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A Klein-bottle-based dictionary for texture representation. (English) Zbl 1328.68279
Summary: 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 \(n\times n\) high-contrast patches from natural images in gray-scale accumulate with high density around a surface \(\mathcal K\subset\mathbb R^{n^2}\) with the topology of a Klein bottle, we present in this paper a novel framework for the estimation and representation of distributions around \(\mathcal K\), of patches from texture images. More specifically, we show that most \(n\times n\) patches from a given image can be projected onto \(\mathcal K\) yielding a finite sample \(S\subset\mathcal K\), whose underlying probability density function can be represented in terms of Fourier-like coefficients, which in turn, can be estimated from \(S\). We show that image rotation acts as a linear transformation at the level of the estimated coefficients, and use this to define a multiscale rotation-invariant descriptor. We test it by classifying the materials in three popular data sets: The CUReT, UIUCTex and KTH-TIPS texture databases.

MSC:
68U10 Computing methodologies for image processing
68T10 Pattern recognition, speech recognition
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62H35 Image analysis in multivariate analysis
62G07 Density estimation
Software:
CUReT; EMD; KTH-TIPS; LMNN
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