Submitted to the IJCV, manuscript No. (will be inserted by the editor) A Generalized Projective Reconstruction Theorem

Abstract This paper presents a generalized version of the classic projective reconstruction theorem which helps to choose or assess depth constraints for projective depth es-timation algorithms. The theorem shows that projective re-construction is possible under a much weaker restriction than requiring all estimated projective depths to be nonzero. This result enables us to present a class of depth constraints under which any reconstruction of cameras and points pro-jecting 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 iter-ative depth estimation algorithms and projective reconstruc-tion via rank minimization. Our theory is verified by running experiments on both synthetic and real data. Keywords multiple view geometry · projective recon-struction · Projective Reconstruction Theorem · projective factorization · projective depths · depth constraints NICTA is funded by the Australian Government as represented by th