Fisher information and model selection for projective transformations of the line

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Maybank Stephen J. 2003Fisher information and model selection for projective transformations of the lineProc. R. Soc. Lond. A.4591829–1849http://doi.org/10.1098/rspa.2002.1096SectionRestricted accessFisher information and model selection for projective transformations of the line Stephen J. Maybank Stephen J. Maybank Department of Computer Science, University of Reading, Whiteknights, PO Box 225, Reading, Berkshire RG6 6AY, UK () Google Scholar Find this author on PubMed Search for more papers by this author Stephen J. Maybank Stephen J. Maybank Department of Computer Science, University of Reading, Whiteknights, PO Box 225, Reading, Berkshire RG6 6AY, UK () Google Scholar Find this author on PubMed Search for more papers by this author Published:08 July 2003https://doi.org/10.1098/rspa.2002.1096AbstractThe Fisher information and the Rao measure are obtained in closed form for a family of probability density functions parametrized by the manifold PSL(2, <B>R</B>) of projective transformations of the real projective line. In addition, the Fisher information and the Rao measure are obtained for the sub-manifold of affine transformations. An application of these results to computer vision is described. The Rao measure is used to obtain a closed-form approximation to the probability of misclassifying a projective transformation of the line as an affine transformation. The approximation is a function of the number of pairs of points that correspond under the projective transformation and the standard deviation of the error in locating a point. Previous Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Maybank S (2008) Approximation to the Fisher–Rao metric for the focus of expansion, Neurocomputing, 10.1016/j.neucom.2007.07.040, 71:10-12, (2037-2045), Online publication date: 1-Jun-2008. Maybank S (2006) Application of the Fisher-Rao Metric to Ellipse Detection, International Journal of Computer Vision, 10.1007/s11263-006-9033-z, 72:3, (287-307), Online publication date: 1-May-2007. Maybank S (2006) Application of the Fisher-Rao Metric to Structure Detection, Journal of Mathematical Imaging and Vision, 10.1007/s10851-006-4533-6, 25:1, (49-62), Online publication date: 1-Jul-2006. Maybank S (2005) The Fisher-Rao Metric for Projective Transformations of the Line, International Journal of Computer Vision, 10.1007/s11263-005-6877-6, 63:3, (191-206), Online publication date: 1-Jul-2005. Maybank S (2004) Detection of image structures using the Fisher information and the Rao metric, IEEE Transactions on Pattern Analysis and Machine Intelligence, 10.1109/TPAMI.2004.122, 26:12, (1579-1589), Online publication date: 1-Dec-2004. This Issue08 July 2003Volume 459Issue 2035 Article InformationDOI:https://doi.org/10.1098/rspa.2002.1096Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/07/2003Published in print08/07/2003 License: Citations and impact KeywordsAffine TransformationFisher InformationRao MetricProjective TransformationComputer VisionMisclassification Probability