**6. Experimentation and simulation results**

294 Fuzzy Inference System – Theory and Applications

(a) (b)

Fig. 14. (a) AnEdge obtained by Type-2 FIS , and (b) its histogram.

Fig. 15. Flow chart of the Edge Detection Algorithm.

Figure 15 shows a flow chart representation of implementation procedure for acquiring the edges. A step by step implementation procedure for acquiring the edges is mentioned below.


Experimentation of above mentioned procedure for obtaining the edges is carried on three different types of image given in Table 2. The image name are mentioned in the first column of table, while second column contains original image, third, fourth and fifth column shows the acquired edges of the images by gradient magnitude, Type-1 FIS, and Type-2 FIS respectively. The result shows that Type-2 FIS outperform *Prewitt* gradient and Type-1 FIS method.

Table 2. Original Images, their name, and obtained edges by GM, Type-1, and Type-2 FIS

Type-2 Fuzzy Logic for Edge Detection of Gray Scale Images 297

[6] Roger Jang J. S. and Gulley Ned. "Fuzzy Logic ToolboxUser's Guide". The MathWorks,

[7] Karnik N. N;. and Mendel, J. M.; "Centroid of a type-2 fuzzy set," *International journal on* 

[8] Liang L., Basallo E., and Looney C. "Image edge detection with fuzzy classifier". In Proceedings of the ISCA 14th International Conference, 2001, pages 279–283. [9] Liang L. and Looney C. "Competitive fuzzy edge detection". *International journal on* 

[10] Lindeberg .T "Edge Detection and Ridge Detection with Automatic Scale Selection", *International Journal of Computer Vision*, vol 30,no. 2, (1998), pages 117—154. [11] Murfhy C. A. "Constitutent Estimation of Classes in R2 in the Context of Cluster

[12] Miosso C. J. and Bauchpiess " A. Fuzzy inference system applied to edge detection in

[13] DP Mandal, C A Murthy. and S K Pal "Utility of multiple choices in detecting ill-

[14] Mandal, D. P.; Murthy C. A. andS. K. Pal,"Determining the shape of a pattern class

[15] Pal,S. K.,Ghosh, A. "Index of area coverage of fuzzy image subsets and object extraction" ,Pattern Recognition Letters, Vol. 11, (1990): pp.831-841. [16] Rosenfeld.A., "The fuzzy geometry of image subsets",Pattern Recognition Lett.

[17] Toussaint G. T "Pattern Recognition and Geometrical Complexity". Proc. 5th

[18] Y. Wang, Q. Chen and B. Zhang. " Image enhancement based on equal area dualistic

[20] Webpage1, Roger Claypoole, Jim Lewis, Srikrishna Bhashyam, Kevin Kelly, (Rice

 www.owlnet.rice.edu/~elec539/Proyects97/morphjrks/moredge.html [21] Webpage2,.http://www.wolfram.com/products/applications/fuzzylogic/examples/p

http://www.doc.ic.ac.uk/~nd/surprise\_96/journal/vol2/jp6/article2.html

[22] Webpage5,.http://www.owlnet.rice.edu/~elec539/Projects97/morphjrks/moredge.ht

[22] Webpage6,.AT&T Laboratories, Cambridge, 2002, "The ORL Database of faces",

[21] Webpage4, http://library.wolfram.com/examples/edgedetection/

http://www.uk.research.att.com/facedatabase.html, [22] Webpage7, Web, The MathWorks, Inc., "Fuzzy Logic Toolbox http://www.mathworks.com/products/matlab/,

digital images". In proceedings of the V Brazilian Conference on Neural Networks,

defined roadlike structures" *International journal on General Systems* vol 64, no 2,

from sampled points Extension to RN'', *International journal on General Systems*,

*International Conference on pattern Recognition* , Miami Beach, 1980, pp. 1324-

sub-image histogram equalization method". *IEEE Trans. on Consumer Electronics.*

University, Huston, U.S.A.), Curso: "ELEC 539 – Digital Image Processing Rice

Analysis" Ph D Thesis Indian Statistical lnstitute Calcutta (1988)

*Information Sciences*, vol. 132, Nov2001.pp. 195-220,

*Applied Soft Computing*, Vol. 3, 2003, pp. 123– 137.

Inc., January 1995.

2001, pages 481–486.

June 1994 pp- 213-228

2(1984),:pp 311-317 5.

vol45,no1,(1999)pp: 68-75.

University" Available:

rocessing.html

[19] Webpage3,

ml

1347. MR 0521237

vol. 26, no. 4, pp. 293--320, 1997.
