Departmental Papers (CIS)

Date of this Version

May 2002

Document Type

Conference Paper

Comments

Postprint version. Published in Lecture Notes in Computer Science, Volume 2351, Proceedings of the 7th European Conference on Computer Vision, Part II, 2002 (ECCV 2002), pages 140-154.
Publisher URL: http://springerlink.metapress.com/link.asp?id=m9lumq54671rt2al

Abstract

The geometry of two uncalibrated views obtained with a parabolic catadioptric device is the subject of this paper. We introduce the notion of circle space, a natural representation of line images, and the set of incidence preserving transformations on this circle space which happens to equal the Lorentz group. In this space, there is a bilinear constraint on transformed image coordinates in two parabolic catadioptric views involving what we call the catadioptric fundamental matrix. We prove that the angle between corresponding epipolar curves is preserved and that the transformed image of the absolute conic is in the kernel of that matrix, enabling thus euclidean reconstruction from two views. We establish the necessary and sufficient conditions for a matrix to be a catadioptric fundamental matrix.

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Date Posted: 30 April 2005