Applications of the kubelka munk color model
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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

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
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

Background kubelka munk theory
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

Background saunderson correction parameters
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

Introduction of k 0 correction parameter
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

Derived correction equations for bidirectional geometry systems
Derived Correction Equations for Bidirectional Geometry Systems

Link to Derivation:

Examples of image layer structure
Examples of Image Layer Structure Systems

(a) Single colorant layer considered in the original Kubelka-Munk model

(b) Multiple colorant layers generally encountered in process color xerographic prints

Applications of the kubelka munk color model

Calculated Sample Reflectance Systems



k0, k1, k2 for toner


Top-most toner layer



K, S for layer n


Second toner layer



K, S for layer 2


Bottom-most toner layer



K, S for layer 1




k0, k1, k2 for substrate




Toner layer thickness measurements
Toner Layer Thickness Measurements Systems

  • 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


Results Systems

Results single layer 45 0
Results - Single Layer, 45/0 Example

dE*CIELAB Average C = 1.83 M = 1.77, Y = 1.26

Results multilayer non planar print
Results - Multilayer Non Planar Print Example

dE*CIELAB Average 5.1, RMS = 5.5

Conclusions Example

  • Benefits of K/M Color Model

    • Based on physical parameters of toner set

    • No print samples needed

    • Good predictions (low color error)