Power spectra and distribution of contrasts of natural images from different habitats

Abstract

Some theories for visual receptive fields postulate that they depend on the image statistics of the natural habitat. Consequently, different habitats may lead to different receptive fields. We thus decided to study how some of the most relevant statistics vary across habitats. In particular, atmospheric and underwater habitats were compared. For these habitats, we looked at two measures of the power spectrum and one of the distributions of contrasts. From power spectra, we analyzed the log-log slope of the fall and the degree of isotropy. From the distribution of contrasts, we analyzed the fall in a semi-log scale. Past studies found that the spatial power spectra of natural atmospheric images fall linearly in logarithmic axes with a slope of about -2 and that their distribution of contrasts shows an approximate linear fall in semi-logarithmic axes. Here, we show that the power spectrum of underwater images have statistically significantly steeper slopes ( approximately -2.5 in log-log axes) than atmospheric images. The vast majority of power spectra are non-isotropic, but their degree of anisotropy is extremely low, especially in atmospheric images. There are also statistical differences across habitats for the distribution of contrasts, with it falling faster for underwater images than for atmospheric ones. We will argue that these differences are due to the optical properties of water and that the differences have relevance for theories of visual receptive fields. These theories would predict larger receptive fields for aquatic animals compared to land animals.

To Be Seen or to Hide: Visual Characteristics of Body Patterns for Camouflage and Communication in the Australian Giant CuttlefishSepia apama

“…The consistent relationship between amplitude and spatial frequency is well documented, with the power spectrum of a given scene falling roughly as the inverse of the square of the spatial frequency (Shapley and Lennie 1985;Bex and Makous 2002;Balboa and Grzywacz 2003). In other words, the amount of visual information that might be classified as fine scale or coarse scale is very similar between scenes regardless of the habitat type and viewing distance, a phenomenon that is probably due to a fractal-like self-simi- Fourier transform (FT) reveals the spatial distribution encoded in a two-dimensional image, and the resulting power spectra enable us to visualize this information.…”

“…The consistent relationship between amplitude and spatial frequency has implications for visual processing because scenes contain the same amount of detail regardless of the scale at which they are viewed. Balboa and Grzywacz (2003) found that underwater images are characterized by a steeper fall in spatial frequency compared with terrestrial ones; this can be attributed to the optics of water, in which light scatter and attenuation act to reduce high-frequency information (Lythgoe 1979).…”

Computational imaging and automated identification for aqueous environments

“…The resulting T 2 spectra are nearly matched in slope to 2 (plotted for comparison as the solid black line with arbitrary o¤set), which is the expected decay rate of power spectra for natural images and scenes (see, e.g., [397], [16], [386] and references therein). A of around 2 3 better corresponds to the slightly higher decay rate observed in underwater images [16]. The fact that T 2 has a a relationship which matches previous research is particularly encouraging considering the assumptions and simpli…cations that were used in the derivation.…”

Second Order Structure of Scale-Space Measurements

“…Last row shows the estimate of [19] find that on a limited set of 6 images containing a varying degree of clutter the Hurst index varies in the range H = 0.41 to H = 0.97. Balboa [2] compares power spectra for underwater scenes with atmospheric scenes and find that atmospheric scenes have power spectra corresponding to a Hurst parameter of H = 0.5 ± 0.02 and underwater scenes have H = 0.75 ± 0.03. The conclusion is that the Hurst index varies with image content and can to some extend be used to cluster images into different categories of content depending on the irregularity of, or clutter in, the image content.…”

“…These invariance properties are generally accepted as being useful in the analysis of natural images and supported by empirical studies [2,3,18,24,25]. However, even if such invariance assumptions would be violated to a smaller or larger extent, statistical models, as the one presented, may function very well as prior to more dedicated image analysis or processing techniques.…”