Computation of the Euler Number of a Binary Image Composed of Hexagonal Cells

 

J. H. Sossa–Azuela*¹, E. V. Cuevas–Jiménez², D. Zaldivar–Navarro²

 

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

 

ABSTRACT

Most of the proposals to compute the Euler number of a binary image have been designed to work with images composed of squared cells. Only a few of these methods (in the case of images composed of hexagonal cells) have been reported in literature, although it is known that images composed of hexagonal cells do not suffer from the problems of connectivity frequently found in the case of images composed of squared cells. In this paper, a new way to compute the Euler number (E) of a binary image composed of hexagonal cells is presented. For this, the perimeter P of the isolated regions in the image, their contact perimeter P_c and the type T of a cell are used to obtain this important invariant. The proposal can be used alone or in combination with other features to describe any binary planar shape composed of hexagonal pixels for its further recognition.

Keywords: Binary image characterization, Perimeter, Contact Perimeter, Euler number or genus, Topological descriptor, Topological invariant.

 

RESUMEN

El principal objetivo de este trabajo es el presentar una nueva clase de controlador de tipo retroalimentado, el cual contiene en su estructura una forma polinomial del llamado error de control, el controlador propuesto es aplicado a un quimiostato sulfato–reductor, el cual pudiera ser usado para varios fines biotecnológicos, como la remoción de metales pesados en aguas residuales. El comportamiento a lazo cerrado del quimiostato considerado es teóricamente analizado y se prueba convergencia práctica a la trayectoria óptima seleccionada. La metodología propuesta es aplicada a un modelo cinético de una bacteria sulfato–reductora experimentalmente validado y experimentos numéricos complementarios muestran un comportamiento a lazo cerrado satisfactorio en comparación con otros controladores.

 

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Acknowledgments

The authors wish to thank SIP–IPN for the economical support under grant number 20100468. The authors also thank the European Union, the European Commission and CONACYT for their economical support. This paper has been prepared by economical support of the European Commission under grant FONCICYT 93829. The content of this paper is an exclusive responsibility of the IPN and the UDEG and it cannot be considered to reflect the position of the European Union. We also thank the reviewers for their comments to improve this paper.

 

Annex