#### Date of Submission

2-28-1999

#### Date of Award

2-28-2000

#### Institute Name (Publisher)

Indian Statistical Institute

#### Document Type

Doctoral Thesis

#### Degree Name

Doctor of Philosophy

#### Subject Name

Computer Science

#### Department

Machine Intelligence Unit (MIU-Kolkata)

#### Supervisor

Murthy, C. A. (MIU-Kolkata; ISI)

#### Abstract (Summary of the Work)

The language of an image is universal. Images were the means of communicating infor- mation in ancient days. Even today, although people from different parts of the world speak in different languages, an image conveys almost the same universal meaning to all. With the rapid development of modern computer technologies and with the increasing attempt in getting information at ones finger tips, the importance of communication of information using images can not be ignored.Images are stored in computers in the form of a collection of bits representing pixels (picture elements). Pictures are to be digitized to store them in computers. The term digital image refers to a two dimensional function defined on a discrete domain and is denoted by 1(r, 9); the value of I at spatial coordinates (2, v) is known as the pixel value and it represents the light intensity of the image at that point. Now onwards, the term image will refer to a digital image.The representation of images with two dimensional function or a two dimensional ar- ray of pixel values is one of the basic forms widely used in image processing. Image processing usually deals with two different aspects. One is improving the image qual- ity for human interpretation, and the other is the processing of image information for machine perception. Contrast enhancement, noise cleaning, magnification or zooming, edge extraction and segmentation are certain basic tasks of image processing.Images can also be represented in terms of the parameters of some suitable mathe- matical models. Here, a class of images are modeled by a mathematical form and the parameters of the form represent the images. The most important and direct benefit of representing an image in terms of the parameters of a mathematical model lies in the reduction in the number of bits required to store it in the computer. This results in reduction of the size of the image data. The task of storing an image in some alternative form, instead of the primitive pixel form, and thereby reducing memory requirement, is called image compression. The representation of an image in the compressed form should he such that the original form of the image can be reconstructed easily when- ver necessary. Some Icacik image transmission and building up digital/video image libraries. The process of image compression along with decompression is an important component of image processing.In an image compression process, the input used is a digital image and the output is its coded version. To develop an efficient image compression-decompression process, one should concentrate first upon the representation of images by a suitable mathematical model.The present thesis deals with certain aspects of fractal based representation of images in the context of compression. This includes development of efficient algorithms and study of convergence of fractal coder. The investigation also provides results demonstrating the effectiveness of fractal representation for performing some other image processing tasks e.g., image magnification and edge extraction. In this regard, efficient algorithms have been developed where the fractal codes of images are used as input. One may note that only a few attempts have been made, so far, to develop image processing operations which are directly applicable on the coded form of an image.The usage of fractals (12, 75, 109) for representing and generating real world objects like clouds, mountains, trees, leaves and so on [12, 38, 106, 137, 139] is well documented. It is amazing how a simple fractal can model complicated real world objects. The fractal model of real life images is available in the literature (11, 78).

#### Control Number

ISILib-TH271

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

#### DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

#### Recommended Citation

Mitra, Suman Kumar Dr., "On Fractal Based Representation of Image with Application to Image Processing." (2000). *Doctoral Theses*. 150.

https://digitalcommons.isical.ac.in/doctoral-theses/150

## Comments

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28842926