The Geometry of Multiple Images: The Laws that Govern the Formation of Multiple Images of a Scene and Some of Their Applications
Over the last forty years, researchers have made great strides in elucidating the laws of image formation, processing, and understanding by animals, humans, and machines. This book describes the state of knowledge in one subarea of vision, the geometric laws that relate different views of a scene. Geometry, one of the oldest branches of mathematics, is the natural language for describing three-dimensional shapes and spatial relations. Projective geometry, the geometry that best models image formation, provides a unified framework for thinking about many geometric problems relevant to vision. The book formalizes and analyzes the relations between multiple views of a scene from the perspective of various types of geometries. A key feature is that it considers Euclidean and affine geometries as special cases of projective geometry.
Images play a prominent role in computer communications. Producers and users of images, in particular three-dimensional images, require a framework for stating and solving problems. The book offers a number of conceptual tools and theoretical results useful for the design of machine vision algorithms. It also illustrates these tools and results with many examples of real applications.
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3D points absolute conic affine basis affine coordinates affine space affine transformation algebraic algorithm calibration canonical frame cap-product Chapter coefficients Computer Vision consider coordinate system coordinate vector cross-ratio defined definition denoted described dual epipolar constraint epipolar geometry epipolar lines epipole equal equivalent Essential matrix estimation example extensors of step Faugeras Figure Fundamental matrix given homography hyperplanes infinity homography INRIA intrinsic parameters Kruppa equations linear mapping method minimization motion nonlinear obtained optical center optical ray orthogonal pair parallel parameterization perspective projection perspective projection matrices pinhole pixel planar homography planar morphism plane at infinity point at infinity point of intersection problem projection matrices projective basis projective coordinates projective geometry projective space projective subspace Proof quadric ratio reconstruction recover relation representation represented respectively retinal plane rigid displacement rotation satisfy scale factor second image Section self-calibration solution stereo rig Theorem three views Trifocal tensor vector space
Page 652 - Professor of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology.
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