Statistical regularities of art images and natural scenes: Spectra, sparseness and nonlinearities

Abstract

Paintings are the product of a process that begins with ordinary vision in the natural world and ends with manipulation of pigments on canvas. Because artists must produce images that can be seen by a visual system that is thought to take advantage of statistical regularities in natural scenes, artists are likely to replicate many of these regularities in their painted art. We have tested this notion by computing basic statistical properties and modeled cell response properties for a large set of digitized paintings and natural scenes. We find that both representational and non-representational (abstract) paintings from our sample (124 images) show basic similarities to a sample of natural scenes in terms of their spatial frequency amplitude spectra, but the paintings and natural scenes show significantly different mean amplitude spectrum slopes. We also find that the intensity distributions of paintings show a lower skewness and sparseness than natural scenes. We account for this by considering the range of luminances found in the environment compared to the range available in the medium of paint. A painting's range is limited by the reflective properties of its materials. We argue that artists do not simply scale the intensity range down but use a compressive nonlinearity. In our studies, modeled retinal and cortical filter responses to the images were less sparse for the paintings than for the natural scenes. But when a compressive nonlinearity was applied to the images, both the paintings' sparseness and the modeled responses to the paintings showed the same or greater sparseness compared to the natural scenes. This suggest that artists achieve some degree of nonlinear compression in their paintings. Because paintings have captivated humans for millennia, finding basic statistical regularities in paintings' spatial structure could grant insights into the range of spatial patterns humans find compelling.

How self-similar are artworks at different levels of spatial resolution?

“…This type of research is in line with the notion that aesthetic artworks share specific and universal properties, which reflect functions of the human visual system in particular and of the human brain in general [Zeki 1999;Reber et al 2004;Redies 2007]. Over the years, different research groups proposed several properties that characterize aesthetic paintings [Birkhoff 1933;Arnheim 1954;Berlyne 1974;Graham and Field 2007;Redies et al 2007;Rigau et al 2008;Forsythe et al 2011]. For example, Redies et al [Redies et al 2007] and Graham and Field [Graham and Field 2007] have shown that, on average, log-log plots of the radially averaged 1d power spectrum of greyscale images tend to drop according to a power law, similar to results that have been described for natural scenes [Field et al 1987;Burton and Moorhead 1987].…”

“…Over the years, different research groups proposed several properties that characterize aesthetic paintings [Birkhoff 1933;Arnheim 1954;Berlyne 1974;Graham and Field 2007;Redies et al 2007;Rigau et al 2008;Forsythe et al 2011]. For example, Redies et al [Redies et al 2007] and Graham and Field [Graham and Field 2007] have shown that, on average, log-log plots of the radially averaged 1d power spectrum of greyscale images tend to drop according to a power law, similar to results that have been described for natural scenes [Field et al 1987;Burton and Moorhead 1987]. This finding indicates that images of artworks and natural scenes share a scale-invariant (fractal-like) power spectrum.…”

Fractals in art and nature: why do we like them?

“…An analogous scale- :4 invariance was found in the grayscale surfaces for a wide range of art images 9,10,18 , in parallel to what is a known characteristic of natural scenes [19][20][21] . Natural images tend to have characteristic frequency spectra in which amplitude falls proportionally with increasing frequency and thus on average varies roughly as f -1 [or with a slope of -1 for log amplitude versus log frequency plot 22 .…”

“…The finding that artworks, which might appear superficially unstructured, contain a measurable degree of regularity was surprising. Building on this initial analysis, a number of groups have extended the range of fractal analysis techniques to quantify the visual complexity of a wide range of art images [6][7][8][9][10][11][12][13][14][15][16][17][18] .…”

Fast fog detection for camera based Advanced Driver Assistance Systems

“…u = f cos θ and v = f sin θ , and construct S( f , θ ). A number of studies have demonstrated ( [15], [16], [17]) that, by using polar coordinates and summing up the power spectra S over all directions θ , most natural images show a power distribution S( f ) which can be approximated by…”