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:

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

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

slide11

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

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

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

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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