Fractal Geometry And Its Applications To Image Compression/Coding

One primary problem we are confronted with in information age is to effectively store and transmit huge amounts of digital images. Except improving the hardware, this casts increasing the urgency to develop new compression algorithms with high performance. In recent 20 years,fractal geometry, by way of one rising mathematical branch, provide a strongly tool of describing and researching the mumerous and complicated natural phenomena. It has received a great deal of attention and study from researchers all over the world in the field of image compression.Fractal image compression, as a fire-new scheme of image compression, based on the self-similarity and proportion of image, it implements the image data compression by eliminating the image geometry redundancy. In this technique, an image is usually represented by a contractive affine transformation, for which the reconstructed image is its fixed point and approximate to the original image. The fractal code of the image consists of the parameters of the contractive transformation. The fractal decoding is a relatively simple iteration procedure, in which the decoded image is approximated by iterating the contractive transformation denoted in the fractal code on an arbitrary initial image.Fractal image coding has received much interest over the past decade in the area of image compression. It is well known that too long encoding time is the main drawback of this technique, in fact, prevent fractal image compression from becoming a practical method for image compression, hence fast encoding has become a hot issue in fractal image compression. But,we pay attention to existed fractal decoding process cann't carry out controllable decoding,restricting its some application. In this dissertation, some fast fractal image encoding and controllable progressive decoding scheme are proposed, as follows:(1) Because of existed fast encoding methods are often at the cost of reconstructed image quality, or can only obtain poor speed-up ratio. On the basis of the authors'results published in this journal[67], this paper further proposed two strategies which improved both quality and speed of fractal encoding: one, a priori adding additive white Gaussian noise into the image being encoded to reduce the domain blocks that are unlikely to meet the constraint on contrast scaling factors; the other, range blocks with small standard deviations are directly approximated by the constant block (i.e., all the...