What is the goal of sensory coding?
Neural Computation
Pyramid-based texture analysis/synthesis
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Multifractal formalism for functions part I: results valid for all functions
SIAM Journal on Mathematical Analysis
Fast texture synthesis using tree-structured vector quantization
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
A Parametric Texture Model Based on Joint Statistics of Complex Wavelet Coefficients
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: modeling, learning, sampling and computing, Part I
Stochastic models for generic images
Quarterly of Applied Mathematics
Probability Models for Clutter in Natural Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Image Processing
Occlusion Models for Natural Images: A Statistical Study of a Scale-Invariant Dead Leaves Model
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: Part II
On Advances in Statistical Modeling of Natural Images
Journal of Mathematical Imaging and Vision
Universal Analytical Forms for Modeling Image Probabilities
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Flexible Noise Model For Designing Maps
VMV '01 Proceedings of the Vision Modeling and Visualization Conference 2001
Probability models for complex systems
Probability models for complex systems
Infinitely divisible cascade analysis of network traffic data
ICASSP '00 Proceedings of the Acoustics, Speech, and Signal Processing, 2000. on IEEE International Conference - Volume 01
The stochastic structure of images
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
On non-scale-invariant infinitely divisible cascades
IEEE Transactions on Information Theory
Analytical form for a Bayesian wavelet estimator of images using the Bessel K form densities
IEEE Transactions on Image Processing
Multifractal Analysis on the Sphere
ICISP '08 Proceedings of the 3rd international conference on Image and Signal Processing
Parallel Hidden Hierarchical Fields for Multi-scale Reconstruction
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Virtual resolution enhancement of scale invariant textured images using stochastic processes
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Virtual Super Resolution of Scale Invariant Textured Images Using Multifractal Stochastic Processes
Journal of Mathematical Imaging and Vision
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We propose to model the statistics of natural images thanks to the large class of stochastic processes called Infinitely Divisible Cascades (IDC). IDC were first introduced in one dimension to provide multifractal time series to model the socalled intermittency phenomenon in hydrodynamical turbulence. We have extended the definition of scalar infinitely divisible cascades from 1 to N dimensions and commented on the relevance of such a model in fully developed turbulence in [1]. In this article, we focus on the particular 2 dimensional case. IDC appear as good candidates to model the statistics of natural images. They share most of their usual properties and appear to be consistent with several independent theoretical and experimental approaches of the literature. We point out the interest of IDC for applications to procedural texture synthesis.