Fractal encoding for inpainting and secure image sharing

Abstract

Fractal Encoding for Inpainting and Secure Image Sharing This thesis is an investigation to explore two new applications of fractal encoding: 1) secure image sharing and 2) image inpainting. Fractal encoding is a lossy compression technique and the encoded data is a parametric representation of an image. Fractal image encoding relies on finding “self-similarities”, and encodes them as “fractal codes”; it is a parametric representation of an image which encapsulates complete details of an image. Fractal codes obtained for one encoding image size can be decoded at any resolution using fractal interpolation. In secure image sharing, we describe a scheme to encode an image using another reference image in such a way that an end user can retrieve the encoded image only with the reference image. The proposed scheme is simple and similar to fractal encoding; and a key feature is that it simultaneously performs compression and encryption in a single step. To speed up the encoding process, PatchMatch algorithm is leveraged. The performance in terms of encoding time and PSNR is examined for the different encoding methods through experiments. The performance of the proposed encoding scheme in terms of the decoded image PSNR was found to be dependent on the choice of reference image. We have come up with a k-means method for selecting a good reference image from a set of reference images. The proposed algorithm is motivated by the intuition that a suitable reference image should have similar block structures as in the input image which is to be encoded. The second application of image inpainting is multiresolution-based in which fractal “interpolation” (or decoding) is used to transfer texture and structure details from every scale to the next finer scale along the image pyramid. Fractal interpolation is capable of retaining texture appearance at all scales by preserving the fractal dimension [1]. Since fractal interpolation replicates structural details at all scales, it appears to have a better visual quality. The proposed method overcomes a limitation of an earlier work on fractal image inpainting which was limited to filling holes of one-pixel width. Experiments are conducted to compare our method with two other standard inpainting algorithms, exemplar and partial differential equation, and the results indicate improvement or equal performance.