. Prediction of the spectral reflectance of laser-generated color prints by combination of an optical model and learning methods. Journal of the Optical Society of America. A Optics, Image Science, and Vision, Optical Society of America, 2015, 32 (9) Recent color printing technologies based on the principle of revealing colors on pre-functionalized achromatic supports by laser irradiation offer advanced functionalities, especially for security applications. However, for such technologies the color prediction is challenging, compared to classic ink-transfer printing systems. The spectral properties of the coloring materials modified by the lasers are not precisely known and may strongly vary, depending on the laser settings, in a nonlinear manner. We show in this study, through the example of the Color Laser Marking technology based on laser-bleaching of a mixture of pigments, that the combination of an adapted optical reflectance model and learning methods to get the model's parameters enables predicting the spectral reflectance of any printable color with rather good accuracy. Even though the pigment mixture is formulated from three colored pigments, an analysis of the dimensionality of the spectral space generated by CLM printing, thanks to a Principal Component Analysis decomposition, shows that at least four spectral primaries are needed for accurate spectral reflectance predictions. A polynomial interpolation is then used to relate RGB laser intensities with virtual coordinates of new basis vectors. By studying the influence of the number of calibration patches on the prediction accuracy, we can conclude that a reasonable number of 130 patches are enough to achieve good accuracy in this application.

International audienceThe present paper discusses the concept of subtractive color mixing widely used in color hardcopy applications and shows that a more realistic concept would be " spectral mixing " : the physical description of the coloration of light by printed surfaces comes from the mixing of light components selectively absorbed by inks or dyes during their patch within the printing materials. Some classical reflectance equations for continuous tone and halftone prints are reviewed and considered as spectral mixing laws. The challenge of extending these models to new inkless printing processes based on laser radiation is also addressed. Color mixing is a key-concept in color reproduction, either by painting, printing, or displaying. It refers to the observation that a large panel of colors (the color gamut) can be achieved by varying the amount of a limited set of base colors, called primaries. With light emitting systems, the primaries are light sources, often with red, green and blue color, that are either superposed or juxtaposed with a shorter period than the visual acuity. Since the tristimulus values of the produced colors is a linear, additive combination of the tristimulus values of the three primaries, this type of color mixing has been called additive color mixing. This concept, based on Grassman's additivity law, enabled the color matching experiments at the basis of colorimetry [1]. In opposition to the light emitting systems, paintings and printed hardcopies selectively attenuate the incident white light in different proportions according to the wavelength. Layers of primaries, paints or inks, are coated on a reflecting support and play a role of spectral filtering of light. This type of color mixing is improperly called subtractive color mixing [2], by reference to the fact that part of the incident light is removed by filtering, but the tristimulus values of paint or ink mixtures cannot be obtained by combining the tristimulus values of the primaries; it is therefore not a color mixing in the sense of colorimetry. However, the subtractive color mixing is also related to a physical experience, which consists in producing many colors by mixing nonscattering dyes, usually of cyan, magenta and yellow color. According to the Beer-Lambert-Bouguer law [1], the spectral absorption coefficient of the dye mixture, () K λ , is a linear, additive combi-The final publication is available at http://link.springer.co