A FUZZY DIFFERENCE BASED EDGE DETECTOR

Document Type: Research Paper

Authors

1 Electrical Engineering Department, Shahid Bahonar Univer- sity of Kerman, Kerman, Iran

2 School of Computer Engineering, Iran University of Science and Technology, Tehran, Iran

3 Electrical Engineering Department, Shahid Bahonar Uni- versity of Kerman, Kerman, Iran

Abstract

In this paper, a new algorithm for edge detection based on fuzzy
concept is suggested. The proposed approach defi nes dynamic membership
functions for diff erent groups of pixels in a 3 by 3 neighborhood of the central
pixel. Then, fuzzy distance and -cut theory are applied to detect the edge
map by following a simple heuristic thresholding rule to produce a thin edge
image. A large number of experiments are employed to confi rm the robustness
of the proposed algorithm. In the experiments diff erent cases such as normal
images, images corrupted by Gaussian noise, and uneven lightening images
are involved. The results obtained are compared with some famous algorithms
such as Canny and Sobel operators, a competitive fuzzy edge detector, and a
statistical based edge detector. The visual and quantitative comparisons show
the e ffectiveness of the proposed algorithm even for those images that were
corrupted by strong noise.

Keywords


[1] O. AbuAarqob, N. Shawagfeh and O. AbuGhneim, Functions de ned on fuzzy real numbers
according to zadehs extension, International Mathematical Forum, (2008), 763-776.
[2] A. J. Baddeley, An error metric for binary images, Robust Computer Vision-Quality of
Vision Algorithms, (1992), 59-78.
[3] M. Basu, Gaussian-based edge-detection methodsa survey, IEEE Transactions on Systems
Man, and CyberneticsPart C, 32(3) (2002), 252-260.
[4] J. C. Bezdek, R. Chandrasekhar and Y. Attikiouzel, A geometric approach to edge detection,
IEEE Transaction on Fuzzy Systems, 6(1) (1998), 52-75.
[5] V. Boskovitz and H. Guterman, An adaptive neuro-fuzzy system for automatic image seg-
mentation and edge detection, IEEE Transactions on Fuzzy Systems, 10 (2002), 247-262.
[6] D. Brzakovic and L. Hong, Road edge detection for mobile robot navigation, In Proceedings
of IEEE International Conference on Robotics and Automation, Scottsdale, AZ , USA, 2
(1989), 1143-1147.
[7] S. M. Chen, New methods for subjective mental workload assessment and fuzzy risk analysis,
Cybernetics and Systems, 27 (1996), 449-472.
[8] K. David A. and B. James C, Edge detection using a fuzzy neural network, Science of Arti cial
Neural Networks, 1710 (1992), 510-521.
[9] C. Ducottet, T. Fournel and C. Barat, Scale-adaptive detection and local characterization of
edges based on wavelet transform, Signal Processing, 84(11) (2004), 2115-2137.
[10] T. Hou and W. Kuo, A new edge detection method for automatic visual inspection, The
International Journal of Advanced Manufacturing Technology, 13 (1997), 407-412.
[11] J. S. R. Jang, C. T. Sun and E. Mizutani, Neuro-fuzzy and soft computing- a computational
approach to learning and machine intelligence, Prentice-Hall of India Pvt. Ltd., New Delhi,
2006.
[12] S. Karungaru, M. Fukumi, N. Akamatsu and T. Akashi, A simple 3D edge template for pose
invariant face detection, Lecture Notes in Computer Science, 4253 (2006), 692-698.
[13] H. Kim, J. Lee, D. Kim, H. Yoon and S. Chi, Motion and natural hand detection for gesture
recognition, SICE-ICASE,International Joint Conference, Busan,Korea, (2006), 313-316.
[14] T. Law, H. Itoh and H. Seki, Image ltering, edge detection, and edge tracing using fuzzy
reasoning, IEEE Transactions on Pattern Analysis and Machine Intelligence, 18 (1996), 481-
491.
[15] L. R. Liang and C. G. Looney, Competitive fuzzy edge detection, Applied Soft Computing, 3
(2003), 123-137.

