The multi-fractal structure of contrast changes in natural images: from sharp edges to textures

Details The multi-fractal structure of contrast changes in natural images: from sharp edges to textures The multi-fractal structure of contrast changes in natural images: from sharp edges to textures

2001-07-14

arxiv.org/abs/cond-mat/0107316v1

Neural Computation {\bf 12}, 763-793 (2000)

Physics

Condensed Matter

Statistical Mechanics

41 pages, 8 figures, LaTeX

Scientific paper

We present a formalism that leads very naturally to a hierarchical description of the different contrast structures in images, providing precise definitions of sharp edges and other texture components. Within this formalism, we achieve a decomposition of pixels of the image in sets, the fractal components of the image, such that each set only contains points characterized by a fixed stregth of the singularity of the contrast gradient in its neighborhood. A crucial role in this description of images is played by the behavior of contrast differences under changes in scale. Contrary to naive scaling ideas where the image is thought to have uniform transformation properties \cite{Fie87}, each of these fractal components has its own transformation law and scaling exponents. A conjecture on their biological relevance is also given.

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