Direct estimation of homogeneous vectors: an ill-solved problem in computer vision

Authors:
Matthew Harker;Paul O'Leary
Affiliations:
Institute for Automation, University of Leoben, Leoben, Austria;Institute for Automation, University of Leoben, Leoben, Austria
Venue:
ICVGIP'06 Proceedings of the 5th Indian conference on Computer Vision, Graphics and Image Processing
Year:
2006

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Abstract

Computer Vision theory is firmly rooted in Projective Geometry, whereby geometric objects can be effectively modeled by homogeneous vectors. We begin from Gauss's 200 year old theorem of least squares to derive a generic algorithm for the direct estimation of homogeneous vectors. We uncover the common link of previous methods, showing that direct estimation is not an ill-conditioned problem as is the popular belief, but has merely been an ill-solved problem. Results show improvements in goodness-of-fit and numerical stability, and demonstrate that “data normalization” is unnecessary for a well-founded algorithm.