Fig. 1.
Visualization of the base representation of images. (A) Example of an image in the van Hateren database of natural images. It consists of 4,167 images, 1,024 × 1,536 pixels in size, ranging from 0 to 215 − 1 in the pixel intensity. (B) In the base representation, the 2D image is isomorphic to a quasi-2D system by stacking layers ℬλ from top λ = 1 to bottom λ = L. Numbers denote λ, with phases for λ = 1, 6, and 15 identified. (C) Layers 4:8 from top to bottom in the binary decomposition are shown separately. The pixel intensity on each layer is either 0 (black) or 1 (white). Traces of a second-order phase transition near λ = 6 are also visualized here. Layers 1:3 and 9:15 are not shown because of space; they are indistinguishable from ordered and disordered layers 1 and 15 (shown in B), respectively. (D) This image is the “negative” representation of A, equivalent to flipping pixel values 0 ↔ 1 of the binary planes.