Application of Smooth Fuzzy Model in Image Denoising and Edge Detection

Abstract

In this paper, the bounded variation property of fuzzy models with smooth compositions have been studied, and they have been compared with the standard fuzzy composition (e.g., min–max). Moreover, the contribution of the bounded variation of the smooth fuzzy model for the noise removal and edge preservation of the digital images has been investigated. Different simulations on the test images have been employed to verify the results. The performance index related to the detected edges of the smooth fuzzy models in the presence of both Gaussian and Impulse (also known as salt-and-pepper noise) noises of different densities has been found to be higher than the standard well-known fuzzy models (e.g., min–max composition), which demonstrates the efficiency of smooth compositions in comparison to the standard composition.

Keywords

• fuzzy models
• bounded variation function
• smooth compositions
• edge detection
• noise reduction