Sains Malaysiana 42(8)(2013): 1167–1179


Reverse Engineering of Planar Objects Using GAs

(Kejuruteraan Balikan Objek Menyatah Menggunakan GAs)


Muhammad Sarfraz*

Department of Information Science, Kuwait University, Kuwait


Misbah Irshad & Malik Zawwar Hussain

Department of Mathematics, University of the Punjab, Lahore, Pakistan


Received: 15 June 2012 /Accepted: 25 January 2013



An automatic approach, for reverse engineering of digitized hand printed and electronic planar objects, is presented which is useful for vectorizing the generic shapes. The rational cubic functions were used to find the optimal solution of the curve fitting problem with the help of a soft computing technique genetic algorithm which finds appropriate values of shape parameters in the description of rational cubic functions.


Keywords: Curve fitting; generic shapes; genetic algorithm; rational functions; reverse engineering



Kaedah automatik untuk kejuruteraan balikan bagi objek cetakan tangan terdigit dan elektronik dibentangkan. Kaedah ini berguna untuk mevektor bentuk generik. Fungsi kubik rasional digunakan untuk mencari penyelesaian optimum masalah pemadanan lengkung menggunakan teknik pengkomputeran algoritma genetik lembut yang mencari nilai yang sesuai bagi parameter bentuk untuk menerangkan fungsi rasional kubik.


Kata kunci: Algoritma genetik; bentuk generik; fungsi rasional; kejuruteraan balikan; pemadanan lengkung


Avrahami, G. & Pratt, V. 1991. Sub-pixel edge detection in character digitization. Raster Imaging and Digital Typography II : 54-64.

Beus, H.L. & Tiu, S.S.H. 1987. An improved corner detection algorithm based on chain coded plane curves. Pattern Recognition 20: 291-296.

Cabrelli, A.C. & Molter, U.M. 1990. Automatic representation of binary images. IEEE Transaction on Pattern Analysis and Machine Intelligence 12(12): 1190-1196.

Chandrasekaran, M., Muralidhar, M., Murali Krishna, C. & Dixit, U.S. 2010. Application of soft computing techniques in machining performance prediction and optimization: A literature review. The International Journal of Advanced Manufacturing Technology 46: 445-464.

Chetrikov, D. & Zsabo, S. 1999. A simple and efficient algorithm for detection of high curvature points in planar curves. Proceedings of the 23rd Workshop of Austrian Pattern Recognition Group.

Davis, L. 1979. Shape matching using relaxation techniques. IEEE Transactions on Pattern Analysis and Machine Intelligence 1(1): 60-72.

Freeman, H. 1961. On the encoding of arbitrary geometric configurations. IEEE Transactions on Electronic Computer 10(2): 260-268.

Goldberg, D.E. 1989. Genetic Algorithms in Search Optimization and Machine Learning. Reading, MA: Addison Wesley.

Ho¨ lzle, G.E. 1983. Knot placement for piecewise polynomial approximation of curves. Computer Aided Design 15(5): 295-296.

Hou, Z.J. & Wei, G.W. 2002. A new approach to edge detection. Pattern Recognition 35(7): 1559-1570.

Itoh, K. & Ohno, Y. 1993. A curve fitting algorithm for character fonts. Electronic Publishing 6(3): 195-198.

Kirkpatrick, S., Gelatt Jr., C.D. & Vecchi, M.P. 1983. Optimization by simulated annealing. Science 220(4598): 671-680.

Plass, M. & Stone, M. 1983. Curve-fitting with piecewise parametric cubics. Computer Graphics 17(3): 229-239.

Sarfraz, M. & Khan, M.A. 2004. An automatic algorithm for approximating boundary of bitmap characters. Future Generation Computing Systems 20(8): 1327-1336.

Sarfraz, M. 2004. Some algorithms for curve design and automatic outline capturing of images. International Journal of Image and Graphics 4(2): 301-324.

Sarfraz, M. & Rasheed, A. 2007. A randomized knot insertion algorithm for outline capture of planar images using cubic spline. The Proceedings of the 22nd ACM Symposium on Applied Computing, Seoul, Korea, March 11-15.

Sarfraz, M. & Razzak, M.F.A. 2002. An algorithm for automatic capturing of font outlines. Computers and Graphics 26(5): 795-804.

Sarfraz, M. & Khan, M. 2000. Towards automation of capturing outlines of Arabic fonts. Proceedings of the third KFUPM workshop on information and computer science: software development for the new millennium, Saudi Arabia, October 22–23.

Sarfraz, M. & Khan, M.A. 2002. Automatic outline capture of Arabic fonts. Information Sciences 140(3-4): 269-281.

Sarfraz, M., Asim, M.R. & Masood, A. 2004. Capturing outlines using cubic Be´ zier curves. Proceedings of 1st IEEE International Conference on Information and Communication Technologies: From Theory to Application, April 19-23. pp. 539-540.

Sarfraz, M. & Raza, S.A. 2001. Capturing outline of fonts using genetic algorithm and splines. The Proceedings of IEEE International Conference on Information Visualization-IV-UK, July 25-27.

Sarfraz, M., Riyazuddin, M. & Baig, M.H. 2005. Capturing planar shapes by approximating their outlines. Journal of Computational and Applied Mathematics 189: 494-512.

Sarfraz, M. & Raza, A.A. 2002. Visualization of data with spline fitting: A tool with a genetic approach. Proceedings of International Conference on Imaging Science, Systems, and Technology, Las Vegas, Nevada, USA, June 24-27.

Sarfraz, M., Masood, A. & Asim, M.R. 2006. A new approach to corner detection. Computer Vision and Graphics 32: 528-533.

Sarfraz, M., Irshad, M. & Hussain, M.Z. 2012, Vectorization of Image Outlines using Rational Spline and Genetic Algorithm, The Proceedings of The International Conference on Image, Vision and Computing (ICIVC 2012). Shanghai, China, August 25-26, 2012, IASCIT Press Singapore.

Schneider, P.J. 1990. An algorithm for automatically fitting digitized curves. Graphics Gems. pp. 612-626.

Sohel, F.A., Karmakar, G.C., Dooley, L.S., Arkinstall, J. 2005. Enhanced Be´ zier curve models incorporating local information. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, USA, March 18-23. .

Tang, Y.Y., Yang, F. & Liu, J. 2001. Basic processes of chinese character based on cubic B-spline wavelet transform. IEEE Transactions on Pattern Analysis and Machine Intelligence 23(12): 1443-1448.

Teh, C.H. & Chin, R.T. 1989. On the detection of dominant points on digital curves. IEEE Transactions on Pattern Analysis and Machine Intelligence 11(8): 859-873.



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