Abstract: In this paper, we review a number of pyramidal image decomposition techniques for image representation and compression. We argue that the design of an efficient pyramidal image decomposition procedure is directly related to the design of an optimal (non-linear in general) image predictor. However, determining such a predictor is not possible in general. To alleviate this problem, we propose four natural constraints, which uniquely identify the `optimal' predictor as being a morphological opening. This choice naturally leads to a morphological pyramidal image decomposition algorithm recently proposed by Heijmans and Toet. Experimental analysis, allows us to study six pyramidal image decomposition techniques, and demonstrate the superiority (in terms of compression performance and computational simplicity) of the Heijmans-Toet algorithm.!8
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