Wavelets, blur, and the sources of variability in the amplitude spectra of natural scenes

A number of recent efforts have been made to account for the response properties of the cells in the visual pathway by considering the statistical structure of the natural environment. Previously, it has been suggested that the wavelet-like properties of cells in primary visual cortex have been proposed to provide an efficient representation of the structure in natural scenes captured by the phase spectrum. In this paper, we take a closer look at the amplitude spectra of natural scenes and its role in understanding visual coding. We propose that one of the principle insights one gains from the amplitude spectra is in understanding the relative sensitivity of cells tuned to different frequencies. It is suggested that response magnitude of cells tuned to different frequencies increases with frequency out to about 20 cycles/deg. The result is a code in which the response to natural scenes with a 1/f falloff is approximately flat out to 20 cycles/deg. The variability in the amplitude spectra of natural scenes is also investigated. Using a measure called the 'thresholded contrast spectrum' (TCS), it is demonstrated that a good proportion of the variability in the spectra is due to the relative sparseness of structure at different frequencies. The slope of the TCS was found to provide a reasonable prediction of blur across a variety of scenes in spite of the variability in their amplitude spectra.