A Generalized Projective Reconstruction Theorem and Depth Constraints for Projective Factorization
Artikel i vetenskaplig tidskrift, 2015

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.

Projective reconstruction

Projective factorization

Projective reconstruction theorem

Projective depths

Multiple view geometry

Constraints on projective depths


Seyed Behrooz Nasihatkon

Chalmers, Signaler och system, Signalbehandling och medicinsk teknik, Digitala bildsystem och bildanalys

R. Hartley

CSIRO Data61

Australian National University

J. Trumpf

Australian National University

International Journal of Computer Vision

0920-5691 (ISSN)

Vol. 115 2 87-114





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