Projective Transformations
Projective Transformations

Author: P. S. Modenov

Publisher: Academic Press

Published: 2014-05-12

Total Pages: 149

ISBN-13: 1483261492

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Geometric Transformations, Volume 2: Projective Transformations focuses on collinearity-preserving transformations of the projective plane. The book first offers information on projective transformations, as well as the concept of a projective plane, definition of a projective mapping, fundamental theorems on projective transformations, cross ratio, and harmonic sets. Examples of projective transformations, projective transformations in coordinates, quadratic curves in the projective plane, and projective transformations of space are also discussed. The text then examines inversion, including the power of a point with respect to a circle, definition and properties of inversion, and circle transformations and the fundamental theorem. The manuscript elaborates on the principle of duality. The manuscript is designed for use in geometry seminars in universities and teacher-training colleges. The text can also be used as supplementary reading by high school teachers who want to extend their range of knowledge on projective transformations.

Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision

Author: Richard Hartley

Publisher: Cambridge University Press

Published: 2004-03-25

Total Pages: 676

ISBN-13: 1139449141

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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.