Abstract
During the manufacturing of textiles, several types of defects occur in the fabrics. This paper explores the characterization of the fabric textures using the conventional approaches such as Gabor filter, Gabor wavelet and Gauss Markov random field (MRF) and the well-known method for surface roughness measurement in the mechanical engineering called topothesy. The topothesy and fractal dimension known as fractal parameters represent not only the roughness but also the affine self-similarity in fabric textures. The fabric texture features are tested on the database of four types of defective fabric samples, viz., torn fabric, oil stain, miss pick and interlacing of two webs, collected from the cloth mills of Berhampur. A comparison of the results of defect detection in fabrics indicates that the topothesy fractal dimension features outperform those of Gabor filter, Gabor wavelets and Gauss MRF.
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The authors are highly thankful to Riby Abraham, Mechanical Engineering Department, I.I.T. Delhi, for introducing the structure function and for rendering the programming support.
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Appendix 1: Computation of topothesy fractal dimension (fractal parameters) features
Appendix 1: Computation of topothesy fractal dimension (fractal parameters) features
Let us take an image of size \(8 \times 8\)
Assume a window size of 3. Then we will have the number of sub-images \(=\) floor (8/3) \(\times \) floor (8/3) \(=\) 4, i. e., \(B1,B2,B3\) and \(B4\).
The sub-images are as follows:
We will get two features from a sub-image and thus have \(2 \times 4=8\) features for the image I of size \(8 \times 8\). The computation of structure function \(S1\) of \(B1\) is done using the following loops:
From the above loops, we compute the elements of the structure function as follows:
For \(\tau = 1\);
For\(\,\tau = 2\);
The values of \(\tau \) and \(S(\tau )\) and the corresponding values of \(\hbox {log}(\tau )\) and \(\hbox {Log} (S(\tau ))\) are listed here.
Curve fitting by the equation \(y=mx+c\) gives slope = 1.6374 and the intercept \(c=1.9095\).
So the fractal dimension \((D) = 2-(\hbox {m}/2) = 2-(1.6374/2) =2-0.8187 =1.1813\).
Topothesy \((\wedge ) = \hbox {exp} (\hbox {c}/(2D-2)) = \hbox {exp}(1.9095/(2\times 1.1813-2)) =193.770\)
The above two fractal parameters are contributed by the first sub-image, i.e., B1. Similarly, the fractal parameters \(D\) and \(\wedge \) of \(B2\) are: \(D=2.6008, \wedge =2.1444\); of \(B3\) are \(D=2.161, \wedge =2,9677\) and of \(B4\) are: \(D=2.3847, \wedge =2.8818\).
After concatenating all the feature values of B1, B2, B3 and B4, we obtain the feature vector of size, 1 \(\times \) 8 as \((1.1813, 195.77, 2.6008, 2.1444, 2.1610, 2.9677, 2.3847, 2. 8818)\).
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Hanmandlu, M., Choudhury, D. & Dash, S. Detection of defects in fabrics using topothesy fractal dimension features. SIViP 9, 1521–1530 (2015). https://doi.org/10.1007/s11760-013-0604-5
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DOI: https://doi.org/10.1007/s11760-013-0604-5