Preface

Fractal analysis is becoming more and more common in all walks of life. This includes biomedical engineering, steganography and art. Writing one book on all these topics is a very difficult task. For this reason, this book covers only selected topics. Interested readers will find in this book the topics of image compression, groundwater quality, establishing the downscaling and spatio-temporal scale conversion models of NDVI, modelling and optimization of 3T fractional nonlinear generalized magneto-thermoelastic multi-material, algebraic fractals in steganography, strain induced microstructures in metals and much more.

For example, one of the chapters covers the application of fractals to steganography. As is well known, steganography includes the technology of hiding watermarks in multimedia files. This technology is important in the field of copyright protection, secret communication and the form of information exchange. Contemporary image analysis and processing methods allow the determination of the presence of embedded watermarks in a stegoimage on the basis of the original image and its statistical features. In this chapter, the authors propose the use of algebraic fractals for steganographic embedding of watermarks in colour images. The authors propose the use of algebraic fractals for an image serving as a secret key, which, according to the authors, allows for more resistant deposition to computer attacks, including compression.

In another chapter, the author describes the use of fractals to analyze the terrain surface using remote sensing. The author created the downscaling models using fractal theory for the parameters of the earth's surface in quantitative remote sensing. Additionally, it is still a hotspot for creating space-time conversion model parameters of the land surface in quantitative remote sensing in the future and marked in this connection, the author developed a multifractal scaling methodology and its availability is proposed.

This book brings together a small collection of chapters covering specific aspects of the fractal field. I would like to thank the publishers (IntechOpen) for their help in preparing this book and the authors of the accepted manuscripts for their work and patience. For interested readers, I would like to suggest that they pay attention to the annual conferences on fractals and their use in various areas of life.

The book will definitely be of interest to scientists dealing with fractal analysis, as well as biomedical engineers or IT engineers. I encourage you to view individual chapters.

> **Robert Koprowski** Faculty of Science and Technology, University of Silesia, Sosnowiec, Poland

**Chapter 1**

**Abstract**

**1. Introduction**

**1**

Compression

*Rafik Menassel*

Optimization of Fractal Image

Fractal encoding is a promising method of image compression. It is built on the basis of the forms found in the image and the generation of repetitive blocks based on mathematical translations. The technique seems to be moved theoretically and practically, but it requires enormous programming time due to the excessive resources required when compressing large volumes of data. On the other hand, metaheuristics represent all of the methods used to solve difficult optimization problems with less consumption of resources. They are marked by their rapid convergence and their lessening in research difficulties. In this chapter, we have tried to apply a new experience around the performance of organic metaheuristics inspired by nature, which are, respectively, the wolf pack algorithm (WPA) and the bat-inspired algorithm (BIA), as bioinspired techniques to optimize the fractal image compression (FIC). Experiments show the enhancement of diverse characteristics (coding time, compression rate (CR), peak signal-to-noise ratio (PSNR), and mean square error (MSE)). In addition, an assessment of the proposed approaches via many other approaches highlights this improvement.

**Keywords:** fractal image compression (FIC), metaheuristics, wolf pack algorithm

Nowadays, a significant size of information is managed and transmitted, and mainly, images have involved prodigious status, particularly in recognition field. Thus, it is important to decrease the size of the data via compression algorithms which can allow their storage and their transmission while using limited resources. Compression is employed to overcome this problem and keep more files. Mainly multimedia files need more storage space than other types of files. Images represent the largest part of the most used multimedia files in almost all fields. Unlike other types of files, a huge amount of image data requires more resources for storage and transmission on computer networks, and compression is therefore presented as an inevitable tool with the aim of more maneuverability of this data. Today, several compression formats exist while presenting their limits (degradations, size, duration, etc.) on somewhat particular images (text images and background areas).

To overcome this difficulty, scientists are constantly developing new techniques to compress images in order to find a perfectionist compression method that can

The compression methods that exist tend to introduce the theory of fractals, which appears to be a strong instrument for boosting image quality and reducing

largely conserve storage space and preserve the quality of the source file.

(WPA), bat-inspired algorithm (BIA), image quality

## **Chapter 1**
