Alternative Way to Compute the Euler Number of a Binary Image

 

J. H. Sossa–Azuela*¹, E. B. Cuevas–Jiménez², D. Zaldivar–Navarro³

 

¹ Centro de Investigación en Computación–IPN, Av. Juan de Dios Bátiz, esquina con Miguel Othón de Mendizábal, Mexico City, C. P. 07738. MEXICO *E–mail: hsossa@cic.ipn.mx

^2,3 Centro Universitario de Ciencias Exactas e Ingenierías (CUCEI) Universidad de Guadalajara Av. Revolución 1500 Col. Olímpica C.P. 44430 Guadalajara, Jalisco, MEXICO.

 

ABSTRACT

In this paper an alternative way to compute the (E) Euler number of a binary image via information about its pixels is presented. The P perimeter of the objects in the image, their P_c contact perimeter and the T–type pixel are used to obtain this important invariant. This is the second time the Euler number is described in terms of the contact perimeter of the objects in an image but with new results. The first paper that reports computing the Euler number of a binary shape in terms of the P and P_c is in [E. Bribiesca, Computation of the Euler number using the contact perimeter, Computers and Mathematics with Applications 60:1364–137 (2010)]. Bribiesca's proposal is useful only for unit–width shapes. In this paper, we extend Bribiesca's method for non–unit–width shapes.

Keywords: Binary image characterization, perimeter, contact perimeter, Euler number, topological descriptor, topological invariant.

 

RESUMEN

En este trabajo se presenta un método alternativo para el cálculo del número de Euler (E) de una imagen binaria mediante información de sus píxeles. El perímetro P de los objetos en la imagen, sus perímetros de contacto P_c y el tipo t de la celda son utilizados para obtener este importante invariante. Esta es la segunda vez que el número de Euler es descrito en términos del perímetro de contacto de los objetos en una imagen. El primer trabajo que reporta el calcular el número de Euler de una forma binaria en términos de P y P_c es en [E. Bribiesca, Computation of the Euler number using the contact perimeter, Computers and Mathematics with Applications 60:1364–137 (2010)]. La propuesta de Bribiesca es útil sólo para formas de grosor unitario. En este trabajo extendemos la propuesta de Bribiesca para el caso de formas de cualquier grosor.

 

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Acknowledgements

The authors thank SPIN–IPN and CONACYT for the economical support under grants number 20111016 and 155014. We kindly thank the reviewers for their comments which contributed to the improvement of this paper.

 

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