An Invariant Metric on the Manifold of Second Order Moments
2009 (English)In: IEEE Color and Reflectance in Imaging and Computer Vision Workshop 2009 - CRICV 2009, IEEE-Computer Society , 2009, 1923-1930 p.Conference paper (Refereed)
We introduce an invariant metric in the space of symmetric,positive definite matrices and illustrate the usage of thisspace together with this metric in color processing. For thismetric closed-form expressions for the distances and thegeodesics, (ie. the straight lines in this metric) are availableand we show how to implement them in the case of matricesof size 2x2. In the first illustration we use the framework toinvestigate an interpolation problem related to the ellipsesobtained in the measurements of just-noticeable-distances.For two such ellipses we use the metric to construct an interpolatingsequence of ellipses between them. In the secondapplication construct a texture descriptor for chromaticitydistributions. We describe the probability distributions ofchromaticity vectors by their matrices of second order moments.The distance between these matrices is independentunder linear changes of the coordinate system in the chromaticityspace and can therefore be used to define a distancebetween probability distributions that is independentof the coordinate system used. We illustrate this invariance,by way of an example, in the case of different white pointcorrections.
Place, publisher, year, edition, pages
IEEE-Computer Society , 2009. 1923-1930 p.
Computer Vision and Robotics (Autonomous Systems)
IdentifiersURN: urn:nbn:se:liu:diva-25579DOI: 10.1109/ICCVW.2009.5457517ISBN: 978-1-4244-4441-0 (online)ISBN: 978-1-4244-4442-7 (print)OAI: oai:DiVA.org:liu-25579DiVA: diva2:248745
2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops 2009; Kyoto; Japan
ProjectsVisuella Världar, The Knowledge Foundation, SwedenGMIP: Groups and Manifolds for Information Processing; Vetenskapsråd