On the distribution of colors in natural images

When analyzing the RGB distribution of colors in natural images we notice that they are organized into spatial structures. This observation is not new, quoting Omer and Werman in [5]: “... when looking at the RGB histogram of real world images, two important facts can clearly be observed; The histogram is very sparse, and it is structured.[...] This is because the colors of almost any given scene create very specific structures in the histogram”. Omer and Werman observed that colors were distributed along elongated clusters and proposed a linear approximation to model these structures (the color lines). The use of a linear model for the distribution of colors agrees with the common assumption that the scenes are composed of lambertian objects, for which the emitted surface color depends on the intensity of the illuminant, the reflectance coefficient and the relative orientation of the surface with respect to the light source (but not with respect to the viewer). In this case the R/G/B ratio at each point of the same object is constant and the colors form a straight line. The non-linearities introduced by the acquisition process (sensor and quantization noise, white balance, gamma-correction, etc.) distort these lines and produce the elongated clusters described in [5]. The basic Lambertian model for matte objects can be improved by incorporating the possibility of specular reflections. Klinker, Shafer and Kanade ([3]) introduced the dichromatic reflection model to account for the distribution of colors of matte objects with highlights under controlled illumination conditions. Both the color of the matte object and the highlight are modeled by straight lines that intersect at some point: “The combined spectral cluster of matte and highlight points looks like a skewed T.”. After the acquisition process these lines are distorted but they still conserve their 1D structure. So far it seems that the linear model is good enough to account for the distribution of colors in natural images. But, is this true in general? As already pointed out in [3]: “A color cluster from an object in an unconstrained scene will generally not be a skewed T composed of linear subclusters because the