A statistical rationalisation of Hartley's normalised eight-point algorithm

Date

2003

Authors

Chojnacki, W.
Brooks, M.
Van Den Hengel, A.
Gawley, D.

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Feretti, M.

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Conference paper

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Proceedings, 12th International Conference on Image Analysis and Processing : Mantova, Italy, September 17 to 19, 2003 / pp. 334-339

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Wojciech Chojnacki, Michael J. Brooks, Anton van den Hengel, Darren Gawley

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International Conference on Image Analysis and Processing (12th : 2003 : Mantova, Italy)

Abstract

The eight-point algorithm of Hartley occupies an important place in computer vision, notably as a means of providing an initial value of the fundamental matrix for use in iterative estimation methods. In this paper, a novel explanation is given for the improvement in performance of the eight-point algorithm that results from using normalised data. A first step is singling out a cost function that the normalised algorithm acts to minimise. The cost function is then shown to be statistically better founded than the cost function associated with the non-normalised algorithm. This augments the original argument that improved performance is due to the better conditioning of a pivotal matrix. Experimental results are given that support the adopted approach. This work continues a wider effort to place a variety of estimation techniques within a coherent framework.

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