Hermite acuity gratings and models of space-variant acuity

A coherent mathematical framework for the psychophysics of contrast perception emerges when contrast sensitivity is posed as an eigenvalue problem. This more general mathematical theory is broad enough to encompass Fourier analysis as it is used in vision research. We present a model of space-variant contrast detection to illustrate the main features of the theory, and obtain a new contrast sensitivity function using acuity gratings based on the Hermite functions. The Hermite gratings have several advantages: they represent a complete orthogonal basis, are easy to manipulate, and are of finite extent. A theoretical Hermite csf results from posing contrast perception as an eigenvalue problem. Surprisingly, the theoretical Hermite csf is determined by a single empirical parameter.