Abstract

One of the main disadvantages of fractal image data compression is a loss time in the process of image compression (encoding) and conversion into a system of iterated functions (IFS). In this paper, the idea of the inverse problem of fixed point is introduced. This inverse problem is based on collage theorem which is the cornerstone of the mathematical idea of fractal image compression. Then this idea is applied by iterated function system, iterative system functions and grayscale iterated function system down to general transformation. Mathematical formulation form is also provided on the digital image space, which deals with the computer. Next, this process has been revised to reduce the time required for image compression by excluding some parts of the image that have a specific milestone. The neural network algorithms have been applied on the process of compression (encryption). The experimental results are presented and the performance of the proposed algorithm is discussed. Finally, the comparison between filtered ranges method and self-organizing method is introduced.

Highlights

  • The mathematics behind fractals began to take shape in the 17th century when mathematician and philosopher Leibniz considered recursive self-similarity [1]

  • Stark first proposed a research to apply the neural network to iterated function system (IFS) [12]

  • The term “artificial” means that neural nets are implemented in computer programs that are able to handle the large number of necessary calculations during the learning process

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Summary

Introduction

The mathematics behind fractals began to take shape in the 17th century when mathematician and philosopher Leibniz considered recursive self-similarity ( he made the mistake of thinking that only the straight line was self-similar in this sense) [1]. (2014) Fractal Image Compression Using Self-Organizing Mapping. Fractal image compression (FIC) was introduced by Barnsley and Sloan [3]. Jacquin [6] presented a more flexible method of FIC than Barnsley’s, which is based on recurrent iterated function systems (RIFSs) introduced first by him. J. Stark first proposed a research to apply the neural network to iterated function system (IFS) [12]. Stark first proposed a research to apply the neural network to iterated function system (IFS) [12] His method was using Hopfield neural network to solve the linear progressive problem and get the Hutchinson metric quickly. His neural network approach cannot obtain the fractal code automatically. The method of clustering by means of Artificial Kohonen neural self-optimizing network is least afflicted with these disadvantages [15]

Neural Networks
The Components of a Neural Net
Competitive Learning and Clustering
Winner Selection
Cost Function
The Inverse Problem of Fractals
Iterated Function System
Fractal Inverse Problem
Fractal Image Compression by Means of Kohonen Network
Global Codebook
Ranges Filtering Algorithm
Results and Discussion
Full Text
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