A Generalized Projective Reconstruction Theorem for Factorization-Based Algorithms

Behrooz Nasihatkon (NICTA)

COMPUTER VISION AND ROBOTICS SERIES

DATE: 2013-08-29
TIME: 16:00:00 - 17:00:00
LOCATION: NICTA - 7 London Circuit
CONTACT: JavaScript must be enabled to display this email address.

ABSTRACT:
In this seminar I will talk about our recent submission on generalizing the classic Theorem of Projective Reconstruction for the analysis of the projective depth estimation algorithms. Especially, the aim is to provide a theoretical basis for the choice and verification of constraints on projective depths for the factorization-based projective reconstruction techniques. In this talk, first we argue that while the classic Theorem of Projective Reconstruction is useful enough for dealing with such approaches as the so-called tensor-based techniques, its assumptions is too limiting for the analysis of a large group of efficient factorization-based algorithms. We then present the generalized theorem showing that projective reconstruction is provable under much weaker assumptions than what presumed in the classic theorem. Especially, we show that it is not necessary to require, in advance, that all the estimated projective depths are nonzero. This gives a lot of flexibility in the choice of valid ways of constraining the projective depths such that any solution to the projective factorization problem is equal to the true camera-point configuration up to projectivity. It also completely specifies the possible wrong configurations allowed under other constraints. The application of the theorem is demonstrated by analysing several constraints used in the literature, as well as presenting new constraints with desirable properties. We also briefly talk about the implications of the theorem on the rank-minimization approach to projective factorization. The talk is concluded by demonstrating numerical experimental results and discussing unsolved problems for further research.

Those who are interested can obtain a copy of the submission here http://users.cecs.anu.edu.au/~u4716751/depth-const.pdf