Fractal image compression by the classification in the wavelet transform domain

2002 ◽  
Author(s):  
D. Endo ◽  
T. Hiyane ◽  
K. Atsduta ◽  
S. Kondo
Keyword(s):  
Wavelet Transform ◽  
Image Compression ◽  
Transform Domain ◽  
Fractal Image Compression ◽  
Fractal Image

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.

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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