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Type: Journal article
Title: Rationalising the renormalisation method of Kanatani
Author: Chojnacki, W.
Brooks, M.
Van Den Hengel, A.
Citation: Journal of Mathematical Imaging and Vision, 2001; 14(1):21-38
Publisher: Kluwer Academic Publ
Issue Date: 2001
ISSN: 0924-9907
Statement of
Wojciech Chojnacki, Michael J. Brooks and Anton Van Den Hengel
Abstract: The renormalisation technique of Kanatani is intended to iteratively minimise a cost function of a certain form while avoiding systematic bias inherent in the common method of minimisation due to Sampson. Within the computer vision community, the technique has generally proven difficult to absorb. This work presents an alternative derivation of the technique, and places it in the context of other approaches. We first show that the minimiser of the cost function must satisfy a special variational equation. A Newton-like, fundamental numerical scheme is presented with the property that its theoretical limit coincides with the minimiser. Standard statistical techniques are then employed to derive afresh several renormalisation schemes. The fundamental scheme proves pivotal in the rationalising of the renormalisation and other schemes, and enables us to show that the renormalisation schemes do not have as their theoretical limit the desired minimiser. The various minimisation schemes are finally subjected to a comparative performance analysis under controlled conditions.
Keywords: statistical methods; surface fitting; covariance matrix; maximum likelihood; renormalisation; conic fitting; fundamental matrix estimation
Description: The original publication can be found at
Rights: © 2001 Kluwer Academic Publishers. Manufactured in The Netherlands.
RMID: 0020010221
DOI: 10.1023/A:1008355213497
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Appears in Collections:Computer Science publications

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