Computing the Euler Number of a Binary Image Based on a Vertex Codification

 

J. H. Sossa-Azuela¹, R. Santiago-Montero², M. Pérez-Cisneros³, E. Rubio-Espino¹

 

¹ Centro de Investigación en Computación-Instituto Politécnico Nacional Av. Juan de Dios Bátiz s/n, Mexico, DF, México.

² Instituto Tecnológico de León Av. Tecnológico S/N, Frac. Julián de Obregón, León, Guanajuato, México.

³ Departamento de Ciencias Computacionales, Universidad de Guadalajara, CUCEI Av. Revolución 1500, Guadalajara, Jalisco, México.

 

ABSTRACT

We describe a method to compute the Euler number of a binary digital image based on a codification of contour pixels of the image's shapes. The overall procedure evolves from a set of lemmas and theorems, their demonstration and their numerical validation. The method is supported through an experimental set which analyzes some digital images and their outcome to demonstrate the applicability of the procedure. The paper also includes a discussion about present and futures steps on this research.

Keywords: binary shape description, Euler number, topological descriptor, topological invariant.

 

RESUMEN

Se describe un método para el cálculo del número de Euler de una imagen digital binaria basado en una codificación del contorno de las formas en la imagen. El procedimiento tiene su base en un conjunto de lemas y teoremas, su demostración y su validación numérica. El método se soporta a través de una experimentación que analiza varias imágenes digitales para demostrar la aplicabilidad del procedimiento. El artículo incluye también una discusión acerca de pasos presentes y futuros de investigación.

 

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Acknowledgements

R. Santiago and M. Pérez thank the ITL and the UDEG, respectively, for the support. H. Sossa thanks SIP-IPN and CONACYT for the economical supports under grants 20121311, 20131182 and 155014, respectively. E. Rubio thanks SIP-IPN for the support under grant 20131505. We all thank the reviewers for their comments on the improvement of this paper.

 

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