Scale invariance does not hold for high dynamic range images, but is reestablished by early retinal nonlinearities

TitleScale invariance does not hold for high dynamic range images, but is reestablished by early retinal nonlinearities
Publication TypeChart
Year of Publication2017
AuthorsGrimaldi A, Kane D, Bertalmío M
Image Source ProgramThe European Conference on Visual Perception (ECVP)
Abstract

The statistics of real world luminances have been extensively investigated for images captured with single exposure photography, which are therefore of standard dynamic range (DR). One commonly reported feature is that the average Fourier amplitude falls off as a function of one over the spatial frequency, a property that implies the scale invariance of natural images. However, it has been reported (Dror et al. 2001) that this 1/f statistic does not hold for some images with a high dynamic range (HDR). We investigate this topic using a HDR natural image database (Adams et al., 2016) and corroborate that the 1/f law commonly fails for natural images of medium and high DR. We fitted the power spectrum with a second order polynomial and find that the leading term is negatively correlated with DR. For HDR images, this value becomes significantly nonzero making the power spectrum fit concave. Taking these images as input to our visual system, we then study the effect on them of two successive processes: light scattering in the eye, modeled by the eye's point spread function (PSF), and the photoreceptors response, modeled by the Naka-Rushton equation. While convolution with the eye's PSF reduces DR, the resulting images still don't follow the 1/f rule. However, the nonlinearity of the photoreceptors' response ensures that the 1/f statistic is recovered at the retinal level for all images tested.