Representation of local geometry in the visual system
Biological Cybernetics
Digital halftoning
Scale and the differential structure of images
Image and Vision Computing - Special issue: information processing in medical imaging 1991
Surface shape and curvature scales
Image and Vision Computing
The Gaussian scale-space paradigm and the multiscale local jet
International Journal of Computer Vision
Journal of Mathematical Imaging and Vision
The Mathematica book (4th edition)
The Mathematica book (4th edition)
Scale-Space Theory in Computer Vision
Scale-Space Theory in 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
Features in Scale Space: Progress on the 2D 2nd Order Jet
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
The Nonlinear Statistics of High-Contrast Patches in Natural Images
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
Jet Based Feature Classification
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 2 - Volume 02
Least Squares and Robust Estimation of Local Image Structure
International Journal of Computer Vision
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Hypotheses for Image Features, Icons and Textons
International Journal of Computer 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
Journal of Mathematical Imaging and Vision
Field of Particle Filters for Image Inpainting
Journal of Mathematical Imaging and Vision
Novel Similarity Measures for Differential Invariant Descriptors for Generic Object Retrieval
Journal of Mathematical Imaging and Vision
Second Order Structure of Scale-Space Measurements
Journal of Mathematical Imaging and Vision
Image and Vision Computing
Basic Image Features (BIFs) Arising from Approximate Symmetry Type
SSVM '09 Proceedings of the Second 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
Maximum likelihood metameres for local 2nd order image structure of natural images
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Using Basic Image Features for Texture Classification
International Journal of Computer Vision
Characterizing breast phenotype with a novel measure of fibroglandular structure
IWDM'12 Proceedings of the 11th international conference on Breast Imaging
A Klein-Bottle-Based Dictionary for Texture Representation
International Journal of Computer Vision
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Characterization of second order local image structure by a 6D vector (or jet) of Gaussian derivative measurements is considered. We consider the affect on jets of a group of transformations—affine intensity-scaling, image rotation and reflection, and their compositions—that preserve intrinsic image structure. We show how this group stratifies the jet space into a system of orbits. Considering individual orbits as points, a 3D orbifold is defined. We propose a norm on jet space which we use to induce a metric on the orbifold. The metric tensor shows that the orbifold is intrinsically curved. To allow visualization of the orbifold and numerical computation with it, we present a mildly-distorting but volume-preserving embedding of it into euclidean 3-space. We call the resulting shape, which is like a flattened lemon, the second order local-image-structure solid. As an example use of the solid, we compute the distribution of local structures in noise and natural images. For noise images, analytical results are possible and they agree with the empirical results. For natural images, an excess of locally 1D structure is found.