Human discrimination of fractal images

In order to transmit information in images efficiently, the visual system should be tuned to the statistical structure of the ensemble of images that it sees. Several authors have suggested that the ensemble of natural images exhibits fractal behavior and, therefore, has a power spectrum that drops off proportionally to 1/f beta (2 less than beta less than 4). In this paper we investigate the question of which value of the exponent beta describes the power spectrum of the ensemble of images to which the visual system is optimally tuned. An experiment in which subjects were asked to discriminate randomly generated noise textures based on their spectral drop-off was used. Whereas the discrimination-threshold function of an ideal observer was flat for different spectral drop-offs, human observers showed a broad peak in sensitivity for 2.8 less than beta less than 3.6. The results are consistent with, but do not provide direct evidence for, the theory that the visual system is tuned to an ensemble of images with Markov statistics.