Stochastic models for generic images
Quarterly of Applied Mathematics
Probability Models for Clutter in Natural Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
An Extended Class of Scale-Invariant and Recursive Scale Space Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Universal Analytical Forms for Modeling Image Probabilities
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Toward a Full Probability Model of Edges in Natural Images
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Scale Adaptive Filtering Derived from the Laplace Equation
Proceedings of the 23rd DAGM-Symposium on Pattern Recognition
On the Axioms of Scale Space Theory
Journal of Mathematical Imaging and Vision
The Monogenic Scale-Space: A Unifying Approach to Phase-Based Image Processing in Scale-Space
Journal of Mathematical Imaging and Vision
Properties of Brownian image models in scale-space
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
α scale spaces on a bounded domain
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
A scale invariant covariance structure on jet space
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Risk bounds of learning processes for Lévy processes
The Journal of Machine Learning Research
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The probability distribution on the set of naturally occurring images is sparse with most of the probability mass on a small subset of all possible images, hence not all images are equally likely to be seen in nature. This can indirectly be observed by studying the marginal statistics of filter responses on natural images. Intensity differences, or equivalently responses of linear filters, of natural images have a spiky distribution with heavy tails, which puts a large proportion of the probability mass on small intensity differences, but at the same time giving a reasonable probability on large differences. This is due to the fact that images consist mostly of smooth regions separated by discontinuous boundaries. We propose to model natural images as stochastic Lévy processes with α kernel distributed intensity differences. We will argue that the scale invariant α kernels of the recently proposed α scale space theory provides a promising model of the intensity difference distribution (or in general linear filter responses) in conjunction with the Lévy process model of natural images.