Improved Fractal Image Compression: Centered BFT with Quadtrees

Computer Scienc

Fractal Image Compression Using Modified Operator (IFS)

Image data Compression based on fractal theory is fundamentally dierent from conventional compression methods, its idea is to generate a contraction operator whose fixed point approximates the original image in a complete metric space of images. The specication of such operator can be stored as the fractal code for the original image. The contraction mapping principle implies that the iteration of the stored operator starting from arbitrary initial image will recover its xed point which is an approximation for the original image. This Contraction mapping is usually constructed using the partitioned IFS(PIFS) technique which relies on the assertion that parts of the image resemble other parts of the same image. It then, nds the fractal code for each part by searching for another larger similar part. This high costly search makes fractal image compression dicult to be implemented in practice, even it has the advantages of a high compression ratio, a low loss ratio, and the resolution independence of the compression rate. In this paper, we investigate fractal image compression(FIC) using Iterated Function Systems(IFS). After reviewing the standard scheme, we state a mathematical formulation for the practical aspect. We then propose a modied IFS that relies on the fact  that, there are very smooth parts in certain images. From the view point of mathematics, we present the modied operator, proving its properties that make it not only a fractal operator but also more eective than the standard one. The experimental results are presented and the performance of the proposed algorithm is discussed

Iterated function systems and shape representation

We propose the use of iterated function systems as an isomorphic shape representation scheme for use in a machine vision environment. A concise description of the basic theory and salient characteristics of iterated function systems is presented and from this we develop a formal framework within which to embed a representation scheme. Concentrating on the problem of obtaining automatically generated two-dimensional encodings we describe implementations of two solutions. The first is based on a deterministic algorithm and makes simplifying assumptions which limit its range of applicability. The second employs a novel formulation of a genetic algorithm and is intended to function with general data input. Keywords: Machine Vision, Shape Representation, Iterated Function Systems, Genetic Algorithms

An In-Depth Look at Fractal Image Compression

Ordinary things that we take for granted, such as the nature surrounding us, are extraordinary fractals in the eyes of mathematicians

A fractal image compression algorithm based on improved imperialist competitive algorithm

Fractal image compression (FIC) is a lossy compression method that has the potential to improve the performance of image transmission and image storage and provide security against illicit monitoring. The important features of FIC are high compression ratio and high resolution of decompressed images but the main problem of FIC is the computational complexity of the algorithm. Besides that, the FIC also suffers from a high number of Mean Square Error (MSE) computations for the best matching search between range blocks and domain blocks, which limits the algorithm. In this thesis, two approaches are proposed. Firstly, a new algorithm based on Imperialist competitive algorithm (ICA) is introduced. This is followed by a two-tier algorithm as the second approach to improve further the performance of the algorithm and reduce the MSE computation of FIC. In the first tier, based on edge property, all the range and domain blocks are classified using Discrete Cosine Transform. In the second tier, ICA is used according to the classified blocks. In the ICA, the solution is divided into two groups known as developed and undeveloped countries to maintain the quality of the retrieved image and accelerate the algorithm operation. The MSE value is only calculated for the developed countries. Experimental results show that the proposed algorithm performed better than Genetic algorithms (GAs) and Full-search algorithm in terms of MSE computation. Moreover, in terms of Peak Signal-to-Noise Ratio, the approaches produced high quality decompressed image which is better than that of the GAs

Fractal image compression and the self-affinity assumption : a stochastic signal modelling perspective

Bibliography: p. 208-225.Fractal image compression is a comparatively new technique which has gained considerable attention in the popular technical press, and more recently in the research literature. The most significant advantages claimed are high reconstruction quality at low coding rates, rapid decoding, and "resolution independence" in the sense that an encoded image may be decoded at a higher resolution than the original. While many of the claims published in the popular technical press are clearly extravagant, it appears from the rapidly growing body of published research that fractal image compression is capable of performance comparable with that of other techniques enjoying the benefit of a considerably more robust theoretical foundation. . So called because of the similarities between the form of image representation and a mechanism widely used in generating deterministic fractal images, fractal compression represents an image by the parameters of a set of affine transforms on image blocks under which the image is approximately invariant. Although the conditions imposed on these transforms may be shown to be sufficient to guarantee that an approximation of the original image can be reconstructed, there is no obvious theoretical reason to expect this to represent an efficient representation for image coding purposes. The usual analogy with vector quantisation, in which each image is considered to be represented in terms of code vectors extracted from the image itself is instructive, but transforms the fundamental problem into one of understanding why this construction results in an efficient codebook. The signal property required for such a codebook to be effective, termed "self-affinity", is poorly understood. A stochastic signal model based examination of this property is the primary contribution of this dissertation. The most significant findings (subject to some important restrictions} are that "self-affinity" is not a natural consequence of common statistical assumptions but requires particular conditions which are inadequately characterised by second order statistics, and that "natural" images are only marginally "self-affine", to the extent that fractal image compression is effective, but not more so than comparable standard vector quantisation techniques

A study and some experimental work of digital image and video watermarking

The rapid growth of digitized media and the emergence of digital networks have created a pressing need for copyright protection and anonymous communications schemes. Digital watermarking (or data hiding in a more general term) is a kind of steganography technique by adding information into a digital data stream. Several most important watermarking schemes applied to multilevel and binary still images and digital videos were studied. They include schemes based on DCT (Discrete Cosine Transform), DWT (Discrete Wavelet Transform), and fractal transforms. The question whether these invisible watermarking techniques can resolve the issue of rightful ownership of intellectual properties was discussed. The watermarking schemes were further studied from malicious attack point of view, which is considered an effective way to advance the watermarking techniques. In particular, the StirMark robustness tests based on geometrical distortion were carried out. A binary watermarking scheme applied in the DCT domain is presented in this research project. The effect of the binarization procedure necessarily encountered in dealing with binary document images is found so strong that most of conventional embedding schemes fail in dealing with watermarking of binary document images. Some particular measures have to be taken. The initial simulation results indicate that the proposed technique is promising though further efforts need to be made

Evolutionary algorithms in artificial intelligence: a comparative study through applications

For many years research in artificial intelligence followed a symbolic paradigm which required a level of knowledge described in terms of rules. More recently subsymbolic approaches have been adopted as a suitable means for studying many problems. There are many search mechanisms which can be used to manipulate subsymbolic components, and in recent years general search methods based on models of natural evolution have become increasingly popular. This thesis examines a hybrid symbolic/subsymbolic approach and the application of evolutionary algorithms to a problem from each of the fields of shape representation (finding an iterated function system for an arbitrary shape), natural language dialogue (tuning parameters so that a particular behaviour can be achieved) and speech recognition (selecting the penalties used by a dynamic programming algorithm in creating a word lattice). These problems were selected on the basis that each should have a fundamentally different interactions at the subsymbolic level. Results demonstrate that for the experiments conducted the evolutionary algorithms performed well in most cases. However, the type of subsymbolic interaction that may occur influences the relative performance of evolutionary algorithms which emphasise either top-down (evolutionary programming - EP) or bottom-up (genetic algorithm - GA) means of solution discovery. For the shape representation problem EP is seen to perform significantly better than a GA, and reasons for this disparity are discussed. Furthermore, EP appears to offer a powerful means of finding solutions to this problem, and so the background and details of the problem are discussed at length. Some novel constraints on the problem's search space are also presented which could be used in related work. For the dialogue and speech recognition problems a GA and EP produce good results with EP performing slightly better. Results achieved with EP have been used to improve the performance of a speech recognition system

Fast Edge Preserving Fractal System

Electrical Engineerin