Monthly
288 pp. per issue
6 x 9, illustrated
ISSN
0899-7667
E-ISSN
1530-888X
2014 Impact factor:
2.21

Neural Computation

April 1, 2000, Vol. 12, No. 4, Pages 763-793
(doi: 10.1162/089976600300015583)
© 2000 Massachusetts Institute of Technology
The Multifractal Structure of Contrast Changes in Natural Images: From Sharp Edges to Textures
Article PDF (576.8 KB)
Abstract

We present a formalism that leads 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 contains only points characterized by a fixed strength 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 (Field, 1987), each of these fractal components has its own transformation law and scaling exponents. A conjecture on their biological relevance is also given.