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Euclidean Reconstruction and Reprojection Up to Subgroups

Authors
  • Ma, Yi1
  • Soatto, Stefano2
  • Košecká, Jana1
  • Sastry, Shankar1
  • 1 UC Berkeley, Berkeley, CA, 94720, USA , Berkeley
  • 2 Washington University, St. Louis, MO, 63130, USA , St. Louis
Type
Published Article
Journal
International Journal of Computer Vision
Publisher
Springer-Verlag
Publication Date
Jul 01, 2000
Volume
38
Issue
3
Pages
219–229
Identifiers
DOI: 10.1023/A:1008143307025
Source
Springer Nature
Keywords
License
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Abstract

The necessary and sufficient conditions for being able to estimate scene structure, motion and camera calibration from a sequence of images are very rarely satisfied in practice. What exactly can be estimated in sequences of practical importance, when such conditions are not satisfied? In this paper we give a complete answer to this question. For every camera motion that fails to meet the conditions, we give explicit formulas for the ambiguities in the reconstructed scene, motion and calibration. Such a characterization is crucial both for designing robust estimation algorithms (that do not try to recover parameters that cannot be recovered), and for generating novel views of the scene by controlling the vantage point. To this end, we characterize explicitly all the vantage points that give rise to a valid Euclidean reprojection regardless of the ambiguity in the reconstruction. We also characterize vantage points that generate views that are altogether invariant to the ambiguity. All the results are presented using simple notation that involves no tensors nor complex projective geometry, and should be accessible with basic background in linear algebra.

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