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Type: Journal article
Title: On the fitting of surfaces to data with covariances
Author: Chojnacki, W.
Brooks, M.
Van Den Hengel, A.
Gawley, D.
Citation: IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000; 22(11):1294-1303
Publisher: IEEE Computer Soc
Issue Date: 2000
ISSN: 0162-8828
Statement of
Wojciech Chojnacki, Michael J. Brooks, Anton van den Hengel and Darren Gawley
Abstract: We consider the problem of estimating parameters of a model described by an equation of special form. Specific models arise in the analysis of a wide class of computer vision problems, including conic fitting and estimation of the fundamental matrix. We assume that noisy data are accompanied by (known) covariance matrices characterizing the uncertainty of the measurements. A cost function is first obtained by considering a maximum-likelihood formulation and applying certain necessary approximations that render the problem tractable. A Newton-like iterative scheme is then generated for determining a minimizer of the cost function. Unlike alternative approaches such as Sampson's method or the renormalization technique, the new scheme has as its theoretical limit the minimizer of the cost function. Furthermore, the scheme is simply expressed, efficient, and unsurpassed as a general technique in our testing. An important feature of the method is that it can serve as a basis for conducting theoretical comparison of various estimation approaches.
Description: Copyright © 2000 IEEE
RMID: 0001001729
DOI: 10.1109/34.888714
Appears in Collections:Computer Science publications

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