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

The <i>peer</i> <i>group</i> 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 <i>fuzzy</i> <i>peer</i> <i>group</i> concept, which extends the <i>peer</i> <i>group</i> concept in the fuzzy setting. A <i>fuzzy</i> <i>peer</i> <i>group</i> will be defined as a fuzzy set that takes a <i>peer</i> <i>group</i> as support set and where the membership degree of each <i>peer</i> <i>group</i> member will be given by its fuzzy similarity with respect to the pixel under processing. The <i>fuzzy</i> <i>peer</i> <i>group</i> of each image pixel will be determined by means of a novel fuzzy logic-based procedure. We use the <i>fuzzy</i> <i>peer</i> <i>group</i> 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 <i>fuzzy</i> <i>peer</i> <i>group</i>. Both steps use the same <i>fuzzy</i> <i>peer</i> <i>group</i>, 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.

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