A Principle Discussion of Edge Detection based on Gaussian Wavelet


  • Ehsan Ehsaeyan Sirjan University of Technology, Electrical Engineering Department, Sirjan, Iran.


Edge Detection, Wavelet Transform, Gaussian Filter, Step Function, Wavelet Bases, Smooth Filter, Canny Edge Detector, Multiscale,


Edge detection is an image processing technique for finding the boundaries of objects within images. It works by detecting discontinuities in brightness. In this paper, we develop the Canny edge detector, introduce wavelet basis functions of nth Gaussian derivative and utilize them to extract the edge. At first, the principle of the edge detection by the wavelet transform is given briefly and new basis of wavelet functions are introduced and admissibility conditions of them are discussed. Then, the theoretical edge detection analysis of three significant edge types (step, ramp and stage) via new wavelet basis functions is studied, and relevant formulas are derived. The theory of the step response in the x, y and arbitrary direction is given and the effect of smoothing filter is obtained. We show that all introduced wavelet functions can detect the breakpoint of the step function. A model of the ramp function is presented and an approximation of it is used to simplify the results


A. Arnéodo, N. Decoster, and S. G. Roux, "A wavelet-based method for multifractal image analysis. I. Methodology and test applications on isotropic and anisotropic random rough surfaces," The European Physical Journal B, vol. 15, no. 3, pp. 567–600, May 2000.

M.-Y. Shih and D.-C. Tseng, "A wavelet-based multiresolution edge detection and tracking," Image and Vision Computing, vol. 23, no. 4, pp. 441–451, Apr. 2005.

Y. Wu, Y. He, and H. Cai, "Optimal threshold selection algorithm in edge detection based on wavelet transform," Image and Vision Computing, vol. 23, no. 13, pp. 1159–1169, Nov. 2005.

J. Sun, D. Gu, Y. Chen, and S. Zhang, "A multiscale edge detection algorithm based on wavelet domain vector hidden Markov tree model," Pattern Recognition, vol. 37, no. 7, pp. 1315–1324, Jul. 2004.

C. Ducottet, T. Fournel, and C. Barat, "Scale-adaptive detection and local characterization of edges based on wavelet transform," Signal Processing, vol. 84, no. 11, pp. 2115–2137, Nov. 2004.

W. Sun, R. Mukherjee, P. Stroeve, A. Palazoglu, and J. A.

Romagnoli, "A multi-resolution approach for line-edge roughness detection," Microelectronic Engineering, vol. 86, no. 3, pp. 340–351,

Mar. 2009.

Z. Zhang, S. Ma, H. Liu, and Y. Gong, "An edge detection approach based on directional wavelet transform," Computers & Mathematics with Applications, vol. 57, no. 8, pp. 1265–1271, Apr. 2009.

H. Douzi, D. Mammass, and F. Nouboud, "Faber-Schauder Wavelet Transform, Application to Edge Detection and Image

Characterization," Journal of Mathematical Imaging and Vision, vol. 14, no. 2, pp. 91–101, 2001.

Y. Tang, "Status of pattern recognition with wavelet analysis," Frontiers of Computer Science in China, vol. 2, no. 3, pp. 268–294, Aug. 2008.

R. T. J. McAteer, P. Kestener, A. Arneodo, and A. Khalil,

"Automated detection of Coronal loops using a Wavelet transform Modulus Maxima method," Solar Physics, vol. 262, no. 2, pp. 387–397, Mar. 2010.

F. Guo, Y. Yang, B. Chen, and L. Guo, "A novel multi-scale edge detection technique based on wavelet analysis with application in multiphase flows," Powder Technology, vol. 202, no. 1-3, pp. 171–177, Aug. 2010.

D. Heric and D. Zazula, "Combined edge detection using wavelet transform and signal registration," Image and Vision Computing, vol. 25, no. 5, pp. 652–662, May 2007.

L. Zhang and P. Bao, "Edge detection by scale multiplication in wavelet domain," Pattern Recognition Letters, vol. 23, no. 14, pp. 1771–1784, Dec. 2002.

Z. Zhu, H. Lu, and Y. Zhao, "Scale multiplication in odd Gabor transform domain for edge detection," Journal of Visual

Communication and Image Representation, vol. 18, no. 1, pp. 68–0,

Feb. 2007.

S. Liu, Z. Niu, G. Sun, and Z. Chen, "Gabor filter-based edge detection: A note," Optik - International Journal for Light and Electron Optics, vol. 125, no. 15, pp. 4120–4123, Aug. 2014.

J. Shen and S. Castan, "An optimal linear operator for step edge detection," CVGIP: Graphical Models and Image Processing, vol. 54, no. 2, pp. 112–133, Mar. 1992.

R. Mehrotra, K. R. Namuduri, and N. Ranganathan, "Gabor filterbased edge detection," Pattern Recognition, vol. 25, no. 12, pp. 479–1494, Dec. 1992.

L. C. Andrews, Special functions of mathematics for engineers, 2nd ed. Bellingham, Wash., USA: SPIE Society of Photo-Optical

Instrumentation Engi, 2005.

L. Fan, F. Song, and S. Jutamulia, "Edge detection with large depth of focus using differential Haar–Gaussian wavelet transform," Optics Communications, vol. 270, no. 2, pp. 169–175, Feb. 2007.

J. Canny, "A computational approach to edge detection," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI-8, no. 6, pp. 679–698, Nov. 1986.




How to Cite

Ehsaeyan, E. (2017). A Principle Discussion of Edge Detection based on Gaussian Wavelet. Journal of Telecommunication, Electronic and Computer Engineering (JTEC), 9(1), 33–39. Retrieved from https://jtec.utem.edu.my/jtec/article/view/1033