Sharp Operator Based Edge Detection

Mohammad Kalimuddin Ahmad¹, Stephan Didas², Alemdar Hasanov³, Javid Iqbal⁴

¹Department of Mathematics, Aligarh Muslim University, Aligarh, India.
²Hochschule Trier, Umwelt-Campus Birkenfeld, Fachbereich Umweltplanung/Umwelttechnik, Postfach 1380, Birkenfeld, Germany.
³Department of Mathematics and Computer Science, Izmir University, Izmir, Turkey.
⁴Department of Mathematics, Baba Ghulam Shah Badshah University, Rajouri, India.

DOI: 10.4236/jsip.2015.62017                

Abstract

Ahmad et al. in their paper [1] for the first time proposed to apply sharp function for classification of images. In continuation of their work, in this paper we investigate the use of sharp function as an edge detector through well known diffusion models. Further, we discuss the formulation of weak solution of nonlinear diffusion equation and prove uniqueness of weak solution of nonlinear problem. The anisotropic generalization of sharp operator based diffusion has also been implemented and tested on various types of images.

Keywords

Maximal Function, Sharp Function, Image Processing, Edge Detection, Nonlinear Diffusion

Conflicts of Interest

The authors declare no conflicts of interest.

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