Introductory remarks

The problem of the application of the linear model in image processing, as developed by Aron and Kurz, involves the interpretation of the experimental data in terms of effects or treatments. Thus, the initial stage is always the selection of the important features, that is, factors to be taken into account and eventually interpreted following the results of any statistical test based on the linear model. The next stage is the introduction of the hypotheses to be tested based on the model that best fits the objectives, the selected factors, and the available data. Finally, the importance to be attached to the eventual results by means of confidence intervals is delineated.

Test statistics based on the theory of the ANOVA within the context of experimental design have been shown to maximize power for all alternatives among all invariant tests with respect to shifting, scaling, and orthogonal transformation of the data. Used in this context, they are generally referred to as UMP.

Several books are devoted to the subject of the ANOVA and it would be rather meaningless to dwell on the theory in this chapter. Instead, we concentrate on the subject of applying ANOVA in image processing problems by providing simple steps to be followed to extract meaningful information from the available data.