Universal Scale Laws for Colors and Patterns in Imagery
This work provides foundational insights into image statistics, potentially impacting fields like neural networks and out-of-equilibrium physics, though it appears incremental in applying known concepts to imagery.
The study identified universal scale laws for colors and patterns in images, finding that fully colored images follow a linear log-scale law with slope -2.00 ± 0.01, and discrete patterns show a universal entropy maximum of 1.74 ± 0.013, with implications for neural networks and physics.
Distribution of colors and patterns in images is observed through cascades that adjust spatial resolution and dynamics. Cascades of colors reveal the emergent universal property that Fully Colored Images (FCIs) of natural scenes adhere to the debated continuous linear log-scale law (slope $-2.00 \pm 0.01$) (L1). Cascades of discrete $2 \times 2$ patterns are derived from pixel squares reductions onto the seven unlabeled rotation-free textures (0000, 0001, 0011, 0012, 0101, 0102, 0123). They exhibit an unparalleled universal entropy maximum of $1.74 \pm 0.013$ at some dynamics regardless of spatial scale (L2). Patterns also adhere to the Integral Fluctuation Theorem ($1.00 \pm 0.01$) (L3), pivotal in studies of chaotic systems. Images with fewer colors exhibit quadratic shift and bias from L1 and L3 but adhere to L2. Randomized Hilbert fractals FCIs better match the laws than basic-to-AI-based simulations. Those results are of interest in Neural Networks, out of equilibrium physics and spectral imagery.