Duality of multi-point and multi-frame geometry: Fundamental shape matrices and tensors

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Scopus citations


We provide a complete analysis of the geometry of N points in 1 image, employing a formalism in which multi-frame and multi-point geometries appear in symmetry: points and projections are interchangeable. We derive bilinear equations for 6 points, trilinear equations for 7 points, and quadrilinear equations for 8 points. The new equations are used to design new algorithms for the reconstruction of projective shape from many frames. Shape is represented by shape descriptors, which are sufficient for object recognition, and for the simulation of new images of the object. We further propose a linear shape reconstruction scheme which uses all the available data- all points and all frames - simultaneously. Unlike previous approaches, the equations developed here lead to direct and linear computation of shape, without going through the cameras' geometry.

Original languageAmerican English
Title of host publicationComputer Vision – ECCV 1996 - 4th European Conference on Computer Vision, Proceedings
EditorsBernard Buxton, Roberto Cipolla
PublisherSpringer Verlag
Number of pages11
ISBN (Print)3540611231, 9783540611233
StatePublished - 1996
Event4th European Conference on Computer Vision, ECCV 1996 - Cambridge, United Kingdom
Duration: 15 Apr 199618 Apr 1996

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference4th European Conference on Computer Vision, ECCV 1996
Country/TerritoryUnited Kingdom

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1996.


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