The International Arab Journal of Information Technology (IAJIT)

..............................
..............................
..............................


Edge Detection Optimization Using Fractional Order Calculus

In computer vision and image processing, time and quality are major factors taken into account. In edge detection process, the smoothing operation by a low-pass filter is commonly performed first in order to reduce noise effect. However, performing the smoothing operation partially requires additional computational time and alters true edges as well. Attempting to resolve such problems, a new approach dealing with edge detection optimization is addressed in this paper. For this purpose, a short edge detector algorithm without smoothing operation is proposed and investigated. This algorithm is based on a fractional order mask used as kernel of convolution for edge enhancement. It has been shown that in the proposed algorithm, the smoothing pre-process is no longer necessary; because, the efficiency of our fractional order mask is expressed in term of immunity to noise and the capability of detecting edges. Simulation results show how the quality of edge detection can be enhanced on adjusting the fractional order parameter. Then, our proposed edge detection method can be very useful in real time applications in some fields such as, satellite and medical imaging.


[1] Abbasi T. and Abbasi M., “A novel FPGA-based Architecture for Sobel Edge Detection Operator,” International Journal of Electronics, vol. 94, no. 9, pp. 889-896, 2007.

[2] Abdou I. and Pratt W., “Quantitative Design and Evaluation of Enhancement/Tresholding Edge Detectors,” Proceedings of the IEEE, vol. 67, no. 5, pp. 753-763, 1979.

[3] Canny J., “A Computational Approach to Edge Detection,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI-8, no. 6, pp. 679-698, 1986.

[4] Dalir M. and Bashour M., “Applications of Fractional Calculus,” Applied Mathematical Sciences, vol. 4, no. 21, pp. 1021-1032, 2010.

[5] Davis L., “A Survey of Edge Detection Techniques,” Computer Graphics and Image Processing, vol. 4, no. 3, pp. 248-270, 1976.

[6] Ferdi Y., Herbeuval J., and Charef A., “A Digital Filter based on the Non-Integer Order Differentiation for Analyzing Electrocardiograph Signals,” ITBM-RBM, vol. 21, no. 4, pp. 205- 209, 2000.

[7] Ferdi Y., Herbeuval J., Charef A., and Boucheham B., “R Wave Detection using Fractional Digital Differentiation,” ITBM-RBM, vol. 24, no. 5-6, pp. 273-280, 2003.

[8] Ferdi Y., “Some Applications of Fractional Order Calculus to Design Digital Filters for Biomedical Signal Processing,” Journal of Mechanics in Medicine and Biology, vol. 12, no. 2, 2012.

[9] Gao C., Zhou J., Lang F., Pu Q., and Liu C., “A Novel Approach to Edge Detection of Color Image Based on Quaternion Fractional Directional Differentiation,” Advances in Automation and Robotics, vol. 1, pp. 163-170, 2012.

[10] Gao C., Zhou J., and Zhang W., “Edge Detection (15) (14) (16) 832 The International Arab Journal of Information Technology, Vol. 16, No. 5, September 2019 Based on the Newton Interpolation’s Fractional 'LIIHUHQWLDWLRQ´The International Arab Journal of Information Technology, vol. 11, no. 3, pp. 223-228, 2014.

[11] Goutas A., Ferdi Y., Herbeuval J., Boudraa M., and Boucheham B., “Digital Fractional Order Differentiation-Based Algorithm for P and T- Waves Detection and Delineation,” ITBM-RBM, vol. 26, no. 2, pp. 127-132, 2005.

[12] Guo H., Li X., Qing-li C., and Ming-Rong W.,“Image Denoising using Fractional Integral,” in Proceedings of the IEEE International Conference on Computer Science and Automation Engineering, Zhangjiajie, 2012.

[13] Hu J., Pu Y., and Zhou J., “A Novel Image Denoising Algorithm Based on Riemann- Liouville Definition,” Journal of Computers, vol. 6, no. 7, pp. 1332-1338, 2011.

