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

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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


Developed color model

Developed Color Model


Correction equations

Correction Equations


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:

http://www.cis.rit.edu/~kmh7483/index.html


Multi layer images

Multi-Layer Images


Examples of image layer structure

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


Applications of the kubelka munk color model

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


Non planar toner layers

Non Planar Toner Layers


Image photomicrographs

Image Photomicrographs


Toner layer thickness measurements

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


Results

Results


Fitted absorption spectra for xerox 5760 cmy toners

Fitted Absorption Spectra for Xerox 5760 CMY Toners


Fitted scattering spectra for xerox 5760 cmy toners

Fitted Scattering Spectra for Xerox 5760 CMY Toners


Results toner layer thickness probability distribution example

Results - Toner Layer Thickness Probability Distribution Example


Results single layer 45 0

Results - Single Layer, 45/0

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


Results multi layer image

Results - Multi-Layer Image

RGB


Results multilayer non planar print

Results - Multilayer Non Planar Print

dE*CIELAB Average 5.1, RMS = 5.5


Conclusions

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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