[16] D. H. Lim, Robust edge detection in noisy images, Computational Statistics and Data Anal-
ysis, 50 (2006), 803-812.
[17] C. Lopez-Molina, H. Bustince, J. Fernandez, P. Couto and B. De Baets, A gravitational
approach to edge detection based on triangular norms, Pattern Recognition, 43(11) (2010),
3730-3741.
[18] S. Lu, Z.Wang and J. Shen, Neuro-fuzzy synergism to the intelligent system for edge detection
and enhancement, Pattern Recognition, 36 (2003), 2395-2409.
[19] D. Marr and E. Hildreth, Theory of edge detection, Proceedings Royal Soc.London, 207
(1980), 187-217.
[20] A. Maturo, On some structures of fuzzy numbers, Iranian Journal of Fuzzy Systems, 6 (2009),
49-59.
[21] R. Medina-Carnicer, A. Carmona-Poyato, R. Muoz-Salinas and F. J. Madrid-Cuevas, Deter-
mining hysteresis thresholds for edge detection by combiningthe advantages and disadvantages
of thresholding methods, IEEE Transactionson Image Processing, 19(1) (2010), 165-173.
[22] R. Medina-Carnicer, F. Madrid-Cuevas, A. Carmona-Poyato and R. M. noz Salinas, On
candidates selection for hysteresis thresholds in edge detection, PatternRecognition, 42(7)
(2009), 1284-1296.
[23] R. Medina-Carnicer and F. Madrid-Cuevas, Unimodal thresholding for edgeDetection, Pattern
Recognition, 41(7) (2008), 2337-2346.
[24] R. Medina-Carnicer, F. Madrid-Cuevas, R. Muoz-Salinas and A. Carmona-Poyato, Solving
the process of hysteresis without determining the optimal thresholds, Pattern Recognition,
43(4) (2010), 1224-1232.
[25] H. Meng, M. Freeman, N. Pears and C. Bailey, Real-time human action recognition on an em-
bedded, recon gurable video processing architecture, Journal of Real-Time Image Processing,
3 (2008), 163-176.
[26] S. Morillas, V. Gregori and Antonio. Hervs, Fuzzy peer groups for reducing mixed gaussian-
impulse noise from color images, IEEE Transaction on Image Processing, 18(7) (2009),
1452-1466.
[27] J. Musevi-Niya and A. Aghagolzadeh, Adaptive directional wavelet-based edge detection, 2nd
International Symposium on Telecommunications (IST2003), Isfahan, Iran, (2003), 191-195.
[28] H. Nezamabadi-pour, S. Saryazdi and E. Rashedi, Edge detection using ant algorithms, Soft
Computing, 10 (2005), 623-628.
[29] E. Pasha, A. Saiedifar and B. Asady, The percentiles of fuzzy numbers and their applications,
Iranian Journal of Fuzzy Systems, 6 (2009), 27-44.
[30] W. K. Pratt, Digital image processing, John Wiley and Sons, 2001.
[31] G. Roy Jun and W. Voxman, Topological properties of fuzzy numbers, Fuzzy Sets and Systems,
10(1-3) (1983), 87-99.
[32] X. Ruoning, A linear regression model in fuzzy environment, Adv. Modelling Simulation, 27
(1991), 31-40.
[33] F. Russo and G. Ramponi, Edge extraction by FIRE operators , in IEEE World Congress on
Computational Intelligence, 1 (1994), 249-253.
[34] J. I. Siddigue and K. E.Barner, Wavelet-based multi-resolution edge detection utilizing gray
level edge maps, International Conference on Image Processing (ICIP 98), (1998), 550-554.
[35] B. Sridevi and R. Nadarajan, Fuzzy similarity measure for generalized fuzzy numbers, Inter-
national Journal of Open Problems in Computer Science and Mathematics, 2 (2009), 240-253.
[36] P. Terry and D. Vu, Edge detection using neural networks, In IEEE Proceedings of 27th
Asilomar Conference on Signals, Systems and Computers, (1993), 391-395.
[37] V. Torre and T. Poggio, On edge detection, Massachusetts Institute of Technology-Arti cial
Intelligence Laboratory, 1984.
[38] D. Van De Ville, M. Nachtegael, D. Van Der Weken, E. Kerre, W. Philips and I. Lemahieu,
Noise reduction by fuzzy image ltering, IEEE Transactions on Fuzzy Systems, 11 (2003),
429-436.
[39] J. Wu, Z. Yin and Y. Xiong, The fast multilevel fuzzy edge detection of blurry images, IEEE
Signal Processing Letters, 14 (2007), 344-347.

[40] R. Xu and C. Li, Multidimensional least-squares tting with a fuzzy model, Fuzzy Sets and
Systems, 119 (2001), 215-223.
[41] F. Yang, S. Wan and Y. Chang, Improved method for gradient-threshold edge detector based
on HVS, Lecture Notes in Computer Science, 3801 (2005), 1051-1056.
[42] S. Yi, D. Labate, G. R. Easley and H. Krim, A shearlet approach to edge analysis and
detection, Trans. Image Proc,18(15) (2009), 1057-7149.
[43] X. Zong and W. Liu, Fuzzy edge detection based on wavelets transform, Machine Learning
and Cybernetics, International Conference, (2008), 2869-2873.