Three-step Approach to Edge Detection of Texts

Kristine Rey O. Recio* and Renier G. Mendoza

Institute of Mathematics, University of the Philippines Diliman,
Quezon City, Metro Manila 1101 Philippines

*Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.




We proposed a three-step image segmentation approach to determine the edges of images containing old texts. In general, texts from old books and articles tend to be very noisy. Thus, we first employed a suitable denoising method to obtain a smooth approximation I_s of a given image I ̃. Then, the fuzzy edge map E ̃ was obtained using the gradient of I_s. This gradient map gave an estimate of the edges of the texts. For the second step, the method of k-means++ with two clusters was employed to separate the edges from rest of the image. Because a smooth approximation of the image was used, the edges obtained are "thick." And so, in the last step of the our method, the binary image generated from the previous step was post-processed using a thinning algorithm. We implemented our method to images containing Baybayin texts from the National Museum of the Philippines.



Image segmentation is a process of dividing the image into regions of meaningful parts such that the image will be simplified and easily analyzable. It is considered as one of the most important processes of image processing. The division of images depends on the image segmentation approach, namely discontinuity detection and similarity detection. The discontinuity approach partitions the image depending on the discontinuities that act as boundaries of the regions. On the other hand, the similarity approach partitions the image depending on the similarity of the data; thus, set of pixels with similar attributes makes a region. . . . read more



