Adaptive Type-2 Fuzzy Filter with Kernel Density Estimation for Impulse Noise Removal

Abstract

Noise is inevitably common in digital images, leading to visual image deterioration. Therefore, a suitable filtering method is required to lessen the noise while preserving the image features (edges, corners, etc.). This article presents the efficient type-2 fuzzy weighted mean filter with an adaptive threshold to remove the impulse noise. The present filter has two primary steps. The first step categorizes images as lightly, medium, and heavily corrupted based on an adaptive threshold by comparing the maximum absolute luminance difference of processed pixels with the upper and lower membership function of the type-2 fuzzy identifier. The second step eliminates corrupted pixels by computing the appropriate weight using Gaussian membership functions with the mean and variance of the uncorrupted pixels in the filter window. The variance of detection and denoising steps are estimated using the kernel density estimate of the respective filter window. Simulation results vividly show that the obtained denoised images preserve image features, i.e., edges, corners, and other sharp structures, compared with different filtering methods.