## Abstract

The geometry of 1 point in N images under perspective projection is thoroughly investigated, identifying bilinear, trilinear, and quadrilinear relations between the projections of 1 point, 2, 3, and 4 frames respectively. A complete description of the problem is provided. A formalism is employed in which multiframe and multi-point geometries appear in symmetry. The bilinear equations for 6 points, trilinear equations for 7 points, and quadrilinear equations for 8 points are derived. It is shown that the quadrilinear equations are dependent on the bilinear and trilinear equations and that adding more points will not generate any new equation. The new equations are used to design new algorithms for the reconstruction of shape from many frames, and for learning invariant relations for indexing into a data-base.

Original language | American English |
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Pages | 58-65 |

Number of pages | 8 |

State | Published - 1995 |

Event | Proceedings of the 1995 IEEE Workshop on Representation of Visual Scenes - Cambridge, MA, USA Duration: 24 Jun 1995 → 24 Jun 1995 |

### Conference

Conference | Proceedings of the 1995 IEEE Workshop on Representation of Visual Scenes |
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City | Cambridge, MA, USA |

Period | 24/06/95 → 24/06/95 |