Abstract
We review and compare a number of linear and nonlinear pyramidal image decomposition techniques which are based on the approach proposed by Burt and Adelson ( IEEE Trans. Comm. 31, 1983, 532-540). We argue that the design of a proper Burt-Adelson type pyramidal decomposition technique is directly related to the design of an optimal (nonlinear in general) image predictor. However, determining such a predictor is not possible in general. We propose four prediction constraints, which uniquely identify the "optimal" predictor as being a morphological opening. This choice naturally leads to one of the morphological image decomposition algorithms proposed by Heijmans and Toet ( Comput. Vision Graphics Image Process. Image Understanding, 54, 1991, 384-400). By using an experimental analysis, based on a collection of four images with a broad spectrum of structural detail, we are able to study the behavior of six pyramidal image representation and compression techniques, and demonstrate the superiority (in terms of compression performance and computational simplicity) of the Heijmans-Toet algorithm.
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