## Three-dimensional Computer Vision: A Geometric ViewpointThis monograph by one of the world's leading vision researchers provides a thorough,mathematically rigorous exposition of a broad and vital area in computer vision: the problems andtechniques related to three-dimensional (stereo) vision and motion. The emphasis is on usinggeometry to solve problems in stereo and motion, with examples from navigation and objectrecognition.Faugeras takes up such important problems in computer vision as projective geometry,camera calibration, edge detection, stereo vision (with many examples on real images), differentkinds of representations and transformations (especially 3-D rotations), uncertainty and methods ofaddressing it, and object representation and recognition. His theoretical account is illustratedwith the results of actual working programs.Three-Dimensional Computer Vision proposes solutions toproblems arising from a specific robotics scenario in which a system must perceive and act. Movingabout an unknown environment, the system has to avoid static and mobile obstacles, build models ofobjects and places in order to be able to recognize and locate them, and characterize its own motionand that of moving objects, by providing descriptions of the corresponding three-dimensionalmotions. The ideas generated, however, can be used indifferent settings, resulting in a general bookon computer vision that reveals the fascinating relationship of three-dimensional geometry and theimaging process.Olivier Faugeras is Research Director of the Computer Vision and Robotics Laboratoryat INRIA Sophia-Antipolis and a Professor of Applied Mathematics at the Ecole Polytechnique inParis. |

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### Contents

Projective Geometry | 7 |

Modeling and Calibrating Cameras | 33 |

Edge Detection | 69 |

derivative | 90 |

magnitude | 108 |

Representing Geometric Primitives and Their Uncertainty | 125 |

Stereo Vision | 165 |

Determining Discrete Motion from Points and Lines | 245 |

Motion Fields of Curves | 341 |

Interpolating and Approximating ThreeDimensional Data | 403 |

Recognizing and Locating Objects and Places | 483 |

robot | 534 |

Answers to Problems | 559 |

A Constrained Optimization | 623 |

635 | |

659 | |