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Computación y Sistemas

Print version ISSN 1405-5546

Comp. y Sist. vol.15 n.2 México Oct./Dec. 2011




Quadrilateral Detection Using Genetic Algorithms


Detección de cuadriláteros usando algoritmos genéticos


Victor Ayala Ramirez, Sergio A. Mota Gutierrez, and Raul E. Sánchez Yanez


Universidad de Guanajuato, División de Ingenierías Campus Irapuato–Salamanca, Carr. Salamanca–Valle de Santiago Km. 3.5+1.8, Comunidad Palo Blanco, 36700, Salamanca, Mexico. E–mail:,,


Article received on 12/03/2010.
Accepted 05/03/2011.



An approach based on the use of genetic algorithms to detect quadrilateral shapes in images is presented in this paper. The proposed approach finds the best sets of four edge points that are the vertices of quadrilateral shapes in the image. The proposed method uses the evidence provided by the image resulting of the application of an edge detection operator to the input image. Individuals having the best fitness scores are those that are supported by the edge evidence as being the vertices of a quadrilateral present in the input image. We use a sharing operator to avoid detecting similar quadrilaterals. This procedure is used to detect multiple quadrilaterals in a single run of our algorithm. Our method can handle perspective distortion and Gaussian noise corruption on the quadrilaterals to be detected. We have fulfilled tests to validate our approach on synthetic, noise–corrupted and real world images. Tests are both quantitative and qualitative. The proposed approach has shown also to be fast for real–time quadrilateral detection.

Keywords: Genetic algorithms, quadrilateral detection, shape recognition.



En este artículo se presenta un enfoque para la detección de formas cuadriláteras en imágenes usando algoritmos genéticos. El enfoque propuesto encuentra los mejores conjuntos de cuatro puntos de borde que son vértices de cuadriláteros presentes en la imagen. El método propuesto usa la evidencia proporcionada por la imagen resultante de la aplicación de un operador de detección de bordes a la imagen de entrada. Los individuos con mejor valor de adecuación son aquéllos que representan a los vértices de cuadriláteros presentes en la imagen. A fin de evitar la detección de cuadriláteros similares entre sí, se usa una función de sharing. Esto permite detectar múltiples cuadriláteros en una sola ejecución del algoritmo. Nuestro método puede manejar la presencia de distorsión perspectiva y de ruido Gaussiano aditivo en los cuadriláteros por ser detectados. Se presentan pruebas para validar nuestro enfoque sobre imágenes sintéticas, imágenes corrompidas por ruido e imágenes reales. Las pruebas son tanto cuantitativas como cualitativas e incluyen también la detección de cuadriláteros en imágenes dibujadas a mano. El enfoque propuesto muestra también ser rápido para la detección de cuadriláteros.

Palabras clave: Algoritmos genéticos, detección de cuadriláteros, reconocimiento de formas.





This work has been partially funded by the Fondos Mixtos Conacyt–Concyteg project "Herramientas mecatrónicas para la implementación de entornos virtuales" Project No. GTO– 2005–C04–18605. The work of Mota–Gutierrez is supported by Mexico's Conacyt scholarship grant No. 253676/213766.



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