### Abstract

A number of recent papers have argued that invariants do not exist for three dimensional point sets in general position. This has often been misinterpreted to mean that invariants cannot be computed for any three dimensional structure. This paper proves by example that although the general statement is true, invariants to exist for structured three dimensional point sets. Projective invariants are derived for two classes of object: the first is for points that lie on the vertices of polyhedra, and the second for objects that are projectively equivalent to ones possessing a bilateral symmetry. The motivations for computing such invariants are twofold: firstly they can be used for recognition; secondly they can be used to compute projective structure. Examples of invariants computed from real images are given.

Original language | English (US) |
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Title of host publication | 1993 IEEE 4th International Conference on Computer Vision |

Publisher | Publ by IEEE |

Pages | 573-582 |

Number of pages | 10 |

ISBN (Print) | 0818638729 |

State | Published - Jan 1 1993 |

Externally published | Yes |

Event | 1993 IEEE 4th International Conference on Computer Vision - Berlin, Ger Duration: May 11 1993 → May 14 1993 |

### Publication series

Name | 1993 IEEE 4th International Conference on Computer Vision |
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### Other

Other | 1993 IEEE 4th International Conference on Computer Vision |
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City | Berlin, Ger |

Period | 5/11/93 → 5/14/93 |

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*1993 IEEE 4th International Conference on Computer Vision*(pp. 573-582). (1993 IEEE 4th International Conference on Computer Vision). Publ by IEEE.

**Extracting projective structure from single perspective views of 3D point sets.** / Rothwell, C. A.; Forsyth, David Alexander; Zisserman, A.; Mundy, J. L.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*1993 IEEE 4th International Conference on Computer Vision.*1993 IEEE 4th International Conference on Computer Vision, Publ by IEEE, pp. 573-582, 1993 IEEE 4th International Conference on Computer Vision, Berlin, Ger, 5/11/93.

}

TY - GEN

T1 - Extracting projective structure from single perspective views of 3D point sets

AU - Rothwell, C. A.

AU - Forsyth, David Alexander

AU - Zisserman, A.

AU - Mundy, J. L.

PY - 1993/1/1

Y1 - 1993/1/1

N2 - A number of recent papers have argued that invariants do not exist for three dimensional point sets in general position. This has often been misinterpreted to mean that invariants cannot be computed for any three dimensional structure. This paper proves by example that although the general statement is true, invariants to exist for structured three dimensional point sets. Projective invariants are derived for two classes of object: the first is for points that lie on the vertices of polyhedra, and the second for objects that are projectively equivalent to ones possessing a bilateral symmetry. The motivations for computing such invariants are twofold: firstly they can be used for recognition; secondly they can be used to compute projective structure. Examples of invariants computed from real images are given.

AB - A number of recent papers have argued that invariants do not exist for three dimensional point sets in general position. This has often been misinterpreted to mean that invariants cannot be computed for any three dimensional structure. This paper proves by example that although the general statement is true, invariants to exist for structured three dimensional point sets. Projective invariants are derived for two classes of object: the first is for points that lie on the vertices of polyhedra, and the second for objects that are projectively equivalent to ones possessing a bilateral symmetry. The motivations for computing such invariants are twofold: firstly they can be used for recognition; secondly they can be used to compute projective structure. Examples of invariants computed from real images are given.

UR - http://www.scopus.com/inward/record.url?scp=0027149309&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027149309&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0027149309

SN - 0818638729

T3 - 1993 IEEE 4th International Conference on Computer Vision

SP - 573

EP - 582

BT - 1993 IEEE 4th International Conference on Computer Vision

PB - Publ by IEEE

ER -