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A Klein-Bottle-Based Dictionary for Texture Representation
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DOI：10.1007/s11263-013-0676-2.png)
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Abstract
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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 high-contrast patches from natural images in gray-scale accumulate with high density around a surface 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 , of patches from texture images. More specifically, we show that most patches from a given image can be projected onto yielding a finite sample , whose underlying probability density function can be represented in terms of Fourier-like coefficients, which in turn, can be estimated from . 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.
Keywords:
Texture representation
Texture classification
Klein bottle
Fourier coefficients
Patch distribution
Density estimation
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