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A KleinBottleBased Dictionary for Texture Representation
(2014)
Jose A. Perea, Gunnar Carlsson
Abstract
A natural object of study in texture representation and material classification is the probability density function, in pixelvalue space, underlying the set of small patches from the given image. Inspired by the fact that small \$\$n\times n\$\$n×nhighcontrast patches from natural images in grayscale accumulate with high density around a surface \$\$\fancyscript\K\\subset \\mathbb \R\\\textasciicircum\n\textasciicircum2\\$\$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 \$\$\fancyscript\K\\$\$K, of patches from texture images. More specifically, we show that most \$\$n\times n\$\$n×npatches from a given image can be projected onto \$\$\fancyscript\K\\$\$Kyielding a finite sample \$\$S\subset \fancyscript\K\\$\$S⊂K, whose underlying probability density function can be represented in terms of Fourierlike 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 multiscale rotationinvariant descriptor. We test it by classifying the materials in three popular data sets: The CUReT, UIUCTex and KTHTIPS texture databases.