Abstract of Thesis for a Master’s Degree in Computer Science

Adaptive version of a fractal compression algorithm and its application to medical images

The theme of this publication is the theme of master's thesis "Adaptive version of a fractal compression algorithm and its application to medical images." This paper presents materials: the topic of master's thesis, the main purpose and object, that were set and resolved, the means and tools used in the paper were given, the scheme of fractal algorithm’s modifications were described, the results of their work were analyzed, the usefulness of mechanisms for allocating a significant areas of medical images processing was justified, an application that implements the first preparatory stage of the adaptive algorithm for fractal image compression — the allocation of significant areas was created, as well as the second step — splitting the image into blocks did. The conclusions about the work results of the chosen algorithms modifications for next application to digitized medical images.

Contents

1. Introduction

   • Relevance
   • Aims and objectives

2. Description of studies

3. Conclusion

4. Literature

1 Introduction

Relevance

Images are widely used in various fields, as people's daily lives, and in specific areas of science. Medical images belong to the class of very informative, so image of this class have a lot of data that are very important for further analysis, which can not be ignored. At the same time, such images often have large size, which may cause difficulties during working with them. In this regard, the processing of images of this kind should be careful to vary the compression ratio and loss of image quality. One solution to this dilemma may be the use of algorithms allocation of significant areas. Thus, as a result of processing such an algorithm may allow to reach the small size of the output file and minimize loss of information, so the development of adaptive compression algorithm, which would ensure a small error of compression is important.

Objectives and tasks that must be resolved

The purpose of this paper is to conduct a comparative analysis of existing methods for the modification of fractal compression algorithm to check the possibility and feasibility of algorithms for significant areas allocation of medical images. As a criterion for comparison is proposed to analyze the main characteristics of the methods and stages of work result in relation to medical images (time of encoding, decoding, compression ratio).

The idea of work is development of a new modification of the of fractal compression algorithm method using the algorithm of significant areas allocation. To achieve this objective in the Master's work were indicated and solved the following tasks:

• describe the requirements and steps to create the software
• prepare images for analysis
• to analyze features of the functioning of existing techniques highlight important areas of the image and the feasibility of algorithms allocation of significant areas for further compress them using a fractal algorithm
• make a comparative analysis of the modification of the fractal algorithm at the stage of selecting a domain-rank
• describe algorithms schemes of chosen modifications
• development of appropriate software components, experiments, comparative results
• conclusions about the usefulness of a fractal compression algorithm for medical images (the emphasis is on quality loss)

2 Description of studies

Supposed to realize the following stages of an adaptive algorithm:

1. Allocation of significant areas
2. Partition of the original image into domains and ranks
3. Selection of a domain-rank pair — FE-algorithm, using the Pearson correlation coefficient, entropy, a nonlinear mapping
4. Image compression
5. Decompression
6. Estimate error

Allocation of significant areas

To implement the phase separation region significant applications in MatLab was created. The area of interest is defined by two opposing points of the proposed area of rectangular shape (top left and bottom right). The selected area is allocated to the source image, the blue lines (the contour). When you click on "PolyMask" is cutting off the part of the image that lies outside the selected area. Thus received a new image that will be directly compressed (Picture 1).

Picture 1 — Visualisation of the first step of work - allocation the part of image. Animation consists of 4 frames with delay in 80 ms between frames; delay to next visualisation is 400 ms; there are 10 cycles.

The next stage of the algorithm is partitioned into blocks (domains and ranks). This stage is equal for all versions of the algorithm involved in the analysis.

For a detailed analysis, we selected 3 versions: FE-algorithm [9], using the Pearson correlation coefficient [6], the rate of entropy [3], a nonlinear mapping [10, 11]. The proposed modifications are applied at the stage of finding a pair of domain-rank [9].

3 Conclusion

An application that implements the first (selection important region) and the second phase (the partition into blocks) was created. Images for processing were prepared. An analysis of existing modifications image compression algorithm (stages of work and possible outcomes, characteristics — time coding, compression ratio, the error of compression for grayscale images with smooth edges).

4 Literature:

1. Самира Эбрахими Кахоу, Адаптивный способ сжатия изображений [Текст] // Вісник Хмельницького національного університету, №2 ’2010. – 295 с.
2. Barnsley, Michael F., Sloan, Alan D., Iterated Systems, Inc. Methods and apparatus for image compression by iterated function system. United States Patent 4941193, July 10, 1990
3. Venkata Rama Prasad VADDELLA, Ramesh Babu INAMPUDI [Электронный ресурс]//Journal of Applied Computer Science & Mathematics, no. 9 (4), 2010, Suceava, http://jacs.usv.ro/getpdf.php?paperid=9_3
4. Umnyashkin S. V. Mathematical methods and algorithms for digital image compression using orthogonal transformation, Abstract, 2001 — 569 pp.
5. Prokhorov V.G. Using Kohonen maps to accelerate fractal image compression // Applied Software, № 2, 2009 — S. 7.
6. Илюшин С.В. Фрактальное сжатие телемедицинских изображений [Электронный ресурс], http://www.elsv.ru/files/actual/130.pdf
7. Ватолин Д.С. Использование ДКП для ускорения фрактального сжатия изображений// Журнал «Программирование», №3, 1999, 51—57 с.
8. Авлеева А.Н. Фрактальное сжатие изображений. Решение задач сжатия изображений с использованием систем итерированных функций. Магистерская диссертация, ДонНТУ, 2006 [Электронный ресурс] http://masters.donntu.ru/2006/fvti/avleeva/index.htm
9. Bublichenko A.V. Algorithms for image compression: a comparative analysis and modification // Qualification Masters work, 2008, 150 pp.
10. Кроновер Р.М. Фракталы и хаос в динамических системах // Основы теории. – М.: Постмаркет, 2000
11. Гмурман В.Е. Теория вероятностей и математическая статистика // Учеб. пособие для ВУЗов, 10-е изд. стер. — М.: Высшая школа, 2004. — 479 с.