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Applications of the Kubelka-Munk Color Model

Applications of the Kubelka-Munk Color Model. Kristen Hoffman  Dr. Edul N. Dalal   RIT Center for Imaging Science  Xerox Corporation, Wilson Center for Research and Technology. Introduction - Goals and Accomplishments.

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Applications of the Kubelka-Munk Color Model

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  1. Applications of the Kubelka-Munk Color Model Kristen Hoffman Dr. Edul N. Dalal RIT Center for Imaging Science Xerox Corporation, Wilson Center for Research and Technology

  2. Introduction - Goals and Accomplishments • Goal: Ability to model the reflectance of a color xerographic sample • Developed: Predictive color model based on Kubelka-Munk theory • Model extended to • Bidirectional Measurement Geometry • MultiLayer Images • Xerographic Print Samples

  3. Background: Kubelka-Munk Theory • Color reflection depends on • Material properties - the absorption and scattering spectra, K() and S() • Sample thickness, X • Substrate reflectance spectrum, Rp () • Model applies to • Uniform thickness samples with complete substrate coverage • Single color images

  4. Background: Saunderson Correction Parameters • Two parameters • k1 and k2 - corrections are made for reflections at the sample surface • Derived for integrating sphere measurement geometry • Applied to reflectance spectrum before the Kubelka-Munk model

  5. Developed Color Model

  6. Correction Equations

  7. Introduction of k0 Correction Parameter • k0 • Describes front surface reflection reaching detector of measurement device • Correlation exists for 45/0 measurement geometry as a function of 75 image gloss • Depends on refractive index ratio at the air-image boundary

  8. Derived Correction Equations for Bidirectional Geometry Systems Link to Derivation: http://www.cis.rit.edu/~kmh7483/index.html

  9. Multi-Layer Images

  10. Examples of Image Layer Structure (a) Single colorant layer considered in the original Kubelka-Munk model (b) Multiple colorant layers generally encountered in process color xerographic prints

  11. Calculated Sample Reflectance Inverse Saunderson k0, k1, k2 for toner R() Top-most toner layer Kubelka- Munk K, S for layer n Rn()corr Second toner layer Kubelka- Munk K, S for layer 2 R2()corr Bottom-most toner layer Kubelka- Munk K, S for layer 1 R1()corr Saunderson Correction k0, k1, k2 for substrate Rp()corr Rp() Substrate

  12. Non Planar Toner Layers

  13. Image Photomicrographs

  14. Toner Layer Thickness Measurements • Layer structure digitized electronically • Measurements made at every 0.5m • Small interval divides print into planar sections • K/M applied to each small planar interval

  15. Results

  16. Fitted Absorption Spectra for Xerox 5760 CMY Toners

  17. Fitted Scattering Spectra for Xerox 5760 CMY Toners

  18. Results - Toner Layer Thickness Probability Distribution Example

  19. Results - Single Layer, 45/0 dE*CIELAB Average C = 1.83 M = 1.77, Y = 1.26

  20. Results - Multi-Layer Image R G B

  21. Results - Multilayer Non Planar Print dE*CIELAB Average 5.1, RMS = 5.5

  22. Conclusions • Benefits of K/M Color Model • Based on physical parameters of toner set • No print samples needed • Good predictions (low color error)

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