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Group Theoretical Structure of Spectral Spaces

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Abstract

It is known that for every selection of illumination spectra there is a coordinate system such that all coordinate vectors of these illumination spectra are located in a cone. A natural set of transformations of this cone are the Lorentz transformations. In this paper we investigate if sequences of illumination spectra can be described by one-parameter subgroups of Lorentz-transformations. We present two methods to estimate the parameters of such a curve from a set of coordinate points. We also use an optimization technique to approximate a given set of points by a one-parameter curve with a minimum approximation error. In the experimental part of the paper we investigate series of blackbody radiators and sequences of measured daylight spectra and show that one-parameter curves provide good approximations for large sequences of illumination spectra.

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Reiner Lenz is associate professor at the Department of Science and Technology, Linköping University, Sweden. He held positions as invited researcher at the ZEISS, Germany, the Advanced Telecommunication Research Institute (ATR), Kyoto, Japan, the Mechanical Engineering Laboratory, Tsukuba, Japan, Rutgers University, USA and AIST, Tsukuba, Japan. He received an honorable mention for the Pattern Recognition Society Award and the SAAB-Combitech Award. He is associated editor for Pattern Recognition and the IEEE-Transactions on Image Processing. He is interested in the application of group-theoretical methods in signal-, color-processing.

Thanh Hai Bui is currently a Ph.D. student at Media group, Institute of Science and Technology, Linköping University. He obtained his B.Sc. in Computer Science from Hanoi University of Technology in 1995, Post-graduate diploma in Manufacturing System Engineering from Asian Institute of Technology in 1999, Master of Applied Computer Science from Vrije Universiteit Brussel in 2000, and Ph. Licentiate in Media Technology from Linköping Universitet in 2003. His work has mainly focused on multispectral database analysis, and applications of group theoretical methods.

Javier Hernández-Andrés received his Ph.D. degree in Physics from the University of Granada, Spain, in 1999. Since 2003 he is an associate professor in the Department of Optics at the same University. His research interests are color-image processing, multispectral color science, applied colorimetry, color vision and atmospheric optics.

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Lenz, R., Hai Bui, T. & Hernández-Andrés, J. Group Theoretical Structure of Spectral Spaces. J Math Imaging Vis 23, 297–313 (2005). https://doi.org/10.1007/s10851-005-0485-5

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