Abstract
Edge detectors have traditionally been an essential part of many computer vision systems. There are different methods that have been proposed for improving edge detection in real images. This paper proposes an edge detection method based on the Sobel technique and generalized type-2 fuzzy logic systems. To limit the complexity of handling generalized type-2 fuzzy logic, the theory of \(\alpha \)-planes is used. Simulation results are obtained with the Sobel operator (without fuzzy logic), then with a type-1 fuzzy logic system (T1FLS), an interval type-2 fuzzy logic system (IT2FLS) and with a generalized type-2 fuzzy logic system (GT2FLS). The proposed generalized type-2 fuzzy edge detection method is tested with synthetic images with promising results. To illustrate the advantages of using generalized type-2 fuzzy logic in combination with the Sobel operator, the figure of merit of Pratt measure is applied to measure the accuracy of the edge detection process.
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References
Abdou I, Pratt W (1979) Quantitative design and evaluation of enhancement/thresholding edge detectors. Proc IEEE 67(5):753–763
Biswas R, Sil J (2012) An improved canny edge detection algorithm based on type-2 fuzzy sets. Procedia Technol 4:820–824
Bowyer K, Kranenburg C, Dougherty S (2001) Edge detector evaluation using empirical ROC curves. Comput Vis Image Underst 84(1):77–103
Bustince H, Barrenechea E, Pagola M, Fernandez J (2009) Interval-valued fuzzy sets constructed from matrices: application to edge detection. Fuzzy Sets Syst 160(13):1819–1840
Canny J (1986) A computational approach to edge detection. IEEE Trans Pattern Anal Mach Intell 8(6):679–698
Castillo O, Melin P (2008) Type-2 fuzzy logic theory and applications. Springer, Berlin
Castro JR, Castillo O, Melin P (2007) An interval type-2 fuzzy logic toolbox for control applications. FUZZ 2007:1–6
Fan Y, Udpa L, Ramuhalli P, Shih W, Stockman GC (2004) Automated rivet inspection for aging aircraft with magneto-optic image. In: International workshop on electromagnetic nondestructive evaluation, East Lansing
Go JF, Atae-allah C, Mart HH, Luque-escamilla PL (2001) A measure of quality for evaluating methods of segmentation and edge detection. Pattern Recognit 34:969–980
Gonzalez RC, Woods RE, Eddins SL (2004) Digital image processing using Matlab. In: Prentice-Hall
Greenfield S, Chiclana F (2013) Defuzzification of the discretised generalised type-2 fuzzy set: experimental evaluation. Inf Sci, 244:1–25
Hu L, Cheng HD, Zhang M (2007) A high performance edge detector based on fuzzy inference rules. Inf Sci 177(21):4768–4784
Jacques C, Bauchspiess A (2001) Fuzzy inference system applied to edge detection in digital images. In: V Brazilian conference on neural networks, Brazil
Jeon G, Anisetti M, Bellandi V, Damiani E, Jeong J (2009) Designing of a type-2 fuzzy logic filter for improving edge-preserving restoration of interlaced-to-progressive conversion. Inf Sci 179(13):2194–2207
Liu F (2008) An efficient centroid type-reduction strategy for general type-2 fuzzy logic system. Inf Sci 178(9):2224–2236
Liu X, Mendel JM, Wu D (2012) Study on enhanced Karnik-Mendel algorithms: Initialization explanations and computation improvements. Inf Sci 184(1):75–91
Lopez-Molina C, De Baets B, Bustince H (2013) Quantitative error measures for edge detection. Pattern Recognit 46(4):1125–1139
Melin P, Mendoza O, Castillo O (2010) An improved method for edge detection based on interval type-2 fuzzy logic. Expert Syst Appl 37(12):8527–8535
Mendel J (2001) Uncertain rule-based fuzzy logic systems: introduction and new directions. Prentice Hall
Mendel JM, John RIB (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10(2):117–127
Mendel JM, Fellow L, Liu F, Zhai D (2009) \(\alpha \) -plane representation for type-2 fuzzy sets: theory and applications. IEEE Trans Fuzzy Syst 17(5):1189–1207
