## Abstract

Suitability of the average mutual information (AMI) as a quality criterion in digital printing reproduction is analyzed. The sensitivity of the AMI to variation in the basic bandwidth measures of quality is discussed on the basis of expressions derived. By defining the AMI as a function of the spatial frequency, comparisons with other quality criteria such as the modulation transfer function (or the coherent transfer function) and signal-to-noise ratio are made. Computed results for digital halftoning and impact printing confirm the applicability of the AMI.

© 1986 Optical Society of America

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### Equations (5)

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(1)
$$\text{APD}={\left[{\displaystyle \sum _{g}{\displaystyle \sum _{f}{p}_{f,g}{\left(g-f\right)}^{2}}}\right]}^{1/2}.$$
(2)
$${H}_{f}=-{\displaystyle \sum _{f}{p}_{f}\phantom{\rule{0.2em}{0ex}}{\text{log}}_{2}\phantom{\rule{0.2em}{0ex}}{p}_{f}}.$$
(3)
$$\text{AMI}={\displaystyle \sum _{g}{\displaystyle \sum _{f}{p}_{f}{p}_{g|f}\phantom{\rule{0.2em}{0ex}}{\text{log}}_{2}\left({p}_{g|f}/{p}_{g}\right)}},$$
(4)
$$\text{AMI}\left(u\right)={\displaystyle \sum _{g}{\displaystyle \sum _{f}{p}_{f\left(u\right)}{p}_{g\left(u\right)|f\left(u\right)}\phantom{\rule{0.2em}{0ex}}{\text{log}}_{2}\left[{p}_{g\left(u\right)|f\left(u\right)}/{p}_{g\left(u\right)}\right]}}.$$
(5)
$$\begin{array}{cc}{p}_{g}={p}_{f}\phantom{\rule{0.2em}{0ex}}\frac{\mathrm{d}f}{\mathrm{d}g};& \phantom{\rule{1.5em}{0ex}}\text{if}\phantom{\rule{0.2em}{0ex}}{p}_{f}=1/{f}_{m},\text{then}\phantom{\rule{0.2em}{0ex}}{p}_{g}=1/{g}_{m},\end{array}$$