Currently, virtual prototyping, i.e. preliminary modelling of processes on a computer has become ubiquitous. It is also applied to modern automobile paints in order to correctly reproduce the colour of the paint. The most practically important task is colour matching: calculation of the paint composition necessary to obtain a given colour. The complexity of modelling the propagation of light in paint is due to its complex structure and the wide variety of pigments, including diffuse ones. This problem can be solved by simulation of the light scattering by the dispersed pigment particles. To do this we need the optical properties of pigments, which are often unknown. In this paper, we propose several different methods for extraction of the pigment properties by measuring the light scattering of specially prepared samples. All methods are based on minimizing the difference between measured and calculated scattering values as a function of pigment properties. The methods differ in the types of paint samples that must be prepared and measured to obtain the pigment data. We describe the operation of the methods and test their robustness. As a result, one method has proven to be much more robust to the measurement errors. The colour of the real sample was also compared with the calculated colour of the paint, in the modelling of which the obtained properties of the pigments were used.
1. Rump, M. et al. Photo‐realistic rendering of metallic car paint from image‐based measurements // Computer Graphics Forum, Vol. 27, # 2, Oxford, UK: Blackwell Publishing Ltd, 2008, pp. 527–536.
2. Kneiphof, T. and Reinhard K. Real-time image-based lighting of metallic and pearlescent car paints // Computers & Graphics, 2022, #105, pp. 36–45; doi:10.1016/j.cag.2022.04.009.
3. Kim, Duck Bong et al. Acquisition and representation of pearlescent paints using an image-based goniospectrophotometer // Optical engineering, 2010, Vol. 49, # 4, pp. 043604–043604; doi:10.1117/1.3407431.
4. Gurevich, M. Über eine rationelle klassifikation der lichtenstreuenden medien // Physikalische Zeitschrift, 1930, # 31, pp. 753–763.
5. Kubelka, P. and Munk, F. An article on optics of paint layers // Z. Tech. Phys, 1931, Vol. 12, # 593–601, pp. 259–274.
6. Kubelka, P. New contributions to the optics of intensely light-scattering materials. Part I. // JOSA, 1948, Vol. 38, # 5, pp. 448–457.
7. Ershov, S., Kolchin, K. and Myszkowski, K. Rendering pearlescent appearance based on paint‐composition modelling // Computer Graphics Forum, 2001, Vol. 20, No. 3. Oxford, UK and Boston, USA: Blackwell Publishers Ltd.
8. Wenzel, J. et al. A comprehensive framework for rendering layered materials // ACM Transactions on Graphics (ToG), 2014, Vol. 33, # 4, pp. 1–14; doi:10.1145/2601097.2601139.
9. Laurent, B. Efficient rendering of layered materials using an atomic decomposition with statistical operators // ACM Transactions on Graphics, 2018, Vol. 37, # 4, pp. 1; doi:10.1145/3197517.3201289.
10. Guo, Jie et al. A Physically‐based Appearance Model for Special Effect Pigments // Computer Graphics Forum, 2018, Vol. 37, No. 4, pp. 67–76.
11. Ergun, Serkan, Sermet Önel, and Aydin Öztürk. A General Micro-flake Model for Predicting the Appearance of Car Paint // EGSR (EI&I), 2016, pp. 65–71.
12. Golla, T. and Klein, R. Interactive interpolation of metallic effect car paints // Proceedings of the conference on vision, modelling, and visualization, 2018, pp. 11–20; doi:10.2312/vmv.20181248.
13. Wu, H., Dorsey, J. and Rushmeier, H. Physically-based interactive bi-scale material design // ACM Transactions on Graphics (TOG), 2011, Vol. 30, # 6, pp. 1–10; doi:10.1145/2070781.2024179.
14. Bati Mégane, Pascal Barla, and Pacanowski, R. An inverse method for the exploration of layered material appearance // ACM Transactions on Graphics (TOG), 2021, Vol. 40, # 4, pp. 176(1–15); doi:10.1145/3450626.3459857
15. Ershov, Sergey, et al. “Reverse engineering approach to appearance-based design of metallic and pearlescent paints.” The Visual Computer 20 (2004): 586–600.
16. Voloboy, A., Ershov S. and Pozdnyakov, S. Interactive modelling automotive paint [Interaktivnoye modelirovaniye avtomobil’noy kraski] // Proceeding of the 22nd conference on computer graphics and vision Graphicon‑2012, 2012, pp. 242–247. (In Russian)
17. Sokolov, V. et al. BSDF Reconstruction of Inks and Paints for Light Guiding Plates // Proceedings of the 31st International Conference on Computer Graphics and Vision, CEUR Workshop Proceedings 3027, 2021, Vol. 31, pp. 135–149; doi:10.20948/graphicon-2021-3027-135-149.
18. Sokolov, V.G. et al. Optimization based on reconstruction of volume scattering medium parameters // Illumination Optics V, 2018, Vol. 10693, SPIE, pp. 247–254; doi:10.1117/12.2312724
19. Pozdnyakov, S.V., S.V. Ershov, S.V., and A.G. Voloboy, A.G. Hybrid approach to design of the composition of automotive paint to match the desired colour based on neural networks and lighting simulation // The Keldysh institute preprints 87, 2022, pp. 1–17; doi:10.20948/prepr-2022-87.
20. Pozdnyakov, S. et al. Reconstruction of volumetric scattering parameters based on measurements of real samples // The Keldysh institute preprints 67, 2019, pp. 1–16; doi:10.20948/prepr-2019-67.
21. Kokhanovsky, A.A. Aerosol optics: light absorption and scattering by particles in the atmosphere // Springer Science & Business Media, 2008; doi:10.1007/978-3-540-49909-1.
22. King, M.D. Determination of the scaled optical thickness of clouds from reflected solar radiation measurements // Journal of the Atmospheric Sciences, 1987, Vol. 44, #13, pp. 1734–1751.
23. Chandrasekhar, S. Radiative Transfer // Oxford University Press, UK, 1950.
24. Prahl, Scott A. The adding-doubling method // Optical-thermal response of laser-irradiated tissue. Boston, MA: Springer US, 1995, pp. 101–129, doi:10.1007/978-1-4757-6092-7_5.
25. The Henyey-Greenstein phase function. URL: https://www.astro.umd.edu/~jph/HG_note.pdf. (accessed 09.09.2023).

• Previous article
• Next article

• dispersed medium
• radiation transfer
• automotive paint
• diffuse pigment
• colour matching
• paint measurement
• fitting