Image Enhancing Research Based On Natural Image Scale Invariance

With higher and higher Proportion of image and video in humancommunication, people have higher requirement for image quality, so imageprocessing is getting more and more attention. To propose more efficient imageprocessing algorithm, natural image statistics attract people’s attention, and areused in image processing. In the area of image processing these natural imagestatistics are used as constraints to improve processing image, and make the resultcloser to original, real image. Scale invariance is proposed as one of importantstatistic properties early, it is very effective in image processing. This paperanalyses and researches natural image scale invariance, and the results are utilizedin image restoration and image super-resolution. The main work and innovationsare as follows:1.Analysis and model of natural image scale invariance.Firstly, natural image scale invariance shows that different scale imagesexhibit similar heavy-tailed distribution when derivative-like filters are applied tothem. We think that the closer response distributions of different scale images are,the more derivative-like filters accord scale invariance.Secondly, for a natural image, it always contains the same contents of differentscales and dually the same contents of same scale exist throughout scales of theimage. According to it, we introduce Gaussian Mixture Model (GMM) to representimage information, and these information are used throughout scales.2.Scale invariant image super-resolution algorithmThis is a simple single image super-resolution algorithm. According to point2in section1, GMM of small scale image is applied on large scale image patchesprocessing across scale. We improve the results of super-resolution in this way,also it is proved that point2in section1is reasonable.3.Scale invariant image restoration algorithm.The algorithm is based on image restoration regularization framework, localtotal variation model and nonlocal adaptive3-D scale invariant sparserepresentation model are used as regularizations, and the minimization problem is solved by split Bregman algorithm. In nonlocal regularization, we use multi-scaleimage patches to form3-D array, and apply GMM of original scale image on smallscale image patches processing according to point2in section1, moreover scaleinvariance determination are executed in GMM components according to point1in section1, it shows that which GMM components are valid.4.Optimal filter based image super-resolution.According to point1in section1, the closer response distributions of differentscale images are, the more derivative-like filters accord scale invariance. Then wecan think that there is an optimal filter which makes response distributions ofdifferent scale images almost same. So we proposed histogram specification basediteration algorithm to train the optimal filter. At the same time, the filter is appliedinto our image super-resolution whose idea is estimating result image according toresponses closest to the actual ones.