Texture Classification Using Spline, Wavelet Decomposition and Fractal Dimension
Applied and Computational Mathematics
Volume 4, Issue 1, February 2015, Pages: 5-10
Received: Dec. 26, 2014; Accepted: Jan. 15, 2015; Published: Jan. 27, 2015
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Saad Al-Momen, Mathematics Department, College of Science, Baghdad University, Baghdad, IRAQ
Loay E. George, Computer Science Department, College of Science, Baghdad University, Baghdad, IRAQ
Raid K. Naji, Mathematics Department, College of Science, Baghdad University, Baghdad, IRAQ
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Feature extraction is an important process for texture classification. This paper suggests two sets of features for texture analysis. In the first set of features, a set of fractal features is obtained from the eight wavelet sub-bands that are generated by applying Haar wavelet transform twice times according to dyadic architecture. The fractal features are determined using the differential box counting method. While for determining the second set of features, the cubic spline representation is applied to decompose the image signal into rough and smooth components; then applying the wavelet transform and finally compute the fractal dimension for all the sub-bands of both images. Each type of these two extracted feature sets is studied individually, and they are used together. Their overall performance is investigated. The proposed features set has been applied on two texture datasets, one consists of textures with directional properties, and the second set consists of textures samples that have directional attributes. The test results showed that the proposed methods give a high level of classification with images that have or do not have directional properties.
Texture Classification, Texture Analysis, Fractal, Wavelet Features, Cubic Spline
To cite this article
Saad Al-Momen, Loay E. George, Raid K. Naji, Texture Classification Using Spline, Wavelet Decomposition and Fractal Dimension, Applied and Computational Mathematics. Vol. 4, No. 1, 2015, pp. 5-10. doi: 10.11648/j.acm.20150401.12
Bhiwani, R. J.; Khan, M. A.; Agrawal, S. M.; "Texture Based Pattern Classification", International Journal of Computer Applications, Vol. 1, No. 1, Pp. 54-56, 2010.
[2] Chen, C. H.; Pau, L. F.; and Wang, P. S. P.; "The Handbook of Pattern Recognition and Computer Vision", Second Edition, Pp. 207-248, World Scientific Publishing Co., 1998.
Prasad, P. S.; Varma, V. T.; Harish, V. S.; and Kumar, K. S.; "Classification of Different Textures Using SVM and Fuzzy logic", International Journal of Advanced Computer Research, Vol. 2, No. 4, Issue 6, Pp. 463-466, December 2012.
Ling, L.; Ming, L.; and YuMing, L.; "Texture Classification and Segmentation Based on Bi-dimensional Empirical Mode Decomposition and Fractal Dimension", First International Workshop on Education Technology and Computer Science, Vol. 2, Pp. 547-577, 2009.
Procházka, A.; Mareš, J.; Yadollahi, M.; and Vyšata, O.; "Biomedical Image Enhancement, Segmentation and Classification Using Wavelet Transform", WSEAS International Conference on Systems; Pp. 160-165, 2012.
Gavlasová, A.; Procházka, A.; and Mudrova, M.; "Wavelet Based Image Segmentation", In Proc. of the 14th Annual Conference Technical Computing, Prague, 2006.
Gonzalez, R. C.; Woods, R. E.; and Eddins, S. L.; "Digital Image Processing Using MATLAB", Second Edition, Gatesmark Publishing, 2009.
Wang, L.; Deng, Z.; and Wang X.; "Application of Wavelet Transform Method for Textile Material Feature Extraction", Wavelet Transforms and their Recent Applications in Biology and Geoscience, Edited by Dr. Dumitru Baleanu, InTech Europe, Pp. 207-224, 2012.
Tou, J. Y.; Tay, Y. H.; and Lau, P. Y.; "Recent Trends in Texture Classification: A Review", Symposium on Progress in Information & Communication Technology, 2009.
Al-Kadi, O. S.; "Combined Statistical and Model Based Texture Features for Improved Image Classification", In: 4th International Conference on Advances in Medical, Signal & Information Processing, Santa Margherita Ligrue, Italy, 14-16 July 2008.
Kim, J. H.; Kim, S. C.; and Kang, T. J.; "Combined Statistical and Model Based Texture Features for Improved Image Classification", Tencon 2006; IEEE Region 10 Conference 2006.
Kang, T. J.; Kim, S. C.; Sul, I. H.; Youn, J. R.; and Chung, K.; "Fabric Surface Roughness Evaluation Using Wavelet-Fractal Method, Part I: Wrinkle, Smoothness and Seam Pucker", Textile Research Journal, Vol. 75, No. 11, Pp. 751-760, November 2005.
Kaplan, L. M.; "Extended Fractal Analysis for Texture Classification and Segmentation", IEEE Transactions on Image Processing, Vol. 8, No. 11, Pp. 1572-1585, November 1999.
Changjiang, S.; Guangrong, J.; and Yangfan, W.; "Study of Texture Images Classification Method Based on Fractal Dimension Calculation", International Joint Conference on Artificial Intelligence, 2009.
Xu, Y.; Quan,Y.; Ling, H.; and Ji, H.; "Dynamic Texture Classification Using Dynamic Fractal Analysis", IEEE International Conference on Computer Vision, Pp. 1219-1226, 2011.
Liu, S.; "An Improved Differential Box-Counting Approach to Compute Fractal Dimension of Gray-Level Image", International Symposium on Information Science and Engineering, 2008.
Yinglei, C.; Jida, S.; Hua, J.; and Xiaochun, L.; "A Method of Calculating Image Fractal Dimension Based on Fractal Brownian Model", International Forum on Information Technology and Applications, 2010.
Li, F.; Gong, W.; Li, Y.; Liang, Y.; and Wang, X.; "Research of Fractal Dimension Calculation Algorithm Based on Mobile Box-Counting Method", Seventh International Conference on Natural Computation, 2011.
Abiyev, R.; and Kilic, K. I.; "An Efficient Fractal Measure for Image Texture Recognition", Fifth International Conference on Soft Computing, Computing with Words and Perceptions in System Analysis, Decision and Control, 2009. ICSCCW 2009.
Blachowski, A.; and Ruebenbauer, K.; "Roughness Method to Estimate Fractal Dimension", ACTA Physica Polonica A, Vol. 115, No. 3, Pp. 636-640, 2009.
Lopes, R.; Betrouni, N.; "Fractal and Multifractal Analysis: A Review", Medical Image Analysis, Vol. 13, Pp. 634-649, 2009.
Long, M.; and Peng, F.; "A Box-Counting Method with Adaptable Box Height for Measuring the Fractal Feature of Images"; Radio Engineering, Vol. 22, No. 1, Pp. 208-213, April 2013.
Agrawal, A.; Shah, A.; and Bharti, R.; "Optimization of PSNR of Zooming Image using Cubic Spline Interpolation Method", International Journal of Engineering and Technical Research (IJETR), Vol. 2, Issue 6, Pp. 220-221, June 2014.
Chitode, J. S.; "Numerical Methods", Technical Publication Pune, 2011.
Al-Momen, S.; George, L.; Naji, R.; "The use of Gradient Based Features for Woven Fabric Images Classification", British Journal of Mathematics and Computer Science, Vol. 6, Issue 1, Pp. 68-78, 2015.
Commowick, O.; Lenglet, C.; and Louchet, C.; "Wavelet Based Texture Classification and Retrieval", Ecole Normale Superieure de Cachan, 2003.
Brodatz, P.; "Textures: A photographic Album for Artists and Designers", Dover Publications, 1999.
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