Stochastic texture analysis for monitoring stochastic processes in industry
Introduction
In several continuous processes, static and dynamic stochastic texture images are acquired and used in quality control (Wang, 1999). Often, industrial machine operators try to visually interpret stochastic texture images, and estimate the manufacturing process condition using their experience in the field. This empirical approach is subjective, and prone to failure, mainly because the human vision is limited in terms of its ability to distinguish between stochastic textures (Scharcanski and Dodson, 2000). Despite advances in texture representation and classification over the past three decades (Fan and Xia, 2003, Arivazhagan and Ganesan, 2003), the problem of stochastic texture feature interpretation and classification remains a challenge for researchers (Zhu et al., 1998), and for a large segment of the industry (Scharcanski and Dodson, 2000).
There have been a variety of methods of extracting texture features from textured images, e.g. geometric, random field, fractal, and signal processing models for textures. A significant part of the recent works on textures concentrate on statistical modelling (Fan and Xia, 2003), which characterizes textures as probability distributions, and uses statistical theories to formulate and solve texture processing problems mathematically. Wavelet-based texture characterization has attracted attention recently because of its usefulness in several important applications, such as texture classification (Arivazhagan and Ganesan, 2003, Do and Vetterli, 2002), and texture segmentation (Choi and Baraniuk, 2001). Several approaches have been proposed to extract features in the wavelet domain with application in texture analysis, such as: (a) wavelet energy signatures, which were found useful for texture classification (Arivazhagan and Ganesan, 2003); (b) second-order statistics of the wavelet transform were also used to improve the accuracy of texture characterization (Wouver et al., 1999); and (c) higher order dependencies of wavelet coefficients were studied for texture analysis (Fan and Xia, 2003, Choi and Baraniuk, 2001, Romberg et al., 2001). These wavelet-based approaches have been found more effective than other methods based on second-order statistics or random fields, which analyze textures in a single resolution without considering the human visual perception of textures (Fan and Xia, 2003, Scharcanski and Dodson, 2000).
Most of the work on texture in the wavelet domain has concentrated on the analysis of visual textures, and were not designed for stochastic texture analysis. For example, often feature extraction is carried out assuming sub-band independence at each resolution (e.g. Arivazhagan and Ganesan, 2003, Do and Vetterli, 2002), which is not verified experimentally. Also, the methods based on higher order statistics generally do not make explicit relevant stochastic texture features, that are important for industrial applications, where process conditions are estimated based on specific texture parameters (e.g. Fan and Xia, 2003, Choi and Baraniuk, 2001, Romberg et al., 2001, Scharcanski and Dodson, 2000).
In this work, a multi-resolution scheme for stochastic texture representation and analysis is proposed. We begin by describing how we measure the image gradients in multiple resolutions. Based on this technique, the local grayscale variability and texture anisotropy are measured in multiple resolutions. Next, a multi-resolution distance measure for stochastic textures is introduced. Finally, we present some applications, experimental results and conclusions.
Section snippets
Our proposed texture representation
In this work, we emphasize specific stochastic texture features that could be used to facilitate texture interpretation, and the discrimination between distinct process conditions.1
Our method relies on multiple resolution texture gradients and their magnitudes. To estimate the local gradients in multiple resolutions, we apply the redundant two-dimensional WT proposed by Mallat and Zhong (1992). The
A stochastic texture distance measure
In our approach, at each resolution, a texture image Ii is represented by a histogram with k disjoint intervals of equal length, {S1, S2, … , Sk}. Under these circumstances, Do and Vetterli (2002) showed that the Kullback–Leibler distance ranks, or classifies, a texture I consistently with maximum likelihood rule. The empirical distributions (i.e. data histograms), usually require large representation overheads (i.e. storing large numbers of histogram bins). Therefore, as detailed before, we model
Experimental results
Stochastic texture images are widely used in manufacture of foil-like materials such as non-woven textiles, paper, polymer membranes, conductor and semiconductor coatings. Paper and non-woven textiles have a definite “grain” caused by the greater orientation of fibers in the machine direction and by the stress/strain imposed during pressing and drying. The directionality of such materials affect substantially their physical properties. Due to fluctuations and irregularities in systems
Concluding remarks
In conclusion, we may say that stochastic texture images are acquired in large quantities in continuous industrial processes, and encode important quality and process information. Consequently, methods for objective stochastic texture interpretation and discrimination are important for a large segment of the industry.
This work presented a new multi-resolution method for stochastic texture interpretation and discrimination based on the wavelet transform. Also, a multi-resolution distance measure
Acknowledgments
The author thanks CNPq (Brazilian Research Council) for financial support, and Mr. Osmar Machado (Riocell, Brazil) for providing experimental data; thanks are due also to Professor Roberto da Silva (Instituto de Informatica, UFRGS, Brazil) and to Professor Robin T. Clarke (Instituto de Pesquisas Hidraulicas, UFRGS, Brazil) for advice and useful discussions.
References (15)
- et al.
Texture classification using wavelet transform.
Pattern Recognition Lett.
(2003) - et al.
Multiscale image segmentation using wavelet-domain hidden markov models
IEEE Trans. Image Process.
(2001) - et al.
Wavelet-based texture retrieval using generalized gaussian density and Kullback–Leibler distance
IEEE Trans. Image Process.
(2002) - Dodson, C., Ng, W.K., Singh, R.R., 1995. Paper stochastic structure analysis—archive 2 (CD-ROM), University of Toronto,...
- et al.
Wavelet-based texture analysis and synthesis using hidden markov models.
IEEE Trans. Circ. Syst.—I: Fundam. Theory Appl.
(2003) - et al.(1979)
- et al.
Characterization of signals from multiscale edges
IEEE Trans. Pattern Anal. Machine Intell.
(1992)