Ten lectures on wavelets
Digital Image Processing
On Advances in Statistical Modeling of Natural Images
Journal of Mathematical Imaging and Vision
An Algorithm for Image Representation as Independent Levels of Resolution
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
Journal of Computational Physics
Steganographic capacity of images, based on image equivalence classes
MM&Sec '01 Proceedings of the 2001 workshop on Multimedia and security: new challenges
Infinitely Divisible Cascades to Model the Statistics of Natural Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Detection of wave fronts in the Indian Ocean from geostationary sunglint satellite imagery
International Journal of Remote Sensing
International Journal of Remote Sensing
Infinite Photography: New Mathematical Model for High-Resolution Images
Journal of Mathematical Imaging and Vision
An optimized algorithm for the evaluation of local singularity exponents in digital signals
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Color texture analysis based on fractal descriptors
Pattern Recognition
Reconstructing an image from its edge representation
Digital Signal Processing
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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.