A hybrid fractal-DCT coding scheme for image compression

We introduce a new way to use fractal coding for image compression, based on the parallel use of a fractal encoder and a DCT encoder. The two encoders are given the complementary roles to capture the information of edge and smooth variation, and the information of detail respectively. We show the advantage of using this hybrid coding scheme over the use of a fractal encoder alone, or a DCT encoder alone. This coding scheme is also the occasion to demonstrate a new concept of coding by nonlinear feature separation based on regular and uniform algorithms, suitable for real-time VLSI implementation. Substantial research has been done in image compression by the method of fractal coding 1, 2]. It is however known that in spite of its good potential for low bit rate compression , fractal coding implies a computationally very intensive encoding. Moreover, unlike DCT coding for example, fractal coding implies an inherently non-regular implementation requiring adaptive subblock partitioning. We brieey recall the principle of fractal coding in Section 2. In this paper, we propose a new way to use fractal coding for image compression. To begin with, we point out that the major part of this computation complexity is required for the encoding of features smaller than the block size. Indeed , as shown in Section 3, a fractal encoder is already capable of well preserving the information of contour and smooth variation of objects larger than the block size, with a very reduced computation complexity. The basic idea of the paper is to use a fractal encoder only for the encoding of these contours and smooth variations. Because we know that using the fractal encoder to also capture the missing image details within the blocks would imply an excessive additional computation complexity, we give this task to a DCT encoder instead, working in parallel. DCT coding is classically good at capturing details within the block size while requiring a small computation complexity. We explain in Section 4 how the DCT encoder can be especially adapted in order to selectively capture the missing details. We also explain how the two parallel outputs of the frac-tal and DCT encoders can be recombined by the decoder in order to reconstruct a single image (method of convex projection or POCS). We give the result of an experiment at the bit rate of 0.18 bit/pixel. We end up with a hybrid fractal-DCT coding scheme …