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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.

DRDC

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.