Fuzzy Peer Groups for Reducing Mixed Gaussian-Impulse Noise From Color Images

The
peer

group
of an image pixel is a pixel similarity-based concept which has been successfully used to devise image denoising methods. However, since it is difficult to define the pixel similarity in a crisp way, we propose to represent this similarity in fuzzy terms. In this paper, we introduce the
fuzzy

peer

group
concept, which extends the
peer

group
concept in the fuzzy setting. A
fuzzy

peer

group
will be defined as a fuzzy set that takes a
peer

group
as support set and where the membership degree of each
peer

group
member will be given by its fuzzy similarity with respect to the pixel under processing. The
fuzzy

peer

group
of each image pixel will be determined by means of a novel fuzzy logic-based procedure. We use the
fuzzy

peer

group
concept to design a two-step color image filter cascading a fuzzy rule-based switching impulse noise filter by a fuzzy average filtering over the
fuzzy

peer

group
. Both steps use the same
fuzzy

peer

group
, which leads to computational savings. The proposed filter is able to efficiently suppress both Gaussian noise and impulse noise, as well as mixed Gaussian-impulse noise. Experimental results are provided to show that the proposed filter achieves a promising performance.