[14] Jalab H. and Ibrahim R., “Denoising Algorithm Based on Generalized Fractional Integral Operator with Two Parameters,” Discrete Dynamics in Nature and Society, vol. 2012, pp. 1-14, 2012.

[15] Jalab H. and Ibrahim R., “Texture Enhancement for Medical Images based on Fractional Differential Masks,” Discrete Dynamics in Nature and Society, vol. 2013, pp. 10, 2013.

[16] Koschan A. and Abidi M., “Detection and Classification of Edges in Color Images: A Review of Vector Valued Techniques,” IEEE Signal Processing Magazine, vol. 22, no. 1, pp. 64-73, 2005.

[17] Li Y., Tang H., and Chen H., “Fractional-Order Derivative Spectroscopy for Resolving Simulated Overlapped Lorenztian Peaks,” Chemometrics and Intelligent Laboratory Systems, vol. 107, no. 1, pp. 83-89, 2011.

[18] Mathieu B., Melchior P., Oustaloup A., and Ceyrak C., “Fractional Differentiation for Edge Detection,” Signal Processing, vol. 83, no. 11, pp. 2421-2432, 2003.

[19] Meer P. and Georgescu B., “Edge Detection with Embedded Confidence,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 23, no. 12, pp. 1351-1365, 2001.

[20] Mekideche M. and Ferdi Y., “A New Edge Detector based on Fractional Integration,” in Proceedings of International Conference on Multimedia Computing and Systems, Marrakech, 2014.

[21] Nakib A., Oulhadj H., and Siarry P., “A Thresholding Method based on Two- Dimensional Fractional Differentiation,” Image and Vision Computing, vol. 27, no. 9, pp. 1343- 1357, 2009.

[22] Nakib A., Schulze Y., Petit E., “Optimal Fractional Filter for Image Segmentation,” in Proceedings of SPIE-The International Society for Optical Engineering, Burlingame, 2012.

[23] Pan X., Ye Y., Cheng J., Wang D., and Jiang B., “Composite Derivative and Edge Detection,” Signal, Image and Video Processing, vol. 8, no. 3, pp. 523-531, 2014.

[24] Pu Y. and Zhou J., “Fractional Differential Mask: A Fractional Differential-based Approach for Multiscale Texture Enhancement,” IEEE Transactions on Image Processing, vol. 19, no. 2, pp. 491-511, 2010.

[25] Rodgers J. and Nicewander W., “Thirteen Ways to Look at the Correlation,” American Statistician, vol. 42, no. 1, pp. 59-66, 1995.

[26] Shakoor P., Almeida R., and Torres D., “Discrete Direct Methods in the Fractional Calculus of Variations,” Computers and Mathematics with Applications, vol. 66, no. 5, pp. 668-676, 2013.

[27] Singh S., Saini A., Saini R., Mandal A., Shekhar C., and Vohra A., “A Novel Real-Time Resource Efficient Implementation of Sobel Operator based Edge Detection on FPGA,” International Journal of Electronics, vol. 101, no. 12, pp. 1705-1715, 2014.

[28] Torre V. and Poggio T., “On Edge Detection,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI-8, no. 2, pp. 147-163, 1986. Mohammed Mekideche received his engineer diploma degree and his MSc diploma degree in electronics in 1988 and 2006 respectively, from the institute of electronics at Constantine University, Algeria. He is working for Ministry of National Education. Currently, his research interests are in signal and image processing, and preparing for obtaining his PhD diploma degree. Youcef Ferdi received his engineer diploma degree in electronics, MSc, and PhD diploma degrees in automatics and signal processing, from Constantine University, Algeria, in 1988, 1992, and 2001, respectively. During academic years (1997-1999), he was on leave at (CRAN) France. He was a full Professor until October 2015 at the department of EEatSkikda University. He joined the National Higher School of Biotechnology at Constantine In November 2015. His main fields of interest are: Biomedical signal processing, applications of fractional calculus to digital filter design and fractal signals synthesis.