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Reflectance Measurements of Pigmented Colorants

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Reflectance Measurements of Pigmented Colorants Reflectance Measurements of Pigmented Colorants Jeffrey B. Budsberg Donald P. Greenberg Stephen R. Marschner Technical Report PCG-06-02 Cornell Program of Computer Graphics September 6, 2006 In this report, we present the results of an experimental study on the appearance of artists’ paint over time. Paint samples were handmade to ensure material quality, using various pigment colorants and adhesive binding media. We present the results of our diffuse reflectance measurements, which show very significant perceptual differences in two different domains: how the appearance of paint changes over time; and how the appearance of one pigmented colorant varies when dispersed in different materials. Acknowledgements This work would not have been possible without the contributions and support from many individuals. The authors would like to thank Stan Taft for his commentary in the early stages of this research. Fabio Pellacini proved to be a great resource for hashing through ideas, as well as aiding in the implementation of the rendering code in graphics hardware. James Ferwerda was very helpful in the discussion of color science and visual perception. We thank Steve Westin for assisting in the setup of the equipment in the light measurement laboratory and Victor Kord for lending his expertise on artists’ materials. This research was supported by the Program of Computer Graphics, the Depart- ment of Architecture and the National Science Foundation ITR/AP 0205438. i Table of Contents 1 Background 1 1.1 Introduction . 1 1.2 Color Spaces . 3 2 Results 5 2.1 Reflectance Data . 5 2.2 Effect of Binding Media . 30 2.3 Effect of Time . 51 3 Interactive viewing 67 3.1 Introduction . 67 3.2 Kubelka Munk theory . 67 3.3 Conversion to Kubelka Munk . 75 3.4 Rendering System . 77 3.5 Implementation issues . 81 References 83 ii 1 Background 1.1 Introduction Our study measured the appearance of artists’ paint, which is dependent on both time and the material that binds the colorant to a surface. The work encompassed a vast amount of handmade paints made from varying pigmented colorants and ad- hesive binding media. A typical paint sample is seen in Figure 1. Diffuse reflectance measurements were taken over the visible spectrum after the samples were freshly painted, after one day, one week, one month, three months, and six months after they were painted. Further details supplementing this report can be found in [Bud07]. Figure 1: A typical painted sample–Chrome yellow in gouache after 1 day. Given are the dimensions for an average painted sample. The measurement range is the area in which the diffuse reflectance is measured. The 11 pigments used in our study are shown in Figure 2. A tint of each of the 10 non-white pigments was also made (50% colored pigment, 50% Titanium dioxide white). Hence, there are a total of 11 pure pigments + 10 tints = 21 pigmented mixtures. The pigmented mixtures were dispersed in the following binding media: acrylic, casein, distemper, encaustic, gouache, oil, tempera, and watercolor. Each of these was applied to primed cotton canvas, mounted on Fome-Cor c board. Diffuse reflectance was measured with the Optronics Single Monochromator (OL 750-M-S) and Integrating Sphere Reflectance attachment (OL 740-70) in the Cornell Program of Computer Graphics Light Measurement Laboratory. Each sample’s re- 1 Figure 2: Left: Magnified view of pigments used in research. Right: magnified further. (a) Lapis lazuli, (b) Cold glauconite, (c) Chrome yellow, (d) Gold ochre, (e) Raw umber, (f) Burnt sienna, (g) Red ochre, (h) Hematite, (i) Cold hematite, (j) Lampblack, (k) Titanium dioxide. 