Representation of local geometry in the visual system
Biological Cybernetics
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of Mathematical Imaging and Vision
Feature Detection with Automatic Scale Selection
International Journal of Computer Vision
Stochastic models for generic images
Quarterly of Applied Mathematics
Probability Models for Clutter in Natural Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Universal Analytical Forms for Modeling Image Probabilities
IEEE Transactions on Pattern Analysis and Machine Intelligence
Toward a Full Probability Model of Edges in Natural Images
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
What Do Features Tell about Images?
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
The Second Order Local-Image-Structure Solid
IEEE Transactions on Pattern Analysis and Machine Intelligence
Second Order Structure of Scale-Space Measurements
Journal of Mathematical Imaging and Vision
Mode estimation using pessimistic scale space tracking
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Generic maximum likely scale selection
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
SSVM'07 Proceedings of the 1st international conference on Scale space and variational 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
Maximum likely scale estimation
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
On α kernels, Lévy processes, and natural image statistics
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
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In this paper it is argued that the Brownian image model is the least committed, scale invariant, statistical image model which describes the second order statistics of natural images. Various properties of three different types of Gaussian image models (white noise, Brownian and fractional Brownian images) will be discussed in relation to linear scale-space theory, and it will be shown empirically that the second order statistics of natural images mapped into jet space may, within some scale interval, be modeled by the Brownian image model. This is consistent with the 1/f2 power spectrum law that apparently governs natural images. Furthermore, the distribution of Brownian images mapped into jet space is Gaussian and an analytical expression can be derived for the covariance matrix of Brownian images in jet space. This matrix is also a good approximation of the covariance matrix of natural images in jet space. The consequence of these results is that the Brownian image model can be used as a least committed model of the covariance structure of the distribution of natural images.