A complete overview of the fundamentals of three-dimensional descriptive geometry From an overview of the history of descriptive geometry to the application of the principles of descriptive geometry to real-world scenarios, Fundamentals of Three-Dimensional Descriptive Geometry provides a comprehensive look at the topic. Used throughout the disciplines of science, engineering, and architecture, descriptive geometry is crucial for everything from understanding the various segments and inter-workings of structural systems to grasping the relationship of molecules in a chemical compound. For those requiring a full accounting of the fundamentals of three-dimensional descriptive geometry, this text is a definitive and comprehensive resource.

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.

The first attempt to investigate this pervasive biological phenomenon from a variety of disciplines, from physics to mathematics to biology.

A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.