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Computational and Mathematical Methods in Medicine
Volume 2017, Article ID 6494390, 13 pages
Research Article

Fast Parabola Detection Using Estimation of Distribution Algorithms

1Division de Ingenierias, Campus Irapuato-Salamanca (DICIS), Universidad de Guanajuato, Carr. Salamanca-Valle Km 3.5+1.8, Palo Blanco, 36885 Salamanca, GTO, Mexico
2CONACYT, Centro de Investigacion en Matematicas (CIMAT), A.C., Jalisco S/N, Col. Valenciana, 36000 Guanajuato, GTO, Mexico
3CONACYT, Centro de Investigacion en Matematicas (CIMAT), A.C., Fray Bartolome de las Casas 314, Barrio La Estacion, 20259 Aguascalientes, AGS, Mexico

Correspondence should be addressed to Juan Gabriel Avina-Cervantes; xm.otgu@aniva

Received 24 September 2016; Revised 4 January 2017; Accepted 15 January 2017; Published 21 February 2017

Academic Editor: Amparo Alonso-Betanzos

Copyright © 2017 Jose de Jesus Guerrero-Turrubiates et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a new method based on Estimation of Distribution Algorithms (EDAs) to detect parabolic shapes in synthetic and medical images. The method computes a virtual parabola using three random boundary pixels to calculate the constant values of the generic parabola equation. The resulting parabola is evaluated by matching it with the parabolic shape in the input image by using the Hadamard product as fitness function. This proposed method is evaluated in terms of computational time and compared with two implementations of the generalized Hough transform and RANSAC method for parabola detection. Experimental results show that the proposed method outperforms the comparative methods in terms of execution time about on synthetic images and on retinal fundus and human plantar arch images. In addition, experimental results have also shown that the proposed method can be highly suitable for different medical applications.