Fractal image compression using self-affine transformations has recently drawn considerable attention. Although some elements of the technique have a well-established foundation, many issues remain unclear. We consider the attractors that are obtained by varying the parameters of the contractive transformation. We show that the parameters can be divided into two groups and that if the parameters in the first group are fixed, the set of attractors obtained by varying the parameters in the second group is a vector space. Based on this observation, an improvement to the collage coding technique for encoding data is obtained. We then present a coder, referred to as the classified transform coder, which is structurally limited in the same way as the fractal coder. However, in the classified transform coder, the design of the pool of subspaces is directly addressed. Finally, some performance results are presented for the classified transform coder.
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