The characterisation of colour printing devices via physical, numerical and LUT models

Abstract

The aim of this study was, to derive well-performed four-color printer device characterisation models (DCMs), which were afterwards used to pack up entries of the look up table (LUT) to perform the actual complex colour-image transformations. Based on both non-linear and non-ideal behaviours of primary colorants, two types of printing device characterisation model approaches were proposed in this work. One is a physical type of bicubic-spline interpolation algorithm (referred to as Ext-SA-Bicubic) which is a modified version of sub-additivity algorithm (SAA). The SAA model, originally proposed by Yule, modelled superimposed inks behaviour of converging to a point. Another is a numerical type of the 2nd-order polynomial regression equations, incorporated with singular-value decomposition (SVD) approach (referred to as 2nd-SVD). Each of two printer DC algorithms integrated a grey-component replacement (GCR) approach into a 3rd-order masking type of three-colour printer model to produce four-colour output. Preliminarily, both "with" and "without" a setup state of output linearization (OL), a function provided by a RIP (Raster image processing) software used to both calibrate the printer in question and produce an optimized tone curve for each primary colorant of CMYK, was applied in the printer characterisation process. Moreover, two different forms of "Equivalent Neutral Density" (END) and "Principal Density" (PD) were separately applied in the three-colour model (i.e. 3rd-order masking equations) for both the numerical and the physical types of DC algorithms mentioned above. Hence, in terms of both END and PD, separately applied using both of "Without" and "With" Output Linearization (OL) in input-output relationship, totally, eight printer DCMs were derived. Each model was also carried out both the forward and the reverse transform processes. An Epson Stylus Pro4000 colour printer plus a RIP of EFI XF v2.6.1 was mainly tested in this study and used as the destination device, and incorporated with a well-characterised EIZO-CG210 LCD (used as source device) with ΔE94 of 1.05 using PLCC Characterisation model to perform a cross-media colour transform from monitor to printer. Performances of DCMs in question were firstly investigated using training/test data sets. Also a set of forced-choice paired-comparison psychological experiments was conducted. It was used to cross verify the prediction performances of those cross-media LUT models packed up using their corresponding mathematical DCMs in question. Overall, the results showed that all the models, with an output-linearization (OL) setup state, gave quite satisfactory prediction performances, but the 2nd-SVD always performed much better than the Ext-SA-Bicubic under every of the same characterisation mechanism. Also all models with OL setup state in the characterisation process were significantly much better than those models using the same algorithms but without OL setup state. However four Ext-SA-Bicubic models (with and without OL) using END/PD approach performed slightly unsatisfactory in shadow areas of tested colour images. It was found that it is because of irregular distribution of training samples, used to model the sub-additivity behaviour, in colorimetric density domain/space; and especially too short distance in neighbourhood (or nearly piling up) of samples which were near shadow region. Therefore, it resulted in inaccurately predicted CMYK values for shadow areas of tested colour images, by using the bicubic-spline interpolation approach, and caused the colour shift and poor-smoothness.