WO: (Applied) Mathematics - Linearization of Spectral Reflectance

Your assignment
Developing, producing, and maintaining qualitative software and machines for production printing requires combined research in various (scientific) disciplines. One such discipline is Color Management: the process of ensuring color consistency when printing on different types of substrate. Color management at the same time acts as a beautiful field of study for an applied mathematician to tackle real-world problems: it involves having to decide on—and sometimes creatively invent—many appropriate (algorithmic) strategies based on the mathematical sub-fields numerical linear algebra, scientific computing, statistics, and data science. In one such problem solving instance, we are interested in finding an invertible mapping that linearizes spectral reflectance measurement data with respect to CMYK tone values.

Namely, color appearance after printing is the result of an interplay between ink and substrate. Putting the same combination and amounts of inks on different types of substrate will often result in different colors. Hence, if color consistency is desired when printing on different types of substrate, then the ink amounts need to be adjusted to each type of substrate. To this end, the relation between CMYK ink amounts put onto a paper and the resulting colors needs to be known. One way of expressing color is by spectral reflectance; i.e., how much of the radiation of a light source is reflected by a uniformly colored object at the different wavelengths of the visible spectrum. Combining spectral reflectance measurements of printed test colors with an interpolation based color prediction model allows us to approximatively determine the resulting color for any chosen CMYK pair.

Before interpolation, we linearize spectral reflectance with respect to CMYK to benefit interpolation. Commonly, linearization is done with elementary principles: simply by applying the negative logarithm to spectral reflectance to obtain spectral density. One can imagine it will be easier to determine spectral density curves corresponding to intermediate Cyan tone values than determining intermediate spectral reflectance curves: the former behaves more linearly with respect to C across the entire considered spectrum—though not yet in an optimal fashion. Hence, your task is to gain more insight into how spectral reflectance behaves with respect to CMYK tone values and investigate alternative strategies for linearization of spectral reflectance.
                 

Your profile

• You are currently studying (applied) mathematics at the Master’s level;
• You are proficient at a prototyping language, such as Matlab or Python;
• You can write academically in English. Either Dutch or English will suffice for daily communication;
• You can independently consult and critique scientific literature;
• This project is fitting for a Master’s internship or graduation assignment.

What’s in it for you?

• A challenging assignment with skilled coaching;
• Internship/Graduation compensation of €500,- per month;
• Travel cost compensation if you don’t have an ‘OV-weekcard’;
• The possibility to network with professionals inside and outside your field of expertise, thanks to our diversity of disciplines which you will work with
• With our company values collaboration, innovation and ownership, we strive to bring out the best in each other, expand boundaries and feel empowered to take ownership of our work.

Interested?

Are you interested in this assignment? Please click on the button 'apply now' at the top on the page where you can upload your resume and motivation letter.
If you would like to receive more information concerning this assignment, please contact Anıl Dural, tel. +31 (0)6 22 56 22 80.

If you have any questions about the internship in general, please contact Milou Geelen, + 31 6 25653192

About Canon Production Printing
Canon Production Printing develops and manufactures high-tech printing products and workflow software for the commercial printing market and is part of Canon, a global provider of imaging technologies and services. Canon Production Printing operates on three continents, with approximately 3300 employees (end 2022) and has its global headquarters in Venlo, the Netherlands.

Further information about Canon Production Printing is available at cpp.canon.