Open Access Open Access  Restricted Access Subscription or Fee Access

Fractal Geometry and Its Application to Image Compression

Tejas Gandhi, Hetal Patel, Darshana Prajapati


This paper presents the concept of fractal and its geometry with the explanation of how natural objects require different geometry rather than traditional Euclidean geometry and also discusses mathematics of fractals with the simulation results of generated fractal and applications of the fractal geometry in image compression. Image compression using fractal has a major drawback of large encoding time and several algorithms have been developed to reduce the encoding time for compression. In this paper, the algorithm of image compression using fractal and DCT for color images is presented with experimental results. In order to minimize the search time for domain blocks no-search technique was used in this algorithm. To avoid low quality of the decompressed image quad tree scheme was used with the algorithm and by predefining appropriate threshold value at each level of quad tree and by choosing suitable contrast scaling factor the accuracy of the output for the algorithm was increased.

Cite this Article
Tejas Gandhi, Hetal Patel, Darshana Prajapati. Fractal Geometry and its Application to Image Compression. Journal of Image Processing & Pattern Recognition Progress. 2015; 2(2): 4–12p.


Fractal, fractal image compression coding, iterated function system, affine transformation, collage theorem, no search.

Full Text:



Barnsley Michael. Fractals Everywhere. 2nd Edn. Academic Press an Imprint of Elsevier; 1988.

Barnsley Michael, Hurd L. Fractal image compression on image processing: mathematical methods and applications. Clarendon Press, Oxford. 1997; 183– 210p.

Saupe D. Lean domain pools for fractal image compression. Proceedings IS&T/SPIE Symposium on Electronic Imaging: Science & Technology still Image Compression. 1996; 2669.

Jacquin A. Image coding based on a fractal theory of iterated contractive image transformations. IEEE. 1992; 1(1): 18–30p.

Hassaballah M, Makky MM, Mahdy YB.A fast fractal image compression method based entropy. Electronic Letters on Computer Vision and Image Analysis. 2005; 5(1): 30–40p.

Mandelbrot B. The fractal geometry. Henry Holt and Company; 1983.

Furao S, Hasegawa O. A fast no search fractal image coding method. Signal Processing: Image Communication. 2004; 19(5): 393–404p.

Salarian M, Hassanpour H. A new fast no search fractal image compression in DCT domain. IEEE Conference. 2007; 62–66p.


  • There are currently no refbacks.