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.

scholarly journals Improving Fractal Image Compression Scheme through Quantization Operation

2007 ◽  
Vol 4 (2) ◽  
pp. 330-337
Author(s):  
Baghdad Science Journal
Keyword(s):  
Image Quality ◽  
Image Compression ◽  
New Method ◽  
Compression Scheme ◽  
Fractal Image Compression ◽  
High Image Quality ◽  
Fractal Image ◽  
Separate Step ◽  
Transform Coefficients

We explore the transform coefficients of fractal and exploit new method to improve the compression capabilities of these schemes. In most of the standard encoder/ decoder systems the quantization/ de-quantization managed as a separate step, here we introduce new way (method) to work (managed) simultaneously. Additional compression is achieved by this method with high image quality as you will see later.

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 Fractal Image Compression Using Block Indexing Technique: A Review

2020 ◽  
pp. 1798-1810
Author(s):  
Zainab J. Ahmed ◽  
Loay E. George ◽  
Zinah S. Abduljabbar
Keyword(s):  
Image Compression ◽  
Iterated Function System ◽  
Image Data ◽  
Main Concern ◽  
Affine Transformations ◽  
Fractal Image Compression ◽  
Fractal Image ◽  
Indexing Method ◽  
The Moment ◽  
Indexing Technique

Fractal image compression depends on representing an image using affine transformations. The main concern for researches in the discipline of fractal image compression (FIC) algorithm is to decrease encoding time needed to compress image data. The basic technique is that each portion of the image is similar to other portions of the same image. In this process, there are many models that were developed. The presence of fractals was initially noticed and handled using Iterated Function System (IFS); that is used for encoding images. In this paper, a review of fractal image compression is discussed with its variants along with other techniques. A summarized review of contributions is achieved to determine the fulfillment of fractal image compression, specifically for the block indexing methods based on the moment descriptor.  Block indexing method depends on classifying the domain and range blocks using moments to generate an invariant descriptor that reduces the long encoding time. A comparison is performed between the blocked indexing technology and other fractal image techniques to determine the importance of block indexing in saving encoding time and achieving better compression ratio while maintaining image quality on Lena image.

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
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