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Optical Engineering

Justice in quantizer formation for rational progressive transmission
Author(s): Jose Antonio Garcia; Rosa Rodriguez-Sanchez; Joaquin Fdez-Valdivia
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Paper Abstract

In rational progressive transmission, the spatial orientation trees define the relationship on the pyramid that results from the wavelet transformation. Each tree is associated with one subregion of the original image. The trees may by grouped together into a reduced number of quantizers that convey structural information about the picture to the transmission system. We propose a quantizer formation that will give neither tree a cause for "reasonable regret" in rational progressive transmission. In this sense, we call it a "just" quantizer formation. We introduce the basic concept of "reasonable regret" for justice and give conditions for a just quantizer formation. We show that the definition of a priori importance of a spatial orientation tree is pivotal in the development of a theory for just quantizer formation. The estimation of the a priori importance of a tree must be solved using a large number of insignificant wavelet coefficients—as measured by their magnitudes—that are still effective via coalitions for the reconstruction of the tree. This problem falls into the realm of cooperative game theory with one exogenously given communication graph that results from the wavelet transformation. We provide a cooperative game in this particular communication situation, named after the "SOT-Restricted Game" that naturally induces a game-theoretic solution to the estimation problem: the "zerotree" solution of an SOT-restricted game. Experimental results illustrate the comparative performance of the rational progressive transmission with a just quantizer formation against the state of the art in progressive transmission.

Paper Details

Date Published: 1 September 2004
PDF: 15 pages
Opt. Eng. 43(9) doi: 10.1117/1.1780544
Published in: Optical Engineering Volume 43, Issue 9
Show Author Affiliations
Jose Antonio Garcia, Univ. de Granada (Spain)
Rosa Rodriguez-Sanchez, Univ. de Granada (Spain)
Joaquin Fdez-Valdivia, Univ. de Granada (Spain)

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