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|Title:||Rationalising the renormalisation method of Kanatani|
Van Den Hengel, A.
|Citation:||Journal of Mathematical Imaging and Vision, 2001; 14(1):21-38|
|Publisher:||Kluwer Academic Publ|
|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 www.springerlink.com|
|Rights:||© 2001 Kluwer Academic Publishers. Manufactured in The Netherlands.|
|Appears in Collections:||Computer Science publications|
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