Luminance histogram

The distribution of pixel luminance values without their spatial arrangement. Moments such as mean, variance and skewness describe aspects of that distribution, while losing relationships among locations.

Permuting pixel locations preserves the multiset of luminance values, hence its histogram and every sum ${\sum }_{i}f(I_i)$, including raw moments. It need not preserve spatial correlations, edges or relations between highlights and shading. This proves nonuniqueness of an image from its histogram; a particular perceptual consequence requires experiment.