Fractals can be an e?ective 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. At the BIPLab several strategies have been designed 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/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 methods have been compared with other fractal coding approaches, showing under which circumstances they perform better in terms of both bit rate and/or computing time.
In this approach a new classi?cation method is designed for fractal image compression. It is based on the approximation error, which is computed deferring range/domain comparisons with respect to a preset block. Two di?erent version of the DRDC method are also described: one based on domain tree and the other implemented with the KD-Tree data structure, showing the di?erences in terms of Time/PSNR ratio and memory usage. Especially for KD-Tree based DRDC, experimental results have shown a signi?cant reduction of the number of operations required to generate a good fractal code for a given image, and consequently a performance improvement of the coding process. Indeed, for applications where speed is more important than extreme accuracy, it could be said that hybrid DRDC is the candidate of choice.
Embedding Quality Measures in PIFS Coding
Fractal image coding is a relatively recent technique based on the representation of an image by a map of self-similarities. In last years, most researchers focused their attention on the problem of speeding up the fractal coding process, while paying little attention to possible improvements of the objective and subjective image quality. At BIPLab, we investigated image quality measures, which could represent a reasonable alternative to the RMSE when ?nding a suitable map of similarities. Subjective assessments have been performed in order to compare performances of the selected quality metrics. Experimental results bear witness to the superiority of such a quality metric based on Fourier coe?cients.