Sensor Transforms to Improve Metamerism-BasedWatermarking

It was suggested [Bala CIC17] that metamerism could be exploited for watermarking applications by utilizing narrowband LED illuminant spectra for breaking apart metamer colors. It was noticed that, for metameric ink reflectances differing only by the K ink contribution, absolute differences between metamer pairs peaked around a few wavelengths: LEDs with those spectra were then used for displaying the watermarks. Here we investigate the idea of interposing a camera and a display system to make the effects produced more pronounced. We develop an optimization to produce a matrix that best transforms the camera sensors such that color differences between erstwhile metamer pairs are maximized, under the new lights. As well, we consider the problem of optimizing on the lighting itself in addition, leading to even more emphatic breaking apart of metamer pairs and thus more visible watermarks. Introduction In [1], Bala et al. examine whether radically changing the illuminant can successfully break metamerism sufficiently to be used in watermarking. There, printed inks metameric under illuminant D50 were used, with spectra for metameric pairs corresponding to the widest difference in K values. It was observed that subtracting these pairs of surface spectral reflectance functions always produced difference spectra that peaked in absolute value at roughly the same two spectral locations, about 518nm and 621nm. Therefore it was considered that illuminating with LED illumination near those spectral values would most increase RGB discriminability. That is, the idea would be to print a document using such metamer pairs for a hidden background and foreground that would be revealed under narrowband LED illumination. This would therefore complement the idea of using substrate fluorescent properties for hidden watermarks [2] by moving into the domain of visible light. The results in that work, while promising, are not as emphatic as desired, in that the separation between background color and foreground color was not convincingly large. Therefore, in this work we follow the same basic idea but interpose a camera, to allow for greater flexibility than simply the human visual system. As well, we subsequently apply what amounts to a sensor matrix transform (reminiscent of spectral sharpening [3]) specifically with the objective of maximizing the difference, under a new illuminant, of the difference between formerly metameric pairs. That is, suppose we decide to interpose a camera and a display, instead of simply using the eye and XYZ tristimulus values. Then is there a matrix transform, applied to the camera RGBs, which will best emphasize the difference between foreground and background ink? To answer this question, we develop an optimization generating a 3× 3 matrix M for linearly transforming the color space such that the difference between background and foreground colors is maximized, for metamer pairs observed under the new, LED lighting. As well, since the availability of LED light chromaticity is very broad [4], we also examine whether a different choice of LED lighting or combination of LEDs provides the most effective discriminability. It turns out that, indeed, a more general combination of LEDs is more effective than using the original two lights suggested in [1]. To do so, we include a vector of binary weights w in our optimization, where w selects whether or not to include narrowband LED spectral colors in the new illumination – i.e., we optimize on color space transform matrix M and simultaneously on the LED illumination to be used so as best to provide discriminability of watermarks visible only under LED lighting. In general, we would also like to optimize on designing ink reflectance spectra as well as illumination spectra, for this application, as in the optimization set out in [5] in another context. Nevertheless, even without further optimization on the inks themselves, one finds that it is already possible do better with a camera than using the eye. Note that in the following we simply use RGB differences to drive an optimization, but certainly one could use perceptual color. As well, here we use only a small set of metamer pairs, in that the paper provides a proof in principle rather than an exhaustive solution to this general problem. Xerox metamers Here, we consider a set of 6 ink patches, divided into 3 sets of metamer pairs. These 3 pairs have close to matching XYZ values under illuminant D50. Reflectance spectra are plotted in Fig. 1, along with the spectral differences between pair members (cf. [1]). These curves are indeed basically metamer pairs under D50: transforming to XYZ and then to CIELAB with normalizing illuminant D50, we obtain ∆E values between color signal pairs, given by metamer reflectances times D50, as follows: Pair ∆E 1–2 0.82 3–4 0.59 5–6 1.05 (And, with flat, equi-energy illumination applied, the reflectance pairs themselves have ∆E nearly zero.) Color space transform Fixed Lights In [1], difference curves were examined for metamer pairs (differing by maximum K value range), and it was pointed out that 400 450 500 550 600 650 700 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7