Efficient Invariant Representations
International Journal of Computer Vision
Algebraic and Geometric Tools to Compute Projective and Permutation Invariants
IEEE Transactions on Pattern Analysis and Machine Intelligence
AFPAC '00 Proceedings of the Second International Workshop on Algebraic Frames for the Perception-Action Cycle
Group Theoretical Structure of Spectral Spaces
Journal of Mathematical Imaging and Vision
Lie Methods in Color Signal Processing: Illumination Effects
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 03
Color measurements with a consumer digital camera using spectral estimation techniques
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Estimation of illumination characteristics
IEEE Transactions on Image Processing
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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.