The standard deviation of luminance as a metric for contrast in random-dot images

Michelson's contrast, C, is an excellent metric for contrast in images with periodic luminance profiles, such as gratings, but is not suitable for images consisting of isolated stimulus elements, eg single bars; other metrics have been devised for such stimuli. But what metric should be used for random-dot images such as are commonly used in stereograms and kinematograms? Previously the standard deviation (SD) of the luminances (equivalent to the root mean square, RMS, of the amplitudes) has been taken as a measure of contrast, but on little more than intuitive grounds. The validity of this speculative usage is tested. Experiments are described in which a wide range of random-dot images of various compositions was used and the adapting power of these images measured. This was taken as an index of their visual effectiveness. The contrast and contrast-reducing effects of the stimuli were expressed in terms of six candidate metrics, including SD, to discover which would give the most lawful description of the experimental data. The usefulness and generality of the SD measure were confirmed. The effects of mean luminance were also measured and a general expression that would take them into account was derived. Finally, on the basis of computational modelling in which spatial filters with properties approximating those of retinal ganglion cells were used, a possible theoretical account for the success of the SD metric is offered.