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The Geometry of Multiple Images: The Laws That Govern the Formation of Multiple Images of a Scene and Some of Their Applications
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TLDR
The state of knowledge in one subarea of vision is described, the geometric laws that relate different views of a scene from the perspective of various types of geometries, which is a unified framework for thinking about many geometric problems relevant to vision.Abstract:
From the Publisher:
with contributions from Theo Papadopoulo
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.read more
Citations
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Journal ArticleDOI
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Book ChapterDOI
Generalized Rank Conditions in Multiple View Geometry with Applications to Dynamical Scenes
Kun Huang,Robert M. Fossum,Yi Ma +2 more
TL;DR: It is shown that geometric constraints that govern multiple images of hyperplanes in Rn, as well as any incidence conditions among these hyperplanes (such as inclusion, intersection, and restriction), can be systematically captured through certain rank conditions on the so-called multiple view matrix.
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Proceedings Article
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