5.6 Border surface following
5.6.1 Outline
5.6.2 Examples of algorithm
5.6.3 Restoration of a figure
5.7 Knot and link
5.7.1 Outline
5.7.2 Reduction of a digital knot
5.8 Voronoi division of a digitized image
6 ALGORITHMS FOR PROCESSING CONNECTED
COMPONENTS WITH GRAY VALUES
6.1 Distance transformation of a gray-tone image
6.1.1 Definition
6.1.2 An example of algorithm
6.2 Thinning of a gray-tone image
6.2.1 Basic idea
6.2.2 Requirements
6.2.3 Principles of thinning
6.3 Examples of algorithms - (1) integration of information
concerning density values
6.3.1 Algorithm
6.3.2 Experimental results
6.4 Examples of algorithms - (2) ridgeline following
6.4.1 Meanings of a ridgeline
6.4.2 Algorithm
6.4.3 Experiments .
7 VISUALIZATION OF 3D GRAY-TONE IMAGES
7.1 Formulation of visualization problem.
7.2 Voxel data and the polygon model.
7.2.1 Voxel surface representation
7.2.2 Marching cubes algorithm ..
7.3 Cross section, surface, and projection
7.3.1 Cross section
7.3.2 Surface
7.3.3 Projection
7.4 The concept of visualization based on ray casting - (1)
projection of a point
7.4.1 Displaying a point
7.4.2 Displaying lines
7.4.3 Displaying surfaces
7.5 The concept of visualization based on ray casting - (2)
manipulation of density values
7.6 Rendering surfaces based on ray casting - surface rendering
7.6.1 Calculation of the brightness of a surface
7.6.2 Smooth shading
7.6.3 Depth coding
7.6.4 Ray tracing
7.7 Photorealistic rendering and rendering for visualizatior
7.8 Displaying density values based on ray casting - volume
rendering
7.8.1 The algorithm of volume rendering
7.8.2 Selection of parameters
7.8.3 Front-to-back algorithm
7.8.4 Properties of volume rendering and surface rendering
7.8.5 Gradient shading