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Lie methods for color robot vision

Published online by Cambridge University Press:  01 July 2008

Reiner Lenz
Reiner Lenz*
Affiliation:
Department of Science and Technology, Linköping University, Linköping 581 83, Sweden
*
*Corresponding author. E-mail: reiner.lenz@itn.liu.se
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Summary

We describe how Lie-theoretical methods can be used to analyze color related problems in machine vision. The basic observation is that the nonnegative nature of spectral color signals restricts these functions to be members of a limited, conical section of the larger Hilbert space of square-integrable functions. From this observation, we conclude that the space of color signals can be equipped with a coordinate system consisting of a half-axis and a unit ball with the Lorentz groups as natural transformation group. We introduce the theory of the Lorentz group SU(1, 1) as a natural tool for analyzing color image processing problems and derive some descriptions and algorithms that are useful in the investigation of dynamical color changes. We illustrate the usage of these results by describing how to compress, interpolate, extrapolate, and compensate image sequences generated by dynamical color changes.

Keywords

Color Spectralorentz groupcolor vision signal processing
Type
Article
Information
Robotica , Volume 26 , Special Issue 4: Geometry in Robotics: Sensing , July 2008 , pp. 453 - 464
Copyright
Copyright © Cambridge University Press 2007

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