Multiple View Geometry in Computer Vision

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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.

Multiple View Geometry in Computer Vision Review

This book is very complete and rigorous in its explanations of the theory. However, I just think I like the approach in An Invitation to 3-D Vision a bit better. This book is better illustrated than that one and is more careful in its explanations, but this book just seems more focused on providing complete proofs than giving you a feel for how you would approach a real problem. Even the exercises are more along the lines of proofs. I like how An Invitation to 3-D Vision ends the book with a complete example. In all fairness, though, this book does have quite a bit of Matlab code on its website.

The book begins with some background material on 2D and 3D geometry. Then the author explains single-view geometry and how cameras map an image in 3D space to an image. Two-view geometry is next, with the author describing the epipolar geometry of two cameras ahd projective reconstruction from resulting image map correspondences. Part three of the book extends ideas to three cameras and the resulting trifocal geometry. The final section of the book takes the algorithms of the book to N views. Thus this book has a simple and straightforward structure that belies the complexity of the material.

If you are really researching this subject you should probably have this book for explanation, illustrations, and rigor, and the Invitation book for enlightenment through a good example-based approach. You should also have Introductory Techniques for 3-D Computer Vision as a text on the individual pieces of algorithms involved in 3D vision. And don't even think about getting into this subject unless you already have a firm foundation in linear algebra, image processing, and computer vision in general as found in Computer Vision, which is my favorite introductory computer vision text.

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