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Two-Way Ambiguity in 2D Projective Reconstruction from Three Uncalibrated 1D Images

Long Quan 1
1 MOVI - Modeling, localization, recognition and interpretation in computer vision
GRAVIR - IMAG - Graphisme, Vision et Robotique, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
Abstract : We show that there is in genral a two-way ambiguity for 2D projective reconstruction from three uncalilbrated 1D views, independent of the number of point correspondences. The two distinct projective reconstructions are exactly related by a quadratic transformation with the three camera centers as fundamental points. Unique 2D reconstruction is possible only when the three camera centers are aligned. By Carlsson duality, there is a dual two-way ambiguity for 2D projective reconstruction from six point correspondences, independent of the number of 1D views. The theoretical results are demonstrated on numerical examples.
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https://hal.inria.fr/inria-00590145
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Submitted on : Tuesday, May 3, 2011 - 9:25:45 AM
Last modification on : Friday, June 26, 2020 - 4:04:03 PM
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Long Quan. Two-Way Ambiguity in 2D Projective Reconstruction from Three Uncalibrated 1D Images. IEEE Transactions on Pattern Analysis and Machine Intelligence, Institute of Electrical and Electronics Engineers, 2001, 23 (2), pp.212--216. ⟨10.1109/34.908971⟩. ⟨inria-00590145⟩

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