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Type: Conference paper
Title: Generalised Principal Component Analysis: exploiting inherent parameter constraints
Author: Chojnacki, W.
van den Hengel, A.
Brooks, M.J.
Citation: Communications in Computer and Information Science, 2007 / Braz, J., Ranchordas, A., Araujo, H., Jorge, J. (ed./s), vol.4 CCIS, pp.217-228
Publisher: Springer
Issue Date: 2007
Series/Report no.: Communications in Computer and Information Science; vol. 4
ISBN: 9783540752721
ISSN: 1865-0929
Conference Name: 1st International Conferences on Computer Vision Theory and Applications (VISAPP 2006) and Computer Graphics Theory and Applications (GRAPP 2006) (25 Feb 2006 - 28 Feb 2006 : Setubal, Portugal)
Editor: Braz, J.
Ranchordas, A.
Araujo, H.
Jorge, J.
Statement of
Wojciech Chojnacki, Anton van den Hengel, and Michael J. Brooks
Abstract: Generalised Principal Component Analysis (GPCA) is a recently devised technique for fitting a multi-component, piecewise-linear structure to data that has found strong utility in computer vision. Unlike other methods which intertwine the processes of estimating structure components and segmenting data points into clusters associated with putative components, GPCA estimates a multi-component structure with no recourse to data clustering. The standard GPCA algorithm searches for an estimate by minimising a simple algebraic misfit function. The underlying constraints on the model parameters are ignored. Here we promote a variant of GPCA that incorporates the parameter constraints and exploits constrained rather than unconstrained minimisation of a statistically motivated error function. The output of any GPCA algorithm hardly ever perfectly satisfies the parameter constraints. Our new version of GPCA greatly facilitates the final correction of the algorithm output to satisfy perfectly the constraints, making this step less prone to error in the presence of noise. The method is applied to the example problem of fitting a pair of lines to noisy image points, but has potential for use in more general multi-component structure fitting in computer vision.
Keywords: Generalised principal component analysis; constrained minimisation; multi-line fitting; degenerate conic
Rights: © Springer-Verlag Berlin Heidelberg 2007
DOI: 10.1007/978-3-540-75274-5_14
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Appears in Collections:Aurora harvest 3
Australian Institute for Machine Learning publications
Computer Science publications

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