Multiresolution Analysis of Fractal Image Compression

Fractals ◽  
1997 ◽  
Vol 05 (supp01) ◽  
pp. 215-229
Author(s):  
Gregory Caso ◽  
C.-C. Jay Kuo
Keyword(s):  
Wavelet Transform ◽  
Image Compression ◽  
Domain Structure ◽  
Multiresolution Analysis ◽  
Transform Coding ◽  
Transform Domain ◽  
Fractal Image Compression ◽  
Fractal Image ◽  
Affine Mappings ◽  
Encoding Method

In this research, we perform a multiresolution analysis of the mappings used in fractal image compression. We derive the transform-domain structure of the mappings and demonstrate a close connection between fractal image compression and wavelet transform coding using the Haar basis. We show that under certain conditions, the mappings correspond to a hierarchy of affine mappings between the subbands of the transformed image. Our analysis provides new insights into the mechanism underlying fractal image compression, leads to a new non-iterative transform-domain decoding algorithm, and suggests a new transform-domain encoding method with extensions to wavelets other than the Haar transform.

scholarly journals A NOVEL FAST FRACTAL IMAGE COMPRESSION METHOD BASED ON DISTANCE CLUSTERING IN HIGH DIMENSIONAL SPHERE SURFACE

Fractals ◽  
2017 ◽  
Vol 25 (04) ◽  
pp. 1740004 ◽  
Author(s):  
SHUAI LIU ◽  
ZHENG PAN ◽  
XIAOCHUN CHENG
Keyword(s):  
Image Compression ◽  
High Dimensional ◽  
Dimensional Sphere ◽  
Compression Method ◽  
Sphere Surface ◽  
Fractal Image Compression ◽  
Fractal Compression ◽  
Fractal Image ◽  
Speed Up ◽  
Encoding Method

Fractal encoding method becomes an effective image compression method because of its high compression ratio and short decompressing time. But one problem of known fractal compression method is its high computational complexity and consequent long compressing time. To address this issue, in this paper, distance clustering in high dimensional sphere surface is applied to speed up the fractal compression method. Firstly, as a preprocessing strategy, an image is divided into blocks, which are mapped on high dimensional sphere surface. Secondly, a novel image matching method is presented based on distance clustering on high dimensional sphere surface. Then, the correctness and effectiveness properties of the mentioned method are analyzed. Finally, experimental results validate the positive performance gain of the method.

Comparative Study of Wavelet Transform Based Fractal Image Compression

2019 ◽  
Vol 28 (1) ◽  
pp. 24-28
Author(s):  
Heba Abedellatif ◽  
Abdelrahman selim ◽  
Taha E. Taha ◽  
Ramadan El-Shanawany ◽  
Osama F. Zahran ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Image Compression ◽  
Comparative Study ◽  
Fractal Image Compression ◽  
Fractal Image

Merging Fractal Image Compression and Wavelet Transform Methods

Fractals ◽  
1997 ◽  
Vol 05 (supp01) ◽  
pp. 3-15 ◽  
Author(s):  
A. van de Walle
Keyword(s):  
Wavelet Transform ◽  
Image Compression ◽  
Iterated Function System ◽  
Wavelet Coefficients ◽  
Convergence Criteria ◽  
Compression Scheme ◽  
Fractal Image Compression ◽  
Transform Methods ◽  
Fractal Image ◽  
Wavelet Space

Fractal image compression and wavelet transform methods can be combined into a single compression scheme by using an iterated function system to generate the wavelet coefficients. The main advantage of this approach is to significantly reduce the tiling artifacts: operating in wavelet space allows range blocks to overlap without introducing redundant coding. Our scheme also permits reconstruction in a finite number of iterations and lets us relax convergence criteria. Moreover, wavelet coefficients provide a natural and efficient way to classify domain blocks in order to shorten compression times. Conventional fractal compression can be seen as a particular case of our general algorithm if we choose the Haar wavelet decomposition. On the other hand, our algorithm gradually reduces to conventional wavelet compression techniques as more and more range blocks fail to be properly approximated by rescaled domain blocks.

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