Geometric Fourier Analysis for Computational Vision |
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Authors: | Jacek Turski |
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Institution: | (1) Department of Computer and Mathematical Sciences, University of Houston-Downtown, USA |
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Abstract: | Projective Fourier analysis — geometric Fourier analysis of the group SL(2, ),
the group identified in the conformal camera that provides image perspective transformations—is
discussed in the framework of representation theory of semisimple Lie groups. The compact model
of projective Fourier analysis is constructed, complementing the noncompact model proposed
before. Detailed mathematical formulation of both models is presented. It is demonstrated that
the projective Fourier analysis provides the data model for efficient perspectively covariant digital
image representation well adapted to the retino-cortical mapping of biological visual system, and
therefore, explicitly designed for the foveated sensors of a silicon retina, the use of which in active
vision systems is presently limited due to the lack of such a model. |
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Keywords: | |
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