Generalised Principal Component Analysis: exploiting inherent parameter constraints

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dc.contributor.authorChojnacki, W.
dc.contributor.authorvan den Hengel, A.
dc.contributor.authorBrooks, M.J.
dc.contributor.conference1st 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)
dc.contributor.editorBraz, J.
dc.contributor.editorRanchordas, A.
dc.contributor.editorAraujo, H.
dc.contributor.editorJorge, J.
dc.date.issued2007
dc.description.abstractGeneralised 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.
dc.description.statementofresponsibilityWojciech Chojnacki, Anton van den Hengel, and Michael J. Brooks
dc.identifier.citationCommunications in Computer and Information Science, 2007 / Braz, J., Ranchordas, A., Araujo, H., Jorge, J. (ed./s), vol.4 CCIS, pp.217-228
dc.identifier.doi10.1007/978-3-540-75274-5_14
dc.identifier.isbn9783540752721
dc.identifier.issn1865-0929
dc.identifier.issn1865-0937
dc.identifier.orcidChojnacki, W. [0000-0001-7782-1956]
dc.identifier.orcidvan den Hengel, A. [0000-0003-3027-8364]
dc.identifier.orcidBrooks, M.J. [0000-0001-9612-5884]
dc.identifier.urihttp://hdl.handle.net/2440/115997
dc.language.isoen
dc.publisherSpringer
dc.relation.ispartofseriesCommunications in Computer and Information Science; vol. 4
dc.rights© Springer-Verlag Berlin Heidelberg 2007
dc.source.urihttps://doi.org/10.1007/978-3-540-75274-5_14
dc.subjectGeneralised principal component analysis; constrained minimisation; multi-line fitting; degenerate conic
dc.titleGeneralised Principal Component Analysis: exploiting inherent parameter constraints
dc.typeConference paper
pubs.publication-statusPublished

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