On degeneracy of linear reconstruction from three views: Linear line complex and applications

Gideon P. Stein, Amnon Shashua

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

5 Scopus citations

Abstract

This paper investigates the linear degeneracies of projective structure estimation from line features across three views. We show that the rank of the linear system of equations for recovering the trilinear tensor of three views reduces to 23 (instead of 26) when the scene is a Linear Line Complex (set of lines in space intersecting at a common line). The LLC situation is only linearly degenerate, and one can obtain a unique solution when the admissibility constraints of the tensor are accounted for. The line configuration described by an LLC, rather than being some obscure case, is in fact quite typical. It includes, as a particular example, the case of a camera moving down a hallway in an office environment or down an urban street. Furthermore, an LLC situation may occur as an artifact such as in direct estimation from spatio-temporal derivatives of image brightness. Therefore, an investigation into degeneracies and their remedy is important also in practice.

Original languageAmerican English
Title of host publicationComputer Vision - ECCV 1998 - 5th European Conference on Computer Vision, Proceedings
EditorsBernd Neumann, Hans Burkhardt
PublisherSpringer Verlag
Pages862-878
Number of pages17
ISBN (Print)3540646132, 9783540646136
DOIs
StatePublished - 1998
Event5th European Conference on Computer Vision, ECCV 1998 - Freiburg, Germany
Duration: 2 Jun 19986 Jun 1998

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1407
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference5th European Conference on Computer Vision, ECCV 1998
Country/TerritoryGermany
CityFreiburg
Period2/06/986/06/98

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1998.

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