CONSTRAINED GENERALISED PRINCIPAL COMPONENT ANALYSIS

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

2006

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 an appropriate 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 the 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.

Paper Citation

in Harvard Style

Chojnacki W., van den Hengel A. and J. Brooks M. (2006). CONSTRAINED GENERALISED PRINCIPAL COMPONENT ANALYSIS . In Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, ISBN 972-8865-40-6, pages 206-212. DOI: 10.5220/0001362102060212

in Bibtex Style

@conference{visapp06,
author={Wojciech Chojnacki and Anton van den Hengel and Michael J. Brooks},
title={CONSTRAINED GENERALISED PRINCIPAL COMPONENT ANALYSIS},
booktitle={Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP,},
year={2006},
pages={206-212},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001362102060212},
isbn={972-8865-40-6},
}

in EndNote Style

TY - CONF
JO - Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP,
TI - CONSTRAINED GENERALISED PRINCIPAL COMPONENT ANALYSIS
SN - 972-8865-40-6
AU - Chojnacki W.
AU - van den Hengel A.
AU - J. Brooks M.
PY - 2006
SP - 206
EP - 212
DO - 10.5220/0001362102060212