2 flectance was measured over the visible spectrum (350-700nm) in 10nm increments, for a total of 36 wavelength-dependant reflectance values for each sample. Ultimately, each of the 168 samples was measured at six intervals in time for a total of 1008 time-dependent reflectance spectra (each of which contains the 36 wavelength-dependent reflectance values). 1.2 Color Spaces The spectral data from the paint sample measurements was converted into various color spaces (XYZ, Munsell HVC, L∗a∗b∗, and RGB). All of the conversions were done using the CIE Standard D65 illuminant. XYZ values are computed from the measured spectra of each sample via: 35 X X = k E(λi)R(λi)¯x(λi) i=0 35 X Y = k E(λi)R(λi)¯y(λi) i=0 35 X Z = k E(λi)R(λi)¯z(λi) (1) i=0 where λi = 350 + 10i is the current wavelength in nanometers E(λi) is the illuminant’s energy (D65 ) at wavelength λi R(λi) is the reflected light from the paint sample at wavelength λi {x,¯ y,¯ z¯} are the standard observer color matching functions (found in [Gla95]) 100 k = is the normalizing factor Pn−1 i=0 E(λi)¯y(λi) The Munsell color space is a perceptually uniform space defined by perceptual stud- 3 ies. XYZ values are typically converted into Munsell HVC (hue, value, chroma) via a three-dimensional look up table. Fortunately, there is free software available [Gre06] to perform this transformation from GretagMacbeth (the company who currently produces the Munsell Book of Color [Mun]). The L∗a∗b∗ space is another perceptually based color system that is frequently used. It is computed mathematically from XYZ: 1 3 116 Y − 16 , Y ≥ .008856 ∗ Yn Yn L = 903.3 Y , otherwise Yn X Y a∗ = 500L∗ f − f Xn Yn Y Z b∗ = 200L∗ f − f (2) Yn Zn where 1 r 3 , r ≥ .008856 f (r) = 16 7.787r + 116 , otherwise By design, the Euclidean distance between any two colors, A and B, in the L∗a∗b∗ color space may be computed from the magnitude of the vector between the colors: q ∗ ∗ ∗ 2 ∗ ∗ 2 ∗ ∗ 2 Eab = (LA − LB) + (aA − aB) + (bA − bB) (3) The important feature of this space is that two pairs of colors with the same distance metric between them are almost perceptually different by the same amount. Linear RGB is computed from XYZ by post multiplying by the 3x3 conversion matrix M (which can be found in [Lin06]): [RGB] = [XYZ][M] (4) 4 2 Results 2.1 Reflectance Data For brevity, in our work, each of the 1008 time dependent reflectance spectra is denoted as (binder) (pigment) (time), where the items in parenthesis are given by Table 1. For example, a wet sample of Lapis lazuli in acrylic is labeled as a ll w. Also, tints are indicated by a subscript t after (pigment). For example, a wet sample of a tint of Lapis lazuli in acrylic is a llt w. Table 1: Shortened notation used in our work. Binding media Pigment Time interval a acrylic ll lapis lazuli w wet c casein cg cold glauconite 0 1 day d distemper cy chrome yellow 1 1 week e encaustic go gold ochre 2 1 month g gouache ru raw umber 3 3 months o oil bs burnt sienna 4 6 months t tempera ro red ochre w watercolor