A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Reflectance and texture of real-world surfaces
ACM Transactions on Graphics (TOG)
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
Universal Analytical Forms for Modeling Image Probabilities
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fragmentation in the Vision of Scenes
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Infinitely Divisible Cascades to Model the Statistics of Natural Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Continuous dimensionality characterization of image structures
Image and Vision Computing
A scale invariant covariance structure on jet space
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Fisher information and the combination of RGB channels
CCIW'13 Proceedings of the 4th international conference on Computational Color Imaging
The Weibull manifold in low-level image processing: An application to automatic image focusing
Image and Vision Computing
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As resolving power increases, image features evolve in an iterative fashion; large scale features will persist, and finer and finer scale features are resolved at each increase in resolution. As such, the observation process is shown to overwhelm natural image statistics. Observation by a linear imaging process imposes natural image statistics to be of random multiplicative nature, rather than additive. The scaling behavior of the random process is driven by the gradient structure in the scene irradiance. From the general structure of multiplicative processes, image statistics are proven to follow a sequential fragmentation process. From these theoretical results, analytical forms for the distributions of image derivative filter responses and gradient magnitude are derived.