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An invitation to 3-D vision. From images to geometric models. (English) Zbl 1043.65040

Interdisciplinary Applied Mathematics 26. New York, NY: Springer (ISBN 0-387-00893-4/hbk). xx, 526 p. (2004).
This very interesting book is a great book teaching how to go from two-dimensional (2D)-images to three-dimensional (3D)-models of the geometry of a scene. It describes algorithms designed to estimate 3D-structure, motion, and camera calibration from a collection of images.
Given a number of 2D images of scenes that satisfy these assumptions, this book discusses the following questions: To what extent and how can we estimate the 3D-shape of each object? To what extent can we recover the motion of each object relative to the camera? To what extent can we recover a model of the geometry of the camera itself?
A good part of this book develops the foundations of an appropriate mathematical approach necessary for solving those difficult problems.
So in chapter V (appendices) basic facts from linear algebra, least-variance estimation and filtering, and nonlinear optimization are presented. The chapter I discusses introductory material, among other things the representation of a 3D moving scene, image formation, and image primitives and correspondence (correspondence of geometric features, local deformation models, matching point features, point feature selection, and tracking line features).
The chapter II (geometry of two views) discusses the reconstruction from two calibrated views, the reconstruction from two uncalibrated views, and the estimation of multiple motions from two views.
In chapter III (geometry of multiple views) the following topics are presented: Multiple-view geometry of points and lines, extension to general incidence relations, and geometry and reconstruction from symmetry.
In chapter IV applications to step-by-step building of a 3D-model from images (feature correspondence, projective reconstruction, visualization) and visual feedback (autonomous car driving, helicopter landing) are discussed.
Exercises (drill exercises, advanced exercises and programming exercises) are provided at the end of each chapter.

MSC:

65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
68-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science
51N05 Descriptive geometry
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
68U10 Computing methodologies for image processing