Modeling the Histogram of the Halftone Image to Determine the Area Fraction of Ink Yat-Ming Wong May...
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Transcript of Modeling the Histogram of the Halftone Image to Determine the Area Fraction of Ink Yat-Ming Wong May...
Modeling the Histogram of Modeling the Histogram of the Halftone Image to the Halftone Image to Determine the Area Determine the Area
Fraction of InkFraction of Ink
Yat-Ming WongMay 8,1998
Advisor: Dr. Jonathan Arney
BackgroundBackground
Drawing useful information from an image is important in various fields that depend upon them
Tools used to interpret an image need to be good enough to give meaningful data
HistogramHistogram
The histogram is a tool that gives a graphical interpretation of an image
It give us an idea of the make up of the image, such as the amount of ink in its composition
HistogramHistogram
The image is read pixel by pixel for their reflectance values
R1,9 = 0.1
R7,10 = 0.9
HistogramHistogram
0
2000
4000
6000
8000
10000
12000
0 0.2 0.4 0.6 0.8 1
Reflectance
Freq
uenc
y
Histogram of halftone dotsHistogram of halftone dots
0
2000
4000
6000
8000
10000
12000
0 0.2 0.4 0.6 0.8 1
Reflectance
Frequency
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0
2000
4000
6000
8000
10000
12000
0 0.2 0.4 0.6 0.8 1
Reflectance
Frequency
-
Ink Population
PaperPopulation
HistogramHistogram
Segmentation of the histogram has so far been done by visual approximation
Visual approximation is a highly inaccurate method of measurement in cases where data needs to be in significant figures
ThresholdThreshold
0
2000
4000
6000
8000
10000
12000
0 0.2 0.4 0.6 0.8 1
Reflectance
Freq
uenc
y Threshold, RT (?)
SolutionSolution
Models to segment histogram computationally:
Gaussian Model
Straight-Edge Model
Gaussian ModelGaussian Model
Reflectance
G1 G2
G1+G2
Gaussian ModelGaussian Model
G1( ) [ /( )]*exp[ ( ) / ]R R R 1 2 21 1
212
G2( ) [ /( )]*exp[ ( ) / ]R R R 1 2 22 2
222
+
Gaussian ModelGaussian Model
f(i) = F*G1(R) + (1-F)*G2(R)
R1 R2
1 2
F 1-F
REFLECTANCE
G1+G2
Sum of two gaussians vs. offset lithographic print dataSum of two gaussians vs. offset lithographic print data
PROBLEM
REFLECTANCE
G1+G2
Data
Sum of two gaussians vs. inkjet “stochastic halftone” dataSum of two gaussians vs. inkjet “stochastic halftone” data
REFLECTANCE
G1+G2
Data
PROBLEM
Straight Edge ModelStraight Edge Model
Halftone dots are a collection of edges
Straight Edge ModelStraight Edge Model
Model of the Halftone Reflection Distribution as a Single “Equivalent Edge”
H
R
Model the Halftone “Equivalent EdgeModel the Halftone “Equivalent Edge
Vary F
H
R
Model the Halftone “Equivalent Edge”Model the Halftone “Equivalent Edge”
H
Change Rmin or Rmax
R
Model the Halftone “Equivalent Edge”Model the Halftone “Equivalent Edge”
x scan
R
x
1
10
0
RR R
a x FR
max minminexp{ ( )}1
where:
R
x
1
10
0
RR R
a x FR
max minminexp{ ( )}1
The Model
H RdR
dx( )
1H
R0 1
The Noise Model
-0.1 0.1R
S(R)
Add A Noise Metric Assume A Reflectance Variation
S RR
( ) exp
1
2 2
2
2
S RR
( ) exp
1
2 2
2
2 h RdR
dx( )
1
H
R0 1
*S(R)
The Noise Model
R
Straight Edge ModelStraight Edge Model
Rmin Rmax
F
1-F
a
Straight edge model vs. offset lithographic print dataStraight edge model vs. offset lithographic print data
H(R)
R0 0.2 0.4 0.60
0.02
0.04
0.06
0.08
Straight edge model vs. inkjet “stochastic halftone” dataStraight edge model vs. inkjet “stochastic halftone” data
0.1 0.2 0.3 0.4 0.5 0.60
0.01
0.02
0.03
H(R)
R
Comparison of models in matching offset lithographic print dataComparison of models in matching offset lithographic print data
Sum of two gaussians Straight Edge
vs.
Comparison of models in matching inkjet “stochastic halftone” dataComparison of models in matching inkjet “stochastic halftone” data
Sum of two gaussians Straight Edge
vs.
Automated computationAutomated computation
Program written in Visual Basic
Opens up a data file and automatically find the best computational match by looking for the set of variables that yields the lowest RMS deviation value.
Problems with the straight edge modelProblems with the straight edge model
H(R)
R
H(R)
R0 10
0.1
Expand
Problems with the straight edge modelProblems with the straight edge model
H(R)
R
H(R)
R
Expand
ConclusionConclusion
Model fits well for Ri and Rp close to each other
For Ri and Rp widely spaced, a single noise metric is inadequate.
The EndThe End