@article{perea_klein-bottle-based_2014,
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{\textbackslash}times n\$\$n×nhigh-contrast patches from natural images in gray-scale accumulate with high density around a surface \$\${\textbackslash}fancyscript\{K\}{\textbackslash}subset \{{\textbackslash}mathbb \{R\}\}{\textasciicircum}\{n{\textasciicircum}2\}\$\$K⊂Rn2with 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 \$\${\textbackslash}fancyscript\{K\}\$\$K, of patches from texture images. More specifically, we show that most \$\$n{\textbackslash}times n\$\$n×npatches from a given image can be projected onto \$\${\textbackslash}fancyscript\{K\}\$\$Kyielding a finite sample \$\$S{\textbackslash}subset {\textbackslash}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.},
author = {Perea, Jose A. and Carlsson, Gunnar},
date = {2014-03-01},
doi = {10.1007/s11263-013-0676-2},
issn = {1573-1405},
journaltitle = {International Journal of Computer Vision},
keywords = {1 - Image analysis, 1 - Texture recognition, 2 - Fourier coefficients, 2 - Klein bottle, 3 - Grayscale images},
langid = {english},
number = {1},
pages = {75--97},
shortjournal = {Int J Comput Vis},
title = {A Klein-Bottle-Based Dictionary for Texture Representation},
url = {https://doi.org/10.1007/s11263-013-0676-2},
urldate = {2020-02-28},
volume = {107}
}