Mendel JM (2010) Comments on alpha-plane representation for type-2 fuzzy sets: theory and applications. IEEE Trans Fuzzy Syst 18(1):229–230
Mendel JM, Fellow L (2013) On KM algorithms for solving type-2 fuzzy set problems. IEEE Trans Fuzzy Syst 21(3):426–446
Mendoza O, Melin P, Licea G (2009) Interval type-2 fuzzy logic for edges detection in digital images. Int J Intell Syst 24(11):1115–1133
Mendoza O, Melin P, Licea G (2009) A hybrid approach for image recognition combining type-2 fuzzy logic, modular neural networks and the Sugeno integral. Inf Sci 179(13):2078–2101
Mendoza O, Melín P, Castillo O (2009) Interval type-2 fuzzy logic and modular neural networks for face recognition applications. Appl Soft Comput 9(4):1377–1387
Mendoza O, Melin P, Licea G (2007) A new method for edge detection in image processing using interval type-2 fuzzy logic. 2007 IEEE Int Conf Granul Comput (GRC 2007), pp 151–151
Pagola M, Lopez-Molina C, Fernandez J, Barrenechea E, Bustince H (2013) Interval type-2 fuzzy sets constructed from several membership functions: application to the fuzzy thresholding algorithm. IEEE Trans Fuzzy Syst 21(2):230–244
Perez-Ornelas F, Mendoza O, Melin P, Castro JR (2012) Interval type-2 fuzzy logic for image edge detection quality evaluation. In: 2012 annual meeting of the North American fuzzy information processing society (NAFIPS) 1:1–6
Pratt WK (2007) Digital image processing. Wiley
Prieto MS, Allen AR (2003) A similarity metric for edge images. Pattern Anal Mach Intell IEEE Trans 25(10):1265–1273
Ramesh J, Rangachar K, Brian GS (1995) Machine vision. In McGraw-Hill
Setayesh M, Zhang M, Johnston M (2012) Effects of static and dynamic topologies in particle swarm optimisation for edge detection in noisy images. In: IEEE congress on evolutionary computation 2012:1–8
Sobel I (1970) Camera models and perception, Ph.D. thesis, Stanford University, Stanford, CA
Tao C, Thompson W, Taur J (1993) A fuzzy if-then approach to edge detection. Fuzzy Syst, pp 1356–1360
Teruhisa S, Futoki S, Hiroshi K, Toshiaki O (2005) Application of an edge detection method to satellite images for distinguishing sea surface temperature fronts near the Japanese coast. Remote sensing of environment 98(1):21–34
Torre V, Poggio TA (1986) On edge detection. IEEE Trans Pattern Anal Mach Intell 8(6):147–163
Verma OP, Sharma R (2011) An optimal edge detection using universal law of gravity and ant colony algorithm. 2011 World Congr Inf Commun Technol, pp 507–511
Wagner C, Hagras H (2010) Toward general type-2 fuzzy logic systems based on zSlices. Fuzzy Syst IEEE Trans 18(4):637–660
Wagner C, Hagras H (2011) Employing zSlices based general type-2 fuzzy sets to model multi level agreement. 2011 IEEE Symp Adv type-2 Fuzzy Log Syst, pp 50–57
Wu D (2013) Approaches for reducing the computational cost of interval type-2 fuzzy logic systems: overview and comparisons. IEEE Trans Fuzzy Syst 21(1):80–99
Zadeh LA (1965) Fuzzy Sets, vol 8. Academic Press Inc., USA
Zhai D, Mendel JM (2011) Uncertainty measures for general Type-2 fuzzy sets. Inf Sci 181(3):503–518
Zhai D, Mendel J (2010) Centroid of a general type-2 fuzzy set computed by means of the centroid-flow algorithm. Fuzzy Syst (FUZZ), 2010 IEEE, pp 1–8
Acknowledgments
We thank the MyDCI program of the Division of Graduate Studies and Research, UABC, and the financial support provided by our sponsor CONACYT contract Grant No.: 44524.
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Communicated by V. Loia.
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Gonzalez, C.I., Melin, P., Castro, J.R. et al. An improved sobel edge detection method based on generalized type-2 fuzzy logic. Soft Comput 20, 773–784 (2016). https://doi.org/10.1007/s00500-014-1541-0
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DOI: https://doi.org/10.1007/s00500-014-1541-0