engleski

Statistical Analysis of CRD Model Terms

The least squares fitting is a commonly used method of output colour device characterization. For this purpose, polynomial models are fitted to the data obtained by measuring the device responses to inputs. As it implies the model form, i.e. the polynomial terms to be chosen prior to fitting the model, this choice affects the model prediction power. Terms of a given order in higher order models can be formed in a large number of ways by combining different powers over the variables in cross-product terms, all resulting in the same order. In the context of output colour device modelling, the choice of maximum polynomial order for a particular device was stressed in many studies. However, the choice of the appropriate predictors was not researched systematically. This study shows how the inclusion of different polynomial model terms changes the model prediction power for different output devices. The experiment included gathering the characterization data of four different printers for two different paper types and quality settings suitable for given paper types. This virtually resulted in eight different processes. A test chart containing 918 patches was used to collect the data. Maximum models of each of the eight processes were determined by fitting the models of different orders to the data and evaluating their performance on the independent test set also containing 918 values. Maximum model of a given order refers to a complete model, i.e. the one containing all possible terms up to the given order. The model from which some terms or blocks of terms are excluded is referred to as the reduced model. Optimal models for the eight processes were determined by performing backward elimination on their maximum models. The backward elimination is the procedure of eliminating terms or blocks of terms from the maximum model, one at a time, and comparing each reduced model to the maximum model in terms of sum of squared differences. The evaluation was performed on the same independent test used to determine maximum models. In this study, partial F test was used to compare performances of different models. The maximum and optimized models were, in addition to statistical evaluation, also evaluated psychophysically by transforming an image and evaluating it visually. Although the statistical evaluation showed slightly worse results, psychophysical evaluation showed that the reduced model performed better than the maximum model.

polynomial model; model terms; term significance

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