Fractal Descriptors in the Fourier Domain Applied to Color Texture Analysis

The present work proposes the development of a novel method to provide descriptors for colored texture images. The method consists in two steps. In the first, we apply a linear transform in the color space of the image aiming at highlighting spatial structuring relations among the color of pixels. In a second moment, we apply a multiscale approach to the calculus of fractal dimension based on Fourier transform. From this multiscale operation, we extract the descriptors used to discriminate the texture represented in digital images. The accuracy of the method is verified in the classification of two color texture datasets, by comparing the performance of the proposed technique to other classical and state-of-the-art methods for color texture analysis. The results showed an advantage of almost 3% of the proposed technique over the second best approach.Comment: Chaos, Volume 21, Issue 4, 201

Modeling of evolving textures using granulometries

This chapter describes a statistical approach to classification of dynamic texture images, called parallel evolution functions (PEFs). Traditional classification methods predict texture class membership using comparisons with a finite set of predefined texture classes and identify the closest class. However, where texture images arise from a dynamic texture evolving over time, estimation of a time state in a continuous evolutionary process is required instead. The PEF approach does this using regression modeling techniques to predict time state. It is a flexible approach which may be based on any suitable image features. Many textures are well suited to a morphological analysis and the PEF approach uses image texture features derived from a granulometric analysis of the image. The method is illustrated using both simulated images of Boolean processes and real images of corrosion. The PEF approach has particular advantages for training sets containing limited numbers of observations, which is the case in many real world industrial inspection scenarios and for which other methods can fail or perform badly. [41] G.W. Horgan, Mathematical morphology for analysing soil structure from images, European Journal of Soil Science, vol. 49, pp. 161–173, 1998. [42] G.W. Horgan, C.A. Reid and C.A. Glasbey, Biological image processing and enhancement, Image Processing and Analysis, A Practical Approach, R. Baldock and J. Graham, eds., Oxford University Press, Oxford, UK, pp. 37–67, 2000. [43] B.B. Hubbard, The World According to Wavelets: The Story of a Mathematical Technique in the Making, A.K. Peters Ltd., Wellesley, MA, 1995. [44] H. Iversen and T. Lonnestad. An evaluation of stochastic models for analysis and synthesis of gray-scale texture, Pattern Recognition Letters, vol. 15, pp. 575–585, 1994. [45] A.K. Jain and F. Farrokhnia, Unsupervised texture segmentation using Gabor filters, Pattern Recognition, vol. 24(12), pp. 1167–1186, 1991. [46] T. Jossang and F. Feder, The fractal characterization of rough surfaces, Physica Scripta, vol. T44, pp. 9–14, 1992. [47] A.K. Katsaggelos and T. Chun-Jen, Iterative image restoration, Handbook of Image and Video Processing, A. Bovik, ed., Academic Press, London, pp. 208–209, 2000. [48] M. K¨oppen, C.H. Nowack and G. R¨osel, Pareto-morphology for color image processing, Proceedings of SCIA99, 11th Scandinavian Conference on Image Analysis 1, Kangerlussuaq, Greenland, pp. 195–202, 1999. [49] S. Krishnamachari and R. Chellappa, Multiresolution Gauss-Markov random field models for texture segmentation, IEEE Transactions on Image Processing, vol. 6(2), pp. 251–267, 1997. [50] T. Kurita and N. Otsu, Texture classification by higher order local autocorrelation features, Proceedings of ACCV93, Asian Conference on Computer Vision, Osaka, pp. 175–178, 1993. [51] S.T. Kyvelidis, L. Lykouropoulos and N. Kouloumbi, Digital system for detecting, classifying, and fast retrieving corrosion generated defects, Journal of Coatings Technology, vol. 73(915), pp. 67–73, 2001. [52] Y. Liu, T. Zhao and J. Zhang, Learning multispectral texture features for cervical cancer detection, Proceedings of 2002 IEEE International Symposium on Biomedical Imaging: Macro to Nano, pp. 169–172, 2002. [53] G. McGunnigle and M.J. Chantler, Modeling deposition of surface texture, Electronics Letters, vol. 37(12), pp. 749–750, 2001. [54] J. McKenzie, S. Marshall, A.J. Gray and E.R. Dougherty, Morphological texture analysis using the texture evolution function, International Journal of Pattern Recognition and Artificial Intelligence, vol. 17(2), pp. 167–185, 2003. [55] J. McKenzie, Classification of dynamically evolving textures using evolution functions, Ph.D. Thesis, University of Strathclyde, UK, 2004. [56] S.G. Mallat, Multiresolution approximations and wavelet orthonormal bases of L2(R), Transactions of the American Mathematical Society, vol. 315, pp. 69–87, 1989. [57] S.G. Mallat, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, pp. 674–693, 1989. [58] B.S. Manjunath and W.Y. Ma, Texture features for browsing and retrieval of image data, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18, pp. 837–842, 1996. [59] B.S. Manjunath, G.M. Haley and W.Y. Ma, Multiband techniques for texture classification and segmentation, Handbook of Image and Video Processing, A. Bovik, ed., Academic Press, London, pp. 367–381, 2000. [60] G. Matheron, Random Sets and Integral Geometry, Wiley Series in Probability and Mathematical Statistics, John Wiley and Sons, New York, 1975