ADAMS R. 1975. Sobolev spaces. New York: Academic Press.
ARTHUR D, VASSILVITSKII S. 2007. K-means++: The advantages of careful seeding. In: SODA ’07: Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete algorithms; 07–09 Jan 2007; New Orleans, LA. 1:1027–35.
AUBERT G, KORNPROBST P. 2006. Mathematical problems in image processing, vol. 147 of Applied Mathematical Sciences, 2nd ed. New York: Springer.
AZEROUAL A, AFDEL K. 2017. Fast Image Edge Detection based on Faber Schauder Wavelet & Otsu Threshold. Heliyon 3(12): e00485
BATRA B, SINGH S, SHARMA J, ARORA S. 2016. Computational analysis of edge detection operators. International Journal of Applied Research 2(11): 257–262.
BASU M. 2002. Gaussian-Based Edge Detection Methods – A Survey. IEEE Transactions on Systems, Man, and Cybernetics – Part C: Applications and Reviews 32(3): 252–260.
BIN L, YEGANEH MS. 2012. Comparison for Image Edge Detection Algorithms, IOSR Journal of Computer Engineering 2(6): 1–4.
BRENNER S, SCOTT R. 2008. The mathematical theory of finite element methods. Springer.
BUADES A, COLL B, MOREL JM. 2005. A review of image denoising algorithms with a new one. Multiscale Modeling & Simulation 4(2): 490–530.
CANNY JF. 1986. A computational approach to edge detection. IEEE Transaction on Pattern Analysis and Machine Intelligence 8: 679–714.
CATTÉ F, LIONS P, MOREL J, COLL T. 1992. Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal on Numerical Analysis 29(1): 182–193.
CHAMBOLLE A, LIONS PL. 1997. Image recovery via total variation minimization and related problems. Numerische Mathematik 76(2): 167–188.
CIORANESCU D, DONATO P, ROQUE M. 2012. Introduction to classical and variational partial differential equations. Quezon City (Philippines): The University of the Philippines Press.
DILL AR, LEVINE MD, NOBLE PB. 1987. Multiple resolution skeletons. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI 9(4): 495–504.
FÜRTINGER S. 2012 An Approach to Computing Binary Edge Maps for the Purpose of Registering Intensity Modulated Images [Ph.D. Thesis]. Graz (Austria): Karl-Franzens University of Graz.
GIRON E, FRERY A, CRIBARI-NETO  F. 2012. Nonparametric Edge Detection n Speckled Imagery. Mathematics and Computers in Simulation 82: 2182–98.
GONZALEZ R, WOODS R. 2002. Digital Image Processing, 2nd ed. Pearson Education.
GUO Z, HALL RW. 1989. Parallel thinning with two-subiteration algorithms. Communications of the ACM 32(3): 359–373.
HUYNH-THU Q, GHANBAR M. 2008. Scope of Validity of PSNR in Image/Video Quality Assessment. Electronic Letters 44(13).
RYU J-W, LEE S-O, SIM D-G, HAN J-K. 2012. No-reference Peak Signal to Noise Ratio Estimation Based on Generalized Gaussian Modelling of Transform Coefficient Distributions. Optical Engineering 51(2): 027401.
LAM L, LEE SW, SUEN CY. 1992. Thinning methodologies – A comprehensive survey. IEEE Trans. Pattern Anal. Mach. Intell. 14(9): 869–885.
LI H, LIAO X, LI C, HUANG H, LI C. 2011. Edge Detection of Noisy Image based on a Cellular Neural Networks. Commun Nonlinear Sci Numer Simulat 16: 3746–59.
LINDENBAUM M, FISCHER M, BRUCKSTEIN A. 1994. On gabor’s contribution to image enhancement. Pattern Recognition 27(1): 1–8.
LLOYD S. 1982. Least squares quantization in pcm. IEEE Transactions on Information Theory  28(2): 129–137.
LU D-S, CHEN C-C. 2008. Edge-Detection Improvement by Ant Colony Optimization, Pattern Recognition Letters 29: 416–425.
LUENBERGER D. 1969. Optimization by vector space methods. John Wiley & Sons.
MAINI R, AGGARWAL H. 2009. Study and comparison of various image edge detection techniques. International Journal of Image Processing (IJIP) 3(1): 1–11.
MARR D, HILDRETH E. 1980. Theory of edge detection. Proceedings of the Royal Society B: Biological Sciences 207:187–217.
MORENO J, JAIME B, SAUCEDO S. 2013. Towards No-Reference of Peak Signal to Noise Ratio based on Chromatic Induction Model. International Journal of Advanced Computer Science and Applications 4(1): 123–130.
MELIN P, GONZALES C, CASTRO J, MENDOZA O, CASTILLO O. 2014. Edge-Detection Method for Image Processing Based on Generalized Type-2 Fuzzy Logic. IEEE Transactions on Fuzzy System 22(6): 1515–25.
MORALLO A. 2018 Apr 23. House panel approves use of baybayin as country’s national writing system. The Philippines Star. Retrieved from
MOSLEH A, BOUGUILA N,HAMZA AB. 2012. Image Text Detection using a Bandlet-Based Edge Detector and Stroke Width Transform. Proceedings of the British Machine Vision Conference: 63.1–63.12.
MUMFORD D, SHAH J. 1989. Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics 42(5): 577–685.
MUTHUKRISHNAN R, RADHA M. 2011. Edge detection techniques for image segmentation. International Journal of Computer Science & Information Technology (IJIP) 3(6): 259–267.
O’CALLAGHAN J, LOVEDAY J. 1973. Quantitative measurement of soil cracking patterns. Pattern Recognition 5(2): 83–98.
OSHER O, BURGER M, GOLDFARB D, XU J, YIN, W. 2004. Using geometry and iterated refinement for inverse problems (1): Total variation based image restoration. In: Department of Mathematics, UCLA, LA, CA 90095, CAM Report. p. 4–13.
PERONA P, MALIK J. 1990. Scale Space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12 (7): 629–639.
PRESTON K, DUFF MJB, LEVIALDI S, NORGREN PE, TORIWAKI J. 1979. Basics of cellular logic with some applications in medical image processing. Proceedings of the IEEE 67(5): 826–856.
PREWITT JMS. 1970. Object enhancement and extraction. In: Picture Processing and Psychopictorics. Lipkin BS, Rosenfield A eds. New York: Academic Press. p. 75–149.
ROBERTS L. 1965. Machine Perception of Three Dimensional Solids, Optical and Electro-optical Information Processing.  MIT Press.
ROKACH L, MAIMON O. 2005. Clustering methods. In: Data Mining and Knowledge Discovery Handbook. Maimon O, Rokach L eds. Boston: Springer. p. 321–352.
RONDI L, SANTOSA F. 2001. Enhanced electrical impedance tomography via the mumford-shah functional. ESAIM: Control, Optimization and Calculus of Variations 6: 517–538.
ROUSHDY M. 2006. Comparative Study of Edge Detection Algorithms Applying on the Grayscale Noisy Images Using Morphological Filter. GVIP Journal 6(4): 17–23.
RUDIN LI, OSHER S, FATEMI E. 1992. Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena 60(1): 259–268.
RUSSO F, LAZZARI A. 2005. Color Edge Detection in Presence of Gaussian Noise Using Nonlinear Prefiltering. IEEE Transactions on Instrumentation and Measurement 54(1): 352–358.
SAIF JAM, HAMMAD MH, ALQUBATI IAA. 2016. Gradient based image edge detection. IACSIT International Journal of Engineering and Technology 8(3):153–156.
SCHUMAKER L. 2007. Spline functions: basic theory, 3rd ed. Cambridge: Cambridge University Press.
SMITH SM, BRADY JM. 1997. Susan—A new approach to low level image processing. International Journal of Computer Vision 23(1): 45–78.
SOBEL I, FELDMAN G. 1973. A 3x3 isotropic gradient operator for image processing. In: Pattern Classification and Scene Analysis. Duda R, Hart P eds. New York: John Wiley & Sons. p. 271–272.
SOLIN P. 2005. Elliptic partial differential equations of second order. John Wiley & Sons.
TADMOR E, NEZZAR S, VESE L. 2004. A multiscale image representation using hierarcal (BV, L2) decompositions. Multiscale Modeling & Simulation 2(4): 554–579.
TIKHONOV A, ARSENIN V. 1977. Solutions of ill-posed problems. Washington: V. H. Winstons & Sons.
VERMA OP, HANMANDLU M, SULTANIA AK, PARIHAR AS. 2013. A Novel Fuzzy System for Edge Detection in Noisy Image using Bacterial Foraging, Multidimensional Systems and Signal Processing 24: 181–198.
YAROSLAVSKY L. 1985. Digital picture processing: an introduction. Springer Verlag.
YAROSLAVSKY L, EDEN M. 1996. Fundamentals of digital optics. Birkhauser.
ZHANG X, LIU C. 2013. An Ideal Image Edge Detection Scheme. Multidimensional Systems and Signal Processing 25(4): 659–681.