Efficient Fractal Image Coding using Fast Fourier Transform

The fractal coding is a novel technique forimage compression. Though the technique has manyattractive features, the large encoding time makes itunsuitable for real time applications. In this paper, anefficient algorithm for fractal encoding which operateson entire domain image instead of overlapping domainblocks is presented.The algorithm drastically reducesthe encoding time as compared to classical full searchmethod. The reduction in encoding time is mainly dueto use of modified crosscorrelation based similaritymeasure. The implemented algorithm employs exhaustivesearch of domain blocks and their isometry transformationsto investigate their similarity with everyrange block. The application of Fast Fourier Transformin similarity measure calculation speeds up theencoding process. The proposed eight isometry transformationsof a domain block exploit the properties ofDiscrete Fourier Transform to minimize the number ofFast Fourier Transform calculations. The experimentalstudies on the proposed algorithm demonstrate that theencoding time is reduced drastically with average speedupfactor of 538 with respect to the classical fullsearch method with comparable values of Peak SignalTo Noise Ratio

Parallel implementation of fractal image compression

Thesis (M.Sc.Eng.)-University of Natal, Durban, 2000.Fractal image compression exploits the piecewise self-similarity present in real images as a form of information redundancy that can be eliminated to achieve compression. This theory based on Partitioned Iterated Function Systems is presented. As an alternative to the established JPEG, it provides a similar compression-ratio to fidelity trade-off. Fractal techniques promise faster decoding and potentially higher fidelity, but the computationally intensive compression process has prevented commercial acceptance. This thesis presents an algorithm mapping the problem onto a parallel processor architecture, with the goal of reducing the encoding time. The experimental work involved implementation of this approach on the Texas Instruments TMS320C80 parallel processor system. Results indicate that the fractal compression process is unusually well suited to parallelism with speed gains approximately linearly related to the number of processors used. Parallel processing issues such as coherency, management and interfacing are discussed. The code designed incorporates pipelining and parallelism on all conceptual and practical levels ensuring that all resources are fully utilised, achieving close to optimal efficiency. The computational intensity was reduced by several means, including conventional classification of image sub-blocks by content with comparisons across class boundaries prohibited. A faster approach adopted was to perform estimate comparisons between blocks based on pixel value variance, identifying candidates for more time-consuming, accurate RMS inter-block comparisons. These techniques, combined with the parallelism, allow compression of 512x512 pixel x 8 bit images in under 20 seconds, while maintaining a 30dB PSNR. This is up to an order of magnitude faster than reported for conventional sequential processor implementations. Fractal based compression of colour images and video sequences is also considered. The work confirms the potential of fractal compression techniques, and demonstrates that a parallel implementation is appropriate for addressing the compression time problem. The processor system used in these investigations is faster than currently available PC platforms, but the relevance lies in the anticipation that future generations of affordable processors will exceed its performance. The advantages of fractal image compression may then be accessible to the average computer user, leading to commercial acceptance

Parallel implementation of fractal image compression

Thesis (M.Sc.Eng.)-University of Natal, Durban, 2000.Fractal image compression exploits the piecewise self-similarity present in real images as a form of information redundancy that can be eliminated to achieve compression. This theory based on Partitioned Iterated Function Systems is presented. As an alternative to the established JPEG, it provides a similar compression-ratio to fidelity trade-off. Fractal techniques promise faster decoding and potentially higher fidelity, but the computationally intensive compression process has prevented commercial acceptance. This thesis presents an algorithm mapping the problem onto a parallel processor architecture, with the goal of reducing the encoding time. The experimental work involved implementation of this approach on the Texas Instruments TMS320C80 parallel processor system. Results indicate that the fractal compression process is unusually well suited to parallelism with speed gains approximately linearly related to the number of processors used. Parallel processing issues such as coherency, management and interfacing are discussed. The code designed incorporates pipelining and parallelism on all conceptual and practical levels ensuring that all resources are fully utilised, achieving close to optimal efficiency. The computational intensity was reduced by several means, including conventional classification of image sub-blocks by content with comparisons across class boundaries prohibited. A faster approach adopted was to perform estimate comparisons between blocks based on pixel value variance, identifying candidates for more time-consuming, accurate RMS inter-block comparisons. These techniques, combined with the parallelism, allow compression of 512x512 pixel x 8 bit images in under 20 seconds, while maintaining a 30dB PSNR. This is up to an order of magnitude faster than reported for conventional sequential processor implementations. Fractal based compression of colour images and video sequences is also considered. The work confirms the potential of fractal compression techniques, and demonstrates that a parallel implementation is appropriate for addressing the compression time problem. The processor system used in these investigations is faster than currently available PC platforms, but the relevance lies in the anticipation that future generations of affordable processors will exceed its performance. The advantages of fractal image compression may then be accessible to the average computer user, leading to commercial acceptance

Fast fractal encoding in frequency domain

Fractal image compression applies the self-similarity property of image. Many researches have been done to study the properties of fractal coding in image domain. In this paper, however, we try to explore the features of fractal coding in frequency domain. We firstly overview the properties of fractal coding in image domain, then we derive the corresponding formula of scaling factor and offset of affine transform in DCT domain. Applying the energy compaction property of DCT, we propose a fast fractal encoding algorithm by using only a small number of low frequency DCT coefficients in measuring the similarity between range block and domain block. We further propose a possible fast hybrid fractal encoding algorithm which combines existing fast search methods, statistical normalization and frequency domain comparison