Robust Filters for Image Smoothing

摘要

The properties of some rank filters such as median, least median squared, andtrimmed median squared, are discussed in the context of robust statistics. The efficient computation of these filters is discussed and their stability to the outlier is compared with the standard median filter. Using the robust estimator as an outliers detector, a new type of filter can be designed which performs smoothing on the remaining pixels after removing the outliers. The Gaussian reweighted median (GRM) filter uses Gaussian weights inhibited at the outlier positions to smooth images. This filter inherits the properties of both median and Gaussian filters. Experimental results are presented showing comparisons between corrupted digital images and the same images processed by the various filters. It is demonstrated experimentally that the GRM filter is the best filter overall since it operates like a median filter on impulse noises and reduces the Gaussian noise. Comparison of the GRM filter and the Gaussian filter shows that the GRM filter can preserve sharp edges while small details of the image are smoothed. Subroutines for finding location estimates are appended.