A range/domain approximation error-based approach for fractal image compression

• Published in: IEEE transactions on image processing Vol. 15; no. 1; pp. 89 - 97
• Main Authors: Distasi, R., Nappi, M., Riccio, D.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Approximation; Approximation error; Authentication; Classification; Coding; Coding, codes; Computer Graphics; Computer Simulation; Data Compression - methods; Data Interpretation, Statistical; Decoding; Exact sciences and technology; feature vector; Fractal analysis; fractal image compression; Fractals; Image coding; Image databases; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Indexing; Information, signal and communications theory; Linearity; Mathematical analysis; Models, Statistical; Numerical Analysis, Computer-Assisted; Pattern recognition; Phase measurement; Signal and communications theory; Signal processing; Signal Processing, Computer-Assisted; Studies; Telecommunications and information theory; Image coding; Fractal; Image processing; Classification; Approximation error; Image compression; Image transmission; fractal image compression; feature vector
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2005.860334

Fractals can be an effective approach for several applications other than image coding and transmission: database indexing, texture mapping, and even pattern recognition problems such as writer authentication. However, fractal-based algorithms are strongly asymmetric because, in spite of the linearity of the decoding phase, the coding process is much more time consuming. Many different solutions have been proposed for this problem, but there is not yet a standard for fractal coding. This paper proposes a method to reduce the complexity of the image coding phase by classifying the blocks according to an approximation error measure. It is formally shown that postponing range/spl bsol/slash domain comparisons with respect to a preset block, it is possible to reduce drastically the amount of operations needed to encode each range. The proposed method has been compared with three other fractal coding methods, showing under which circumstances it performs better in terms of both bit rate and/or computing time.