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In Chapter 1 we formulated a rational system for transmission. In Chapters 4 and 5 we integrated rationality and cooperative action to show how disproportionately large benefit gains for quantizers and strong oscillations in gain at very low bit rates can be prevented. In this last chapter we study the quantizer formation to provide a just approach for rational transmission. Figure 6.1 summarizes the relationship among rationality, cooperative action, and justice in the problem of progressive transmission. In a rational system for transmission, a discrete wavelet transform provides a representation of the original image, and the SOT naturally defines the spatial relationship in the pyramid that results from the transformation. Each node of the tree corresponds to a pixel, and its direct descendants (offspring) correspond to the pixels of the same spatial orientation in the next finer level of the pyramid. Transform coefficients in an SOT correspond to a particular region of the original image, and thus, each SOT is associated with one spatial region. Individual SOTs may be grouped together to form a reduced number of quantizers that convey structural information about the picture to the rational transmission. A prioritization protocol, whereby the order of importance is determined by means of a rational approach, involves a choice at each truncation time among alternative quantizers for further transmission in such a way as to avoid certain forms of behavioral inconsistency, as described in Chapter 1.
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