Blurring and Deblurring Digital Images Using the Dihedral Group

In this book we introduce a new method of blurring and deblurring digital images using new filters that generated from Average filter using HB Markov basis. We call these filters HB-filters. These new filters cause a motion blur and remove it from the images. Also we study the action of the Dihedral group on HB-filters to find another HB-filters that give another different types of blur by using the action of the largest subgroup of Dihedral group. We apply our method on gray and RGB (Lena Baboon and Pepper) images with using the two formats (jpg. format) and (png. format). Finally the enhanced images by HB-filters and other methods are compared like Average Gaussian and Motion by using two standard distortion measures; peak signal to noise ratio (PSNR) and Root mean square error (RMSE). The results and analyses showed that the HB-filters are better in PSNR and RMSE.