To compute the response of the human eye to a given two-dimensional luminance field, the Fourier amplitude spectrum of the field is multiplied by a contrast sensitivity function to generate the internal representation which visual psychophysicists believe is the basis for the human percept.
A representation of the contrast sensitivity function in frequency space is shown in the first figure.
The horizontal and vertical frequency scales range between -34 and +34 cycles/degree, and the colors range from red for the lowest values to yellow for the highest.
The next figure represents a test pattern to which the procedure was applied.
It depicts a 15 degree square luminance field in real space with colors ranging from blue for the lowest intensity to yellow for the highest.
The final figure represents the perceived field using the same color scaling as the original.
Not only are the intensity contrasts greatly reduced, especially at lower intensities, but the Mach bands are also quite pronounced at the boundaries between regions of different intensity.
The mathematical representation of the contrast sensitivity function shown above is based on optimal smoothing spline fits to vertical and oblique contrast sensitivity measurements. Unlike most of the approximations in current use, which assume isotropy, this new representation incorporates the dependence on orientation revealed by the measurements.
For more information see: Rust, Bert W. and Rushmeier, Holly E., (1997) "A New Representation of the Contrast Sensitivity Function for Human Vision", (postscript, 19.4M bytes), Proceedings of the International Conference on Imaging Science, Systems, and Technology, CISST'97, H.R. Arabnia, ed., CSREA, Las Vegas, pp. 1-15.
or: "MS-Luminance.ps.gz", (zipped postscript, 1.54M bytes).