## Applications of Invariance in Computer Vision: Second Joint European - US Workshop, Ponta Delgada, Azores, Portugal, October 9 - 14, 1993. ProceedingsThis book is the proceedings of the Second Joint European-US Workshop on Applications of Invariance to Computer Vision, held at Ponta Delgada, Azores, Portugal in October 1993. The book contains 25 carefully refereed papers by distinguished researchers. The papers cover all relevant foundational aspects of geometric and algebraic invariance as well as applications to computer vision, particularly to recovery and reconstruction, object recognition, scene analysis, robotic navigation, and statistical analysis. In total, the collection of papers, together with an introductory survey by the editors, impressively documents that geometry, in its different variants, is the most successful and ubiquitous tool in computer vision. |

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### Contents

Cartans Moving Frame Method and Its Application to the Geometry and Evolution of Curves in the Euclidean Affine and Projective Planes | 11 |

Representation of ThreeDimensional Object Structure as CrossRatios of Determinants of Stereo Image Points | 47 |

A Case Against Epipolar Geometry | 69 |

Image Correspondence Constraints and 3D Structure Recovery | 89 |

How to Use the Cross Ratio to Compute Projective Invariants from two Images | 107 |

On Geometric and Algebraic Aspects of 3D Affine and Projective Structures from Perspective 2D Views | 127 |

An Effective Tool for Computing Invariants in Computer Vision | 145 |

Matching Perspective Views of Parallel Plane Structures | 165 |

Affine Reconstruction from Perspective Image Pairs Obtained by a Translating Camera | 297 |

Using Invariance and QuasiInvariance for the Segmentation and Recovery of Curved Objects | 317 |

Representations of 3D Objects that Incorporate Surface Markings | 341 |

Modelbased invariant Functions and Their Use for Recognition | 357 |

Recognition | 379 |

Integration of Multiple Feature Groups and Multiple Views into A 3D Object Recognition System | 381 |

Hierarchical Object Description Using Invariants | 397 |

Generalizing Invariants for 3D to 2D Matching | 415 |

Invariants for Recovering Shape from Shading | 185 |

Fundamental Difficulties with Projective Normalization of Planar Curves | 199 |

Invariant Size Functions | 215 |

Recovery | 235 |

Euclidean Reconstruction from Uncalibrated Views | 237 |

Accurate Projective Reconstruction | 257 |

Applications of Motion Field of Curves | 277 |

Alignment and Invariance | 435 |

Statistics | 451 |

Classification Based on the Cross Ratio | 453 |

Correspondence of Coplanar Features Through P˛Invariant Representations | 473 |

Integrating Algebraic Curves and Surfaces Algebraic Invariants and Bayesian Methods for 2D and 3D Object Recognition | 493 |

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### Common terms and phrases

3D object affine invariant affine structure affine transformation algebraic algorithm arc length axis calibration camera Circular PRGCs coefficients collinear Computer Vision configuration conic constraints contours coplanar corresponding points cross ratio cross-section defined denote derived determine differential distance epipolar geometry epipole equation Euclidean Euclidean transformation example Faugeras Figure five-tuples four points frames of order fundamental matrix given hypotheses IEEE image coordinates image plane image points image space indexing intersection invariant functions linear combinations Mahalanobis distance matching measuring function method model group motion Mundy noise object recognition obtained pair parameters perspective pixel planar curves plane at infinity polynomial problem Proceedings projective invariants projective transformation properties recognition system reconstruction recovered reference points repeated structure representation rotation scaling scene shape SHGC shown solution stereo structure from motion surface symmetry Table Theorem tion translation twisted cubic uncalibrated values vector views Zisserman

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