Revisiting Spectral Printing: A Data Driven Approach

Spectral printing is a well–established part of imaging that can boast of a rich body of literature. Nonetheless there has been limited commercial uptake of this approach to visual content reproduction, in spite of its clear benefits. The aim of the present paper is therefore to explore what may lie behind this apparent mismatch by looking at how colorimetric (metameric) and spectral reproduction compare on an 11–ink printing system. To aid the above exploration, the paper proposes a new metric for evaluating spectral reproduction in a visually meaningful way and presents an analysis of the spectral properties of colorimetric and spectral reproductions of a variety of original content including spot colors and fine art. Introduction A key choice when making a print is to decide how it is to relate to original content. This can range from the print becoming the first „original‟ (e.g., fine art created digitally, where its viewing on a display is only an intermediate step of the creative process), via its aim being to please (e.g., holiday snaps) to it being as close to a facsimile as possible (e.g., fine art reproduction, proofing). In the last case, the question arises of how broadly the match needs to hold: only under specific viewing conditions or under any (or a broad range of) lighting and viewing. Here the former is a colorimetric (metameric) reproduction while the latter is a spectral one, which has the benefits of mimicking an original more closely so that looking at it gives the same visual experience as looking at the original would, regardless of where they are viewed and who does the viewing. Conversely, the colorimetric case is set up for specific lighting (typically D50 or D65) and with a specific viewer in mind (usually the 2° CIE Standard Observer) and tends to break down under other conditions (hence its „metameric‟ label). As the case looks very strong for spectral reproduction, it is worth putting two caveats on the table: first, how accurately a spectral match can be achieved and second, how much closer it is to an original than the spectral match obtained when colorimetric matching is set up. The two questions are related in that both spectral and colorimetric reproduction have potentially the same spectral variety at their disposal (being a consequence of the inks, substrate and their interactions) where the difference between an explicit spectral match and the spectral fit of the colorimetrically– selected match may be significantly smaller than the mismatch of either of these to the original reflectance spectrum. In other words, a key question is the spectral „compatibility‟ of the original content and printing system‟s potential. Spectral printing is a topic that can boast of a rich body of literature exploring its various aspects, developing its component building blocks (e.g., spectral capture, printer models (e.g., Taplin 1996), gamut mapping, error metrics for minimization) and applying it in various ways (e.g., fine art reproduction, proofing – including of textiles). Given such a well–established field, it is maybe surprising that it has not found more commercial application and the aim of the present paper is also to look for possible reasons for this fact. Two test cases will therefore be considered: fine art reproduction and spot color proofing, both of which are, in principle, a very good match to the benefits of spectral reproduction. The spectral properties of originals and the way they relate to the spectral variety accessible using two printing setups will then be evaluated. Finally the closest achievable matches will be quantified using an evolution of existing multi–illuminant ∆E metrics that aims to be more representative of an original–reproduction pair being viewed under a broad variety of viewing conditions. Before proceeding with an overview of the state of the art, it may be worth underlining why the above two aspects of spectral characteristics (a physical, „device dependent‟ feature) and perceived difference under a variety of conditions (a psychophysical, „device independent‟ aspect) are considered side by side. The reason for this is that image reproduction is concerned precisely with the interplay between reproduction capabilities and their effects on a viewer – i.e., the device dependent seen in a device independent way. State of the art of spectral match metrics Before turning to the analysis outlined above, two areas of the literature will be reviewed: dimensionality reduction (allowing for an analysis of spectral „compatibility‟) and metrics for evaluating spectral matches. In terms of dimensionality reduction, the basic idea is that the underlying variance in spectral data is often of lower dimensionality than that of the measured reflectance space (i.e., typically having 31D for a 400–700nm range sampled at 10nm steps) and that it can therefore be expressed as a weighted combination of a smaller number of bases. In other words: R=B*w, where R is a 31x1 reflectance vector, B is a 31xn matrix containing n bases and w is an nx1 set of weights for combining the bases linearly. Then there are numerous choices of how to obtain the bases, how many of them to use and what space to use this representation in. Here Ramanath et al. (2004) present a survey that compares Principal Component Analysis (PCA), Independent Component Analysis (ICA) and Neural Networks (NN) and also covers methods for obtaining sets of all–positive bases (e.g., Non– negative Matrix Factorization) and their results show similar performance for these approaches when using three bases, with PCA performing best for their data. Tzeng (1999) introduces an important consideration to dimensionality reduction – that the choice of space in which bases are computed and where their combinations are made plays an important role. He then goes on to show that the dimensionality reduction of spectra measured from an IT8.7/2 chart (a three–dye photographic print) suggests that six bases are needed, while it is known that there are only three independent components at play. Tzeng shows how a conversion into the Kubelka Munk K/S absorption space before PCA results in the same level of variance >99.9% being spanned by only three bases. Finally, an important question is, how much variance coverage is enough? One approach is to state that 99.9% ought to be plenty and then select the number of bases that give the necessary coverage. Another is to look for meeting a 1 ∆E threshold under a reference illuminant and choose the number of dimensions to achieve it. Finally, a very well reasoned approach is to use psychophysics to find how many bases it takes to match hyperspectrally–captured scenes. Here Nascimento et al. (2005) report that 8 bases were needed for a 55% discrimination threshold (corresponding to a mean ∆E*ab of 0.7–0.8, which corresponds to a ∆E00 of around 0.4 (Sun and Morovič, 2002)) even though 5 bases would have been sufficient to get to the unit ∆E threshold. Turning to the evaluation of spectral match metrics, Imai et al. (2000) and Viggiano (2004) presented two excellent surveys, comparing metrics that range from spectral–only methods like RMS (the root mean square difference between two reflectance spectra) and GFC (Hernández–Andrés et al.‟s (2001) goodness of fit coefficient), via various weighted version of RMS, e.g., using the diagonal of Fairman‟s (1987) matrix R derived from tristimulus weights for a given illuminant and observer, to metamerism indices (which report the color difference under a test illuminant – e.g., A – for a match under a reference illuminant – e.g., D65) and even a combined spectral and colorimetric metric: CSCM (López–Álvarez et al., 2005). The conclusions of both these surveys are that none of these metrics can be universally recommended over the others and that their choice is a matter of what application it is being used for. The basic challenge here is that while RMS expresses the physical difference between a pair of spectra, it is not visually meaningful. The fact that the starting point is often a mismatch already under a reference illuminant rather than a strict match is a complication, which means that metamerism indices are often applied not directly to an original–reproduction pair, but to one that has been „corrected‟ (e.g., using Fairman‟s (1997) method) to force a match so that the metameric difference under a test illuminant can be expressed. A different approach is then taken by Alsam and Hardeberg (2004) and Bastani et al. (2007) who consider ∆E statistics under multiple illuminants: 6 in the former and 11 in the latter case. Given the above approaches to dimensionality reduction and spectral match metrics, the following sections will first introduce a new alternative to the reflectance or absorption based PCA approaches, proceed to make a more explicit comparison between original and reproducible spectra, propose a new spectral match metric that extends the multi–illuminant methods mentioned previously and finally apply them to the example original and print conditions.