Abstract
All the elements of a Fourier analysis can be derived from the experiments of Graham and Robson on contrast sensitivity. Once their experiment is posed as an eigenvalue problem, a complete orthonormal set of eigenfunctions results from solving the associated differential equation. Neither sine and cosine nor Gabor functions result. Instead, the Hermite functions arise as the eigenfunctions of a space-variant differential operator used to model the contrast sensitivity of human observers. These functions, up to a constant, are their own Fourier transforms, and in principle can be used to exactly represent the Fourier transform of naturally occuring visual images.
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Stewart, A.L., Pinkham, R. A space-variant differential operator for visual sensitivity. Biol. Cybern. 64, 373–379 (1991). https://doi.org/10.1007/BF00224704
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DOI: https://doi.org/10.1007/BF00224704