h hematite ch cold hematite lb lampblack td titanium dioxide The complete set of color conversions from the 1008 reflectance spectra follows. The actual spectra are included along with this work in spectra.zip. 5 Table 2: Paint sample color conversions. XYZ HVC L∗ a∗ b∗ RGB a ll w 19.16 20.16 49.27 2.65PB 5.04 8.06 52.02 0.21 -37.02 0.07 0.21 0.49 a ll 0 10.04 10.50 28.19 2.54PB 3.76 7.06 38.73 0.67 -33.74 0.02 0.11 0.28 a ll 1 10.95 11.66 31.34 2.02PB 3.95 7.46 40.67 -0.76 -34.99 0.02 0.13 0.31 a ll 2 11.23 11.81 32.17 2.41PB 3.97 7.60 40.91 0.20 -35.73 0.02 0.13 0.32 a ll 3 11.32 12.00 31.51 2.15PB 4.00 7.31 41.22 -0.44 -34.28 0.03 0.13 0.31 a ll 4 11.14 11.92 31.08 1.81PB 3.99 7.25 41.10 -1.23 -33.88 0.02 0.13 0.31 a cg w 19.49 22.36 21.14 0.46G 5.28 2.33 54.41 -8.39 5.03 0.18 0.24 0.19 a cg 0 13.67 15.62 11.46 5.36GY 4.50 2.76 46.47 -7.06 12.81 0.15 0.17 0.10 a cg 1 13.75 15.73 11.60 5.52GY 4.52 2.77 46.62 -7.25 12.68 0.15 0.17 0.10 a cg 2 13.94 15.95 11.81 5.56GY 4.55 2.77 46.91 -7.28 12.64 0.15 0.17 0.10 a cg 3 14.04 16.05 12.13 5.73GY 4.56 2.70 47.03 -7.17 11.98 0.15 0.17 0.10 a cg 4 13.97 16.01 12.11 5.88GY 4.56 2.73 46.99 -7.41 11.94 0.15 0.17 0.10 a cy w 69.69 73.15 10.57 4.77Y 8.74 12.68 88.52 0.73 87.85 1.08 0.70 0.00 a cy 0 69.02 71.94 9.69 4.55Y 8.68 12.96 87.94 1.79 89.47 1.08 0.68 -0.01 a cy 1 68.39 71.50 9.04 4.68Y 8.66 13.16 87.73 1.31 91.18 1.07 0.68 -0.01 a cy 2 66.85 70.27 8.51 4.90Y 8.59 13.20 87.13 0.50 91.87 1.04 0.67 -0.02 a cy 3 65.12 67.84 9.13 4.60Y 8.47 12.71 85.93 1.81 87.76 1.02 0.65 -0.01 a cy 4 62.31 64.30 10.04 4.27Y 8.29 11.99 84.12 3.14 81.82 0.98 0.61 0.01 a go w 39.26 34.72 15.27 6.09YR 6.38 7.31 65.53 21.26 36.15 0.66 0.28 0.11 a go 0 30.06 26.11 9.34 6.53YR 5.65 7.55 58.15 21.34 39.19 0.53 0.20 0.06 a go 1 30.15 26.19 9.49 6.46YR 5.65 7.51 58.21 21.39 38.84 0.53 0.20 0.06 a go 2 29.96 26.10 9.54 6.58YR 5.65 7.43 58.14 20.99 38.55 0.52 0.20 0.06 a go 3 30.01 26.13 9.46 6.58YR 5.65 7.48 58.16 21.11 38.85 0.52 0.20 0.06 a go 4 30.03 26.14 9.83 6.41YR 5.65 7.35 58.17 21.13 37.74 0.52 0.20 0.07 a ru w 11.63 11.00 10.67 1.87YR 3.84 1.49 39.58 8.91 3.17 0.15 0.10 0.10 a ru 0 8.48 7.86 6.25 5.11YR 3.28 2.08 33.68 9.50 8.11 0.12 0.07 0.05 a ru 1 8.39 7.78 6.24 5.10YR 3.26 2.04 33.51 9.37 7.89 0.12 0.07 0.05 a ru 2 8.43 7.86 6.33 5.54YR 3.28 1.98 33.69 8.96 7.82 0.12 0.07 0.06 a ru 3 8.61 8.05 6.60 5.37YR 3.32 1.92 34.08 8.87 7.39 0.12 0.07 0.06 a ru 4 8.65 8.12 6.70 5.60YR 3.33 1.88 34.23 8.62 7.27 0.12 0.07 0.06 a bs w 11.82 10.37 11.49 9.89RP 3.74 2.47 38.50 14.88 -1.00 0.17 0.08 0.11 a bs 0 9.02 7.78 6.20 0.76YR 3.26 2.81 33.52 14.78 8.04 0.14 0.06 0.05 a bs 1 9.00 7.77 6.30 0.49YR 3.26 2.75 33.50 14.72 7.62 0.14 0.06 0.06 a bs 2 9.17 7.97 6.47 0.78YR 3.30 2.70 33.91 14.34 7.65 0.14 0.06 0.06 a bs 3 9.18 8.01 6.64 0.56YR 3.31 2.61 34.01 14.08 7.13 0.14 0.06 0.06 a bs 4 9.16 8.03 6.55 1.12YR 3.31 2.60 34.05 13.75 7.55 0.14 0.06 0.06 a ro w 15.12 11.89 9.25 6.41R 3.98 5.03 41.03 25.31 9.99 0.26 0.08 0.08 a ro 0 13.26 10.43 6.70 9.57R 3.75 5.08 38.61 24.12 14.83 0.24 0.07 0.06 a ro 1 13.41 10.58 6.87 9.47R 3.77 5.04 38.86 24.06 14.56 0.24 0.07 0.06 a ro 2 13.46 10.69 7.01 9.59R 3.79 4.93 39.05 23.53 14.35 0.24 0.07 0.06 a ro 3 13.41 10.67 7.06 9.56R 3.79 4.88 39.02 23.38 14.13 0.24 0.07 0.06 a ro 4 13.37 10.65 7.05 9.62R 3.79 4.84 38.99 23.20 14.09 0.23 0.07 0.06 Continued on Next Page.
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