## Abstract

Object recognition starts from a set of image measurements (including locations of points, lines, surfaces, color, and shading), which provides access into a database where representations of objects are stored. We describe a complexity theory of indexing, a meta-analysis which identifies the best set of measurements (up to algebraic transformations) such that: (1) the representation of objects are linear subspaces and thus easy to learn; (2) direct indexing is efficient since the linear subspaces are of minimal rank. The index complexity is determined via a simple process, equivalent to computing the rank of a matrix. We readily re-derive the index complexity of the few previously analyzed cases. We then compute the best index for new cases: 6 points in one perspective image, and 6 directions in one para-perspective image; the most efficient representation of a color is a plane in 3D space. For future applications with any vision problem where the relations between shape and image measurements can be written down in an algebraic form, we give an automatic process to construct the most efficient database that can be directly obtained by learning from examples.

Original language | English |
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Title of host publication | Computer Vision – ECCV 1996 - 4th European Conference on Computer Vision, Proceedings |

Editors | Bernard Buxton, Roberto Cipolla |

Publisher | Springer Verlag |

Pages | 660-670 |

Number of pages | 11 |

ISBN (Print) | 3540611223, 9783540611226 |

DOIs | |

State | Published - 1996 |

Event | 4th European Conference on Computer Vision, ECCV 1996 - Cambridge, United Kingdom Duration: 15 Apr 1996 → 18 Apr 1996 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1064 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 4th European Conference on Computer Vision, ECCV 1996 |
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Country/Territory | United Kingdom |

City | Cambridge |

Period | 15/04/96 → 18/04/96 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 1996.