Polynomial roots from companion matrix eigenvalues
Mathematics of Computation
Reflectance and texture of real-world surfaces
ACM Transactions on Graphics (TOG)
The Earth Mover's Distance as a Metric for Image Retrieval
International Journal of Computer Vision
Representing and Recognizing the Visual Appearance of Materials using Three-dimensional Textons
International Journal of Computer Vision
Toward a Full Probability Model of Edges in Natural Images
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
When Is ''Nearest Neighbor'' Meaningful?
ICDT '99 Proceedings of the 7th International Conference on Database Theory
The Nonlinear Statistics of High-Contrast Patches in Natural Images
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
A Statistical Approach to Texture Classification from Single Images
International Journal of Computer Vision - Special Issue on Texture Analysis and Synthesis
A Sparse Texture Representation Using Local Affine Regions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Creating Efficient Codebooks for Visual Recognition
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
International Journal of Computer Vision
The Second Order Local-Image-Structure Solid
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Local Behavior of Spaces of Natural Images
International Journal of Computer Vision
Distance Metric Learning for Large Margin Nearest Neighbor Classification
The Journal of Machine Learning Research
A Statistical Approach to Material Classification Using Image Patch Exemplars
IEEE Transactions on Pattern Analysis and Machine Intelligence
Using Basic Image Features for Texture Classification
International Journal of Computer Vision
Persistent Cohomology and Circular Coordinates
Discrete & Computational Geometry - Special Issue: 25th Annual Symposium on Computational Geometry; Guest Editor: John Hershberger
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A natural object of study in texture representation and material classification is the probability density function, in pixel-value space, underlying the set of small patches from the given image. Inspired by the fact that small $$n\times n$$ n 脳 n high-contrast patches from natural images in gray-scale accumulate with high density around a surface $$\fancyscript{K}\subset {\mathbb {R}}^{n^2}$$ K 驴 R n 2 with the topology of a Klein bottle (Carlsson et al. International Journal of Computer Vision 76(1):1---12, 2008), we present in this paper a novel framework for the estimation and representation of distributions around $$\fancyscript{K}$$ K , of patches from texture images. More specifically, we show that most $$n\times n$$ n 脳 n patches from a given image can be projected onto $$\fancyscript{K}$$ K yielding a finite sample $$S\subset \fancyscript{K}$$ S 驴 K , whose underlying probability density function can be represented in terms of Fourier-like coefficients, which in turn, can be estimated from $$S$$ S . We show that image rotation acts as a linear transformation at the level of the estimated coefficients, and use this to define a multi-scale rotation-invariant descriptor. We test it by classifying the materials in three popular data sets: The CUReT, UIUCTex and KTH-TIPS texture databases.