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Type: Journal article
Title: On the consistency of the normalized eight-point algorithm
Author: Chojnacki, W.
Brooks, M.
Citation: Journal of Mathematical Imaging and Vision, 2007; 28(1):19-27
Publisher: Kluwer Academic Publ
Issue Date: 2007
ISSN: 0924-9907
Statement of
Wojciech Chojnacki and Michael J. Brooks
Abstract: A recently proposed argument to explain the improved performance of the eight-point algorithm that results from using normalized data (Chojnacki, W., et al. in IEEE Trans. Pattern Anal. Mach. Intell. 25(9):1172–1177, 2003) relies upon adoption of a certain model for statistical data distribution. Under this model, the cost function that underlies the algorithm operating on the normalized data is statistically more advantageous than the cost function that underpins the algorithm using unnormalized data. Here we extend this explanation by introducing a more refined, structured model for data distribution. Under the extended model, the normalized eight-point algorithm turns out to be approximately consistent in a statistical sense. The proposed extension provides a link between the existing statistical rationalization of the normalized eight-point algorithm and the approach of Mühlich and Mester for enhancing total least squares estimation methods via equilibration. The paper forms part of a wider effort to rationalize and interrelate foundational methods in vision parameter estimation.
Keywords: Epipolar equation; Consistency; Fundamental matrix; Bias; Data normalization; Eight-point algorithm
RMID: 0020072391
DOI: 10.1007/s10851-007-0009-6
Appears in Collections:Computer Science publications

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