K-statistical operators for set mathematical morphology

  • Juan Santiago Díaz de León Universidad Politécnica de Pachuca
  • Arturo Gamino Universidad Politécnica de Pachuca
  • Julio Salgado Universidad Politécnica de Pachuca
  • Valentín Trujillo Universidad Politécnica de Pachuca
Keywords: Mathematical morphology, dilatation, erosion, opening, closing

Abstract

A generalization of the basic operators in mathematical morphology is presented in this paper. The resulting generalization lead to the construction of the k-statistical operators, due to its ability to obtain geometricaly the statistical descriptors within the range of the operator (Z={0,1}). These operators can be less strict as to the expected result as in the basic operators of dilation and erosion. Furthermore, a single k-statistical operator represents a functional complete set that includes erosion and dilation as particular cases. In a k-statistical operator, the condition to obtain the resulting set depends on whether the area (number of elements) of intersection between the translated structural set and the original set is at least equal to k. As a consecuence, a single parameter (k) is able to create a manifold of operators ranging from erosion to dilation. Hence, other kinds of openings and closings with new behavior are created as alternative solutions to binary image processing problems.

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Author Biographies

Juan Santiago Díaz de León, Universidad Politécnica de Pachuca

Departamento de Ingeniería Telemática

Arturo Gamino, Universidad Politécnica de Pachuca

Departamento de Ingeniería Telemática

Julio Salgado, Universidad Politécnica de Pachuca

Departamento de Ingeniería Telemática

Valentín Trujillo, Universidad Politécnica de Pachuca

Departamento de Ingeniería Telemática

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Published
2013-08-30
How to Cite
Díaz de León J. S., Gamino A., Salgado J., & Trujillo V. (2013). K-statistical operators for set mathematical morphology. Revista Facultad De Ingeniería Universidad De Antioquia, (48), 216-215. Retrieved from https://revistas.udea.edu.co/index.php/ingenieria/article/view/16532