article

A Klein-Bottle-Based Dictionary for Texture Representation

Authors:

Gunnar CarlssonAuthors Info & Claims

International Journal of Computer Vision, Volume 107, Issue 1

Pages 75 - 97

https://doi.org/10.1007/s11263-013-0676-2

Published: 01 March 2014 Publication History

Abstract

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 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 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 n patches from a given image can be projected onto $$\fancyscript{K}$$ K yielding a finite sample $$S\subset \fancyscript{K}$$ S 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.

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Chung YLawson A(2022)Persistence Curves: A canonical framework for summarizing persistence diagramsAdvances in Computational Mathematics10.1007/s10444-021-09893-448:1Online publication date: 1-Feb-2022
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cover image International Journal of Computer Vision

International Journal of Computer Vision Volume 107, Issue 1

March 2014

97 pages

ISSN:0920-5691

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Copyright © Copyright © 2014 Springer Science+Business Media New York.

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Kluwer Academic Publishers

United States

Publication History

Published: 01 March 2014

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https://dl.acm.org/doi/10.1007/s10444-021-09893-4
Nguyen TNguyen T(2021)A Comprehensive Taxonomy of Dynamic Texture RepresentationACM Computing Surveys10.1145/348789255:1(1-39)Online publication date: 23-Nov-2021
https://dl.acm.org/doi/10.1145/3487892
Kališnik S(2019)Tropical Coordinates on the Space of Persistence BarcodesFoundations of Computational Mathematics10.1007/s10208-018-9379-y19:1(101-129)Online publication date: 1-Feb-2019
https://dl.acm.org/doi/10.1007/s10208-018-9379-y
Belchí F(2019)Optimising the Topological Information of the $$A_\infty $$A?-Persistence GroupsDiscrete & Computational Geometry10.1007/s00454-019-00094-x62:1(29-54)Online publication date: 1-Jul-2019
https://dl.acm.org/doi/10.1007/s00454-019-00094-x
Shi ZOsher SZhu W(2018)Generalization of the Weighted Nonlocal Laplacian in Low Dimensional Manifold ModelJournal of Scientific Computing10.1007/s10915-017-0549-x75:2(638-656)Online publication date: 1-May-2018
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Perea J(2018)Multiscale Projective Coordinates via Persistent Cohomology of Sparse FiltrationsDiscrete & Computational Geometry10.1007/s00454-017-9927-259:1(175-225)Online publication date: 1-Jan-2018
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Ribeiro Tde Oliveira ABarcelos C(2018)Frequency Analysis of Topological Projections onto Klein Bottle for Texture CharacterizationProgress in Pattern Recognition, Image Analysis, Computer Vision, and Applications10.1007/978-3-030-13469-3_40(342-350)Online publication date: 19-Nov-2018
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Couto LBackes ABarcelos C(2017)Texture characterization via deterministic walks direction histogram applied to a complex network-based image transformationPattern Recognition Letters10.1016/j.patrec.2017.07.01397:C(77-83)Online publication date: 1-Oct-2017
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