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
The Gaussian scale-space paradigm and the multiscale local jet
International Journal of Computer Vision
Stochastic models for generic images
Quarterly of Applied Mathematics
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Contour and Texture Analysis for Image Segmentation
International Journal of Computer Vision
What Do Features Tell about Images?
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
GRADE: Gibbs Reaction and Diffusion Equitions
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
On Advances in Statistical Modeling of Natural Images
Journal of Mathematical Imaging and Vision
State of the art on automatic road extraction for GIS update: a novel classification
Pattern Recognition Letters
The Second Order Local-Image-Structure Solid
IEEE Transactions on Pattern Analysis and Machine Intelligence
Properties of Brownian image models in scale-space
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in 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
A Klein-Bottle-Based Dictionary for Texture Representation
International Journal of Computer Vision
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We investigate the statistics of local geometric structures in natural images. Previous studies [13,14] of high-contrast 3 脳 3 natural image patches have shown that, in the state space of these patches, we have a concentration of data points along a low-dimensional non-linear manifold that corresponds to edge structures. In this paper we extend our analysis to a filter-based multiscale image representation, namely the local 3-jet of Gaussian scale-space representations. A new picture of natural image statistics seems to emerge, where primitives (such as edges, blobs, and bars) generate low-dimensional non-linear structures in the state space of image data.