Fuzzy Filters for Noise Reduction in Color Images

This paper presents two fuzzy filters for the removal of both Impulse and Gaussian noise in color images. A combination of these two filters also helps in eliminating a mixture of these two noises. For dealing with the Impulse noise, an algorithm is developed to search for a set of uncorrupted pixels in the neighbourhood of the pixel of interest (i.e. the central pixel) and to compute the median of this set. A fuzzy filter consisting of two sub filters is proposed to cancel out the impulse noise. The first sub filter detects the noisy pixel along with the amount of noise in it by utilizing three fuzzy membership functions, defined for this purpose. The corrupted pixels are then corrected using the median of the noise free pixels. The second sub filter makes use of the relation between different color components of a pixel to remove the residual noise in the color image. For the removal of the Gaussian noise, we propose an adaptive distance between color component pairs of the central pixel and the neighbourhood pixel so as to determine the weight of the latter. The weighted average of the weights of all the neighbourhood pixels helps compute the correction term for the Gaussian filter. A cascade combination of the two fuzzy filters in which the output of the Impulse filter is fed to the input of the Gaussian filter is shown to effectively eliminate the mixture of Gaussian and Impulse noises from color images. The results on several color images prove the efficacy of the proposed fuzzy filters.