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.
Highlights
Nonlinear diffusion filtering is a well-established tool for image denoising and simplification
We show that the results of these diffusion filters are comparable to classical versions while the underlying sharp operator has a rich theoretical background
Motivated by the available diffusion processes in image processing, we propose an extension of the sharp operator for measuring anisotropic structures
Summary
Nonlinear diffusion filtering is a well-established tool for image denoising and simplification. Starting with the pioneering work by Perona and Malik [2] in 1990, it has attracted the attention of many researchers working in the domain of mathematics and image processing (see [3]-[9], for example) This filter class makes it possible to smooth images while the edges as main source of information are preserved. Based on this idea, John and Nirenberg [11] introduced the concept of bounded mean oscillation (BMO) functions.
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