Color, Math, and Visualization Roxana Bujack Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA Author Text UNCLASSIFIED
Color space is infinite dimensional image: wikimedia.org Roxana Bujack Title Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA UNCLASSIFIED Roxana Bujack Color, Math, and Visualization LA-UR-17-31395
Human Color Vision is 3D images: wikimedia.org Roxana Bujack Title Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA Guild, J. (1931). The colorimetric properties of the spectrum. Phil. Trans. R. Soc. Lond. A , 230 (681-693), 149-187. UNCLASSIFIED Roxana Bujack Color, Math, and Visualization LA-UR-17-31395
CIE 1931 RGB and XYZ ? Roxana Bujack Title Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA image: wikimedia.org UNCLASSIFIED Roxana Bujack Color, Math, and Visualization LA-UR-17-31395
Perceptually Uniform Colorspaces animation: wikimedia.org CIELAB1976 Helm, C. E. (1964). Multidimensional ratio scaling analysis of perceived color relations. JOSA , 54 (2), 256-262. Roxana Bujack Title Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA image: wikimedia.org UNCLASSIFIED Roxana Bujack Color, Math, and Visualization LA-UR-17-31395
State of the Art Non-Euclidean colorspaces, images: wikimedia.org because of •Hue super-importance •Diminishing returns := ∆ E ( 2000 Roxana Bujack Title Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA Judd, D. B. (1968). Ideal color space: Curvature of color space and its implications for industrial image: handprint.com color tolerances. Palette, 29(21-28), 4-25. UNCLASSIFIED Roxana Bujack Color, Math, and Visualization LA-UR-17-31395
Colormapping colormap R d data C ⊂ R 3 → R → your data the colormap what we see Roxana Bujack Title Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA UNCLASSIFIED Roxana Bujack Color, Math, and Visualization LA-UR-17-31395
P1: Competing Requirements •Long •Smooth •Invertible Roxana Bujack Title Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA •Uniform •Low curvature/torsion image: wikimedia.org UNCLASSIFIED Roxana Bujack Color, Math, and Visualization LA-UR-17-31395
P2: Non-Euclideanness •No visualization of space or path •No straight forward definition of • linearity • curvature • torsion images: wikimedia.org • spline Roxana Bujack Title Operated by Los Alamos National Security, LLC for the U.S. •Bugs Department of Energy's NNSA • discontinuities • triangle inequality image: handprint.com UNCLASSIFIED Roxana Bujack Color, Math, and Visualization LA-UR-17-31395
Reactions •Use a Euclidean space (CIELAB76, CIECAM02 UCS) Luo, M. R., Cui, G., & Li, C. (2006). Uniform colour spaces based on CIECAM02 colour appearance model. Color Research & Application, 31(4), 320-330. •Approximate with a Euclidean space Urban, P., Rosen, M. R., Berns, R. S., & Schleicher, D. (2007). Embedding non-Euclidean color spaces into Euclidean color spaces with minimal isometric disagreement. JOSA A, 24(6), 1516-1528. •Approximate with a Riemannian space Roxana Bujack Title Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA Raj Pant, D., & Farup, I. (2012). Riemannian formulation and comparison of color difference formulas. Color Research & Application, 37(6), 429-440. UNCLASSIFIED Roxana Bujack Color, Math, and Visualization LA-UR-17-31395
Local Speed CIELAB2000 Bujack, R., Turton, T. L., Samsel, F., Ware, C., Rogers, D. H., & Ahrens, J. (2017). The Good, the Bad, and the Ugly: A Theoretical Framework for the Assessment of Continuous Colormaps. IEEE transactions on visualization and computer graphics . •We assume a metric space, which provides a distance D i,j := ∆ E ( x ( t i ) , x ( t j )) and metric speed D i,j V i,j := Roxana Bujack Title Operated by Los Alamos National Security, LLC for the U.S. | t j − t i | Department of Energy's NNSA Rainbow PV Greyscale PV Cool Warm Divergent matplotlib Viridis UNCLASSIFIED Roxana Bujack Color, Math, and Visualization LA-UR-17-31395
Interpolation Roxana Bujack Title Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA UNCLASSIFIED Roxana Bujack Color, Math, and Visualization LA-UR-17-31395
Tools for non-Euclidean Spaces •Done: •Description of • Order • Uniformity images: wikimedia.org • Discriminative power •Interpolation •ToDo: •Optimization •Generation Roxana Bujack Title Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA •Smoothness •Splines image: handprint.com UNCLASSIFIED Roxana Bujack Color, Math, and Visualization LA-UR-17-31395
Thank you :) •Color perception is non-Euclidean. •We have to deal with it! •Please approach me if you want to talk about color :) CIELAB 2000 Roxana Bujack Title Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA UNCLASSIFIED Roxana Bujack Color, Math, and Visualization LA-UR-17-31395
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