A Generalized Projective Reconstruction Theorem and Depth Constraints for Projective Factorization

Behrooz Nasihatkon*, Richard Hartley, Jochen Trumpf

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    11 Citations (Scopus)

    Abstract

    This paper presents a generalized version of the classic projective reconstruction theorem which helps to choose or assess depth constraints for projective depth estimation algorithms. The theorem shows that projective reconstruction is possible under a much weaker constraint than requiring all estimated projective depths to be nonzero. This result enables us to present classes of depth constraints under which any reconstruction of cameras and points projecting into given image points is projectively equivalent to the true camera-point configuration. It also completely specifies the possible wrong configurations allowed by other constraints. We demonstrate the application of the theorem by analysing several constraints used in the literature, as well as presenting new constraints with desirable properties. We mention some of the implications of our results on iterative depth estimation algorithms and projective reconstruction via rank minimization. Our theory is verified by running experiments on both synthetic and real data.

    Original languageEnglish
    Pages (from-to)87-114
    Number of pages28
    JournalInternational Journal of Computer Vision
    Volume115
    Issue number2
    DOIs
    Publication statusPublished - 1 Nov 2015

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