Fundamentals of Three-dimensional Digital Image Processing

Self-contained, accessible, and mathematically precise, this book serves as an introduction to the field of 3-D digital image processing, providing information that can be used immediately in practical algorithms for the analysis of 3-D data sets.

This book is a detailed description of the basics of three-dimensional digital image processing. A 3D digital image (abbreviated as 3D image below) is a digitalized representation of a 3D object or an entire 3D space, stored in a computer as a 3D array. Whereas normal digital image processing is concerned with screens that are a collection of square shapes called pixels and their corresponding density levels, the image plane in three dimensions is represented by a division into cubical graphical elements (called voxels) that represent corresponding density levels. Inthecontextofimageprocessing,in manycases3Dimageprocessingwill refer to the input of multiple 2D images and performing processing in order to understand the 3D space (or scene) that they depict. This is a result of research into how to use input from image sensors such as television cameras as a basis for learning about a 3D scene, thereby replicating the sense of vision for humans or intelligent robots, and this has been the central problem in image processing research since the 1970s. However, a completely di?erent type of image with its own new problems, the 3D digital image discussed in this book, rapidly took prominence in the 1980s, particularly in the ?eld of medical imaging. These were recordings of human bodies obtained through computed (or computerized) tomography (CT),imagesthatrecordednotonlytheexternal,visiblesurfaceofthesubject but also, to some degree of resolution, its internal structure. This was a type of image that no one had experienced before.

Explains fundamental techniques for 3-dimensional image processing and analysis For each technique, uniform and coherent theories are described, with a detailed description of the algorithms for reducing the theories to practice Balanced descriptions of the theories and algorithms facilitate the readers' precise understanding of the techniques, in an accessible way

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There are many areas of science and engineering where three-dimensional (3-D) discrete data are collected and analyzed, such as medical imaging and geoscience. To design and to prove the validity of computational procedures for processing and analysis of such data, the need for a mathematical theory and algorithms for image processing is essential.

Self-contained, accessible, and mathematically precise, this book serves as an introduction to the field of 3-D digital image processing, providing information that can be used immediately in practical algorithms for the analysis of 3-D data sets. By presenting problems of processing and analysis of practical 3-D data sets, readers will find the descriptions clear and accessible as concepts and methods are carefully introduced, defined, and illustrated with examples.

A key textbook for graduates and resource for all working in areas of multidimensional image processing and analysis, this book is also excellent for self-study for practitioners in the field of 3-D digital image processing.

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From the contents

Introduction.- Models of Images and Image Operations.- Continuous and Digitized Images.- Model of Image Operations.- Algorithm of Image Operations.- Local Processing of 3D Images.- Classification of Local Operations.- Smoothing Filter.- Difference Filter.- Differential Features of Curved Surface.- Geometric Properties of Three-Dimensional Digitized Images.- Neighbourhood and Connectivity.- Simplex and Simplicious Decomposition.- Local Patterns and their Characterization.- Calculation of the Euler Number.- Algorithm of Binary Image Processing.- Labeling of a Connected Component.- Distance Transformation and Skeleton.- Algorithms for Processing Connected Components with Gray Values.- Distance Transformation of a Gray-Tone Image.- Thinning of a Gray-Tone Image.- Visualization of 3D Gray-Tone Images.- Concept of Visualization Based upon Ray Casting (1) Projection of a Point.- Concept of Visualization Based on Ray Casting (2) Manipulation of Density Values.