Fractal Models Of Discrete Sequences With Genetic Optimization

2nd International Symposium on …, 2006

The main problem of all fractal compression implementations is the execution time. The algorithms can spend hours and hours to compress a single image. So the major variants of the standard algorithm were proposed to speed up computation time. But most of them lead to a bad quality, or a lower compression ratio. For example, the Fisher's proposed classification pattern has greatly accelerated the algorithm, but image quality was poor, due to the search space reduction imposed by the classification, which eliminates a lot of good solutions. By using genetic algorithms to address the problem, we want to optimize the domain blocks search, we explore all domain blocks presents in the image, but not in exhaustive way (like standard algorithm), and without omitting any possible block (solution) like does classification pattern. A genetic algorithm is the unique method to satisfy theses constraints. And it is away to be a random search, because the genetic one is directed by fitness selection which produce optimal solutions. Our goal in this work is to use genetic algorithm to solve the IFS inverse problem, and build a fractal compression algorithm based on genetic optimization of domain blocks search. We have also implemented Barnsley standard algorithm, Y. Fisher algorithm based on classification and the genetic compression algorithm with quadtree partitioning. A population of transformations was evolved for each range block and the result is compared with standard Barnsley algorithm, and Yuval fisher algorithm based classification. We deduced an optimal set of values for the best parameters combination, and we can also specify the best combination for each desired criteria: best compression ratio, best image quality or quick compression process. By running many test images ,we experimentally found the following set of optimal values of all the algorithm parameters which ensure compromise between execution time and solutions optimality : Population Size=100 ; Maximum generations = 20 ; Crossover rate = 0.7 ;Mutation rate = 0.1 ;RMS limit = 5 ; Decomposition error limit = 10 ;Flips and isometrics count = 8. In our proposed algorithm, results were much better than those obtained in both Vences & Rudomin and Marc M. Lankhorst [46] approaches.

… Symposium on Control …, 2006

Lobachevskii Journal of Mathematics, 2013

We introduce new method of optimization for finding free parameters of affine iterated function systems (IFS), which are used for fractal approximation. We provide the comparison of effectiveness of fractal and quadratic types of approximation, which are based on a similar optimization scheme, on the various types of data: polynomial function, DNA primary sequence, price graph and graph of random walking.

The Eurographics Association, 1994

2012

Compressing an image is nothing but storing that image in less number of bytes without degrading the quality of an image to an unaccepted level. Compressed image gives less data for the transmission, which results into fast transfer of data over limited bandwidth. Various techniques are available to compress the images. Fractal Image Compression (FIC) is the one which uses self similarity property of the image and compress the images compactly. But algorithm takes more time in order to find self similar parts within an image. This results into large amount of time to compress the image. The solution to this problem is to use of Genetic Algorithm (GA) to find similar parts in an image. With genetic algorithm the task of finding similar parts become very easy and can be completed in less time. So we are optimizing the time required to fractal image compression by using genetic algorithm.

2007

Reducing the search complexity of matching between range block and domain block in fractal image compression is one of the most active research areas lately. This paper puts forward an improved genetic algorithm proposed for obtaining matching domain blocks to pre- vent the premature convergence of GA to a suboptimal individual, to make individual diversity and to improve GA's search efficiency. For each range block, an improved GA's strategy is to encode the position of searching domain block with Gray code, define fitness for minimum dis- tance of current range block matching with searching domain block, select optimal individual protection strategy and adjust GA's controlled parameters of crossover and mutation probability adaptively. Experimental results show that compared with Jacquin coding scheme, our coding scheme achieves an average of 85% reduction in encoding time and improves the efficiency of search. At the same time, the compression ratio and quality of dec...

Optical Memory and Neural Networks, 2017

Abstract⎯The problem of neural network model synthesis using the fractal analysis is addressed in the paper. The set of indicators characterizing the data sample properties from the unified position based on the fractal analysis principles is proposed. The methods of sample fractal dimension determining are proposed. These methods and indicators can be used to solve the problem of data dimensionality reduction. The set of indicators characterizing properties of neural network model is proposed. These indicators can be used in the process of neural network synthesis for the weights set contrasting, also as to find and remove the non-informative features and non-informative connections from the neural network model. The developed indicators and methods are implemented in software and studied at practical problem solving.

Vol 9, No 1, Special Issue, NJNS, 2024

As artificial intelligence advances, more and more tasks that formerly required human discretion can be automated. The proposed study aims to create an automated supervised, hybrid computing algorithm for the synthesis and analysis of engineering and scientific data and gaining insightful knowledge about the data. A novel iterated function approach has been designed by integrating rational C Bezier function with classical fractal function. Sufficient conditions on the scaling and shape factors have been calculated to obtain various simulating patterns occurring in data. The developed model is trained and tested on a set of data values to predict prevalent shape characteristics of the data. Numerical examples validate the suggested approach.

International Journal of Imaging Systems and Technology, 1999

This paper presents a fractal image compression method that utilized a genetic optimization algorithm for optimal domain block selection. The technique successfully addresses the problem of finding an optimal domain block pool for a given range partition, one of the most important issues in fractal image compression. This technique utilizes a genetic optimization algorithm that starts with a source image and generates both a random range partition and a random set of candidate domain blocks for each element of the range partition. Each member of the candidate domain block set was mapped to the corresponding element of the range partition. It was subsequently tested via a quantitative objective function, ranked using a linear fitness scheme and modified, as required, using crossover and mutation operators. This evolutionary process converged to produce an optimal iterated function system (IFS) representation of the source image within a few generations in a robust and efficient manner.

Using statistical information of domain and range blocks, this paper proposes a novel two-phase algorithm for fractal image compression problem. At first the statistical information of the domain and range blocks is extracted. Then at the first phase of the algorithm Genetic Algorithm (GA) finds the best matched domain block for each range block using the difference between the variance of the range and domain blocks as a fast estimation for fitness function. The first step provides a good starting point for Quantum Evolutionary Algorithm (QEA) to start its search process finding good solutions. At the second phase QEA searches among domain pool for best matched domain blocks. The proposed algorithm is tested on several images and experimental results show better performance for the proposed algorithm than GA and QEA.