The concepts of statistical decision theory were applied to the photographic tone reproduction system to develop an objective measurement of tone reproduction accuracy called the "expected loss." Reproductions were made of four scenes using systems with a wide range of tone reproduction characteristics. The expected loss for each system/scene combination was calculated, and the perceived tone reproduction accuracy was determined using the psychophysical scaling method of magnitude estimation. A statistically significant relationship was found between the subjectively determined accuracy and the system expected loss, but the degree of correlation was low enough to indicate that additional factors may need to be included.
Kevin E. Spaulding,
Peter G. Engeldrum,
"A Decision Theory Approach To Tone Reproduction", Proc. SPIE 0549, Image Quality: An Overview, (2 July 1985); doi: 10.1117/12.948799; https://doi.org/10.1117/12.948799