Color, Math, and Visualization Roxana Bujack Operated by Los - - PowerPoint PPT Presentation

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Color, Math, and Visualization Roxana Bujack Operated by Los - - PowerPoint PPT Presentation

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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

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Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA

Author Text

UNCLASSIFIED

Color, Math, and Visualization Roxana Bujack

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Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA

UNCLASSIFIED

Roxana Bujack Title

Color, Math, and Visualization Roxana Bujack

LA-UR-17-31395

Color space is infinite dimensional

image: wikimedia.org

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Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA

UNCLASSIFIED

Roxana Bujack Title

Color, Math, and Visualization Roxana Bujack

LA-UR-17-31395

Human Color Vision is 3D

images: wikimedia.org

Guild, J. (1931). The colorimetric properties

  • f the spectrum. Phil.
  • Trans. R. Soc. Lond. A,

230(681-693), 149-187.

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Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA

UNCLASSIFIED

Roxana Bujack Title

Color, Math, and Visualization Roxana Bujack

LA-UR-17-31395

CIE 1931 RGB and XYZ

image: wikimedia.org

?

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Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA

UNCLASSIFIED

Roxana Bujack Title

Color, Math, and Visualization Roxana Bujack

LA-UR-17-31395

Perceptually Uniform Colorspaces

animation: wikimedia.org image: wikimedia.org Helm, C. E. (1964). Multidimensional ratio scaling analysis of perceived color relations. JOSA, 54(2), 256-262.

CIELAB1976

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Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA

UNCLASSIFIED

Roxana Bujack Title

Color, Math, and Visualization Roxana Bujack

LA-UR-17-31395

State of the Art

Non-Euclidean colorspaces, because of

  • Hue super-importance
  • Diminishing returns

images: wikimedia.org Judd, D. B. (1968). Ideal color space: Curvature of color space and its implications for industrial color tolerances. Palette, 29(21-28), 4-25.

2000

:= ∆E(

image: handprint.com

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Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA

UNCLASSIFIED

Roxana Bujack Title

Color, Math, and Visualization Roxana Bujack

LA-UR-17-31395

Colormapping

Rd data → R

colormap

→ C ⊂ R3

your data the colormap what we see

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Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA

UNCLASSIFIED

Roxana Bujack Title

Color, Math, and Visualization Roxana Bujack

LA-UR-17-31395

P1: Competing Requirements

image: wikimedia.org

  • Long
  • Smooth
  • Invertible
  • Uniform
  • Low curvature/torsion
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Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA

UNCLASSIFIED

Roxana Bujack Title

Color, Math, and Visualization Roxana Bujack

LA-UR-17-31395

P2: Non-Euclideanness

  • No visualization of

space or path

  • No straight forward

definition of

  • linearity
  • curvature
  • torsion
  • spline
  • Bugs
  • discontinuities
  • triangle inequality

images: wikimedia.org image: handprint.com

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SLIDE 10

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA

UNCLASSIFIED

Roxana Bujack Title

Color, Math, and Visualization Roxana Bujack

LA-UR-17-31395

Reactions

  • Use a Euclidean space (CIELAB76, CIECAM02 UCS)
  • Approximate with a Euclidean space
  • Approximate with a Riemannian space

Luo, M. R., Cui, G., & Li, C. (2006). Uniform colour spaces based on CIECAM02 colour appearance model. Color Research & Application, 31(4), 320-330. 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. Raj Pant, D., & Farup, I. (2012). Riemannian formulation and comparison of color difference formulas. Color Research & Application, 37(6), 429-440.

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Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA

UNCLASSIFIED

Roxana Bujack Title

Color, Math, and Visualization Roxana Bujack

LA-UR-17-31395

Local Speed

PV Cool Warm Divergent Rainbow PV Greyscale matplotlib Viridis

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.

CIELAB2000

  • We assume a metric space,

which provides a distance and metric speed

Di,j := ∆E(x(ti), x(tj)) Vi,j := Di,j |tj − ti|

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Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA

UNCLASSIFIED

Roxana Bujack Title

Color, Math, and Visualization Roxana Bujack

LA-UR-17-31395

Interpolation

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Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA

UNCLASSIFIED

Roxana Bujack Title

Color, Math, and Visualization Roxana Bujack

LA-UR-17-31395

Tools for non-Euclidean Spaces

images: wikimedia.org

  • Done:
  • Description of
  • Order
  • Uniformity
  • Discriminative power
  • Interpolation
  • ToDo:
  • Optimization
  • Generation
  • Smoothness
  • Splines

image: handprint.com

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Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA

UNCLASSIFIED

Roxana Bujack Title

Color, Math, and Visualization Roxana Bujack

LA-UR-17-31395

CIELAB 2000

Thank you :)

  • Color perception is non-Euclidean.
  • We have to deal with it!
  • Please approach me if you want to talk about color :)