Transcript COMPARISON OF QUADRATIC FORM BASED COLOR INDEXING …

Histograms Analysis of the Microstructure
of Halftone Images
J.S. Arney & Y.M. Wong
Center for Imaging Science, RIT
Given by
Linh V. Tran
ITN, Campus Norrköping, Linköping University
In Digital Halftoning Course. Jan. 17, 2003
Linh V. Tran - Graduate course in Digital Halftoning
Outline
• J.S. Arney & Y.M. Wong. ”Histograms Analysis
of the Microstructure of Halftone Images”. 1999
– Problem definition
• Ideal case
• More Complicated cases in Reality
– Solution: Modeling the bimodal histogram
– Experiments
• MatLab Halftoning Toolbox
Developed in University of Texas at Austin, TX, USA
• Comparison several halftoning methods
Done by Michael Bruce deLeon, Stanford, USA
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Problem
• Estimate
– The mean reflectance of the paper between the
halftone dots, RP
– The mean reflectance of the dots, RI and
– The halftone dot area fraction, F
of a given printed patch.
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Ideal case
Ink
• Perfect ink drops
• No dot gain
Paper
F
1-F
0
Ri
Rp
A perfect frequency occurrence of gray levels of
reflectance consists of 2 delta functions.
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Microdensitometry
• CCD Camera:
1000x1000 pixels
CCD
Camera
• Can measure also
Microscope
paper
- Resolutions
- Granularity
- Micro-distribution of
color in the image
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Experiments
• Histogram of 65 LPI AM halftone printed by offset
lithography, measured at 5 mm field of view (FOV)
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More Difficult
• Histograms at 5mm FOV of error diffusion dot pattern
printed by thermal ink jet at 300 dpi with F = 0.5
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More and More Difficult
• Histograms at 5mm FOV of error diffusion dot pattern
printed by thermal ink jet at 300 dpi with F = 0.05
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Modelling the Bimodal Histogram
Rmax  Rmin
R
 Rmin
1  exp a( x  b)
The edge modeled with
Rmin = 0.3, Rmax = 0. 7
a = 10, and b = 0.5
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Frequency Occurence of R
R
Rmax  Rmin

 Rmin
1  exp a ( x  b)
 dR 
H ( R)   
 dx 
1
dx
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Add Gaussian Noise
 ( R  0.5) 2 
1
S ( R) 
exp

2
 2
 2

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
Five unknowns: Rmax
Rmin
a, b
Curve Fitting
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R
x( R)   H ( R)
0
1
 H ( R)
0
Inverse Model
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Implementation
• Main results published earlier in Wong’s B.Sc.
Thesis:
”Modeling the Halftone Image to Determine
the Area Fraction of Ink”
CIS, RIT, 1998
• www.cis.rit.edu/research/thesis/bs/1998/wong
• Simulations mainly done in MathCAD
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Halftoning MatLab Toolbox
Developed in University of Texas at Austin, TX, USA
• Grayscale halftoning methods
–
–
–
–
–
Classical and user-defined screens
Classical error diffusion methods
Edge enhancement error diffusion
Green noise error diffusion
Block error diffusion
• Figures of merit measures for grayscale halftones
–
–
–
–
Peak signal-to-noise ratio (PSNR)
Weighted signal-to-noise ratio (WSNR)
Linear distortion measure (LDM)
Universal quality index (UQI)
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Figures of Merit
• PSNR: Peak Signal to Noise Ratio of the
output image with respect to the input image in
dB
 imsize  peakgraylevel 2 
PSNR  10  log10 

2
Out  In 

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Linh V. Tran - Graduate course in Digital Halftoning
Figures of Merit
• WSNR: Weighted Signal to Noise Ratio of
output image with respect to the input image
in dB. A weighting appropriate to the human
visual system is used.
J. Mannos and D. Sakrison, "The effects of a visual fidelity
criterion on the encoding of images", IEEE Trans. Inf. Theory, IT20(4), pp. 525-535, July 1974
• LDM: Linear Distortion Ratio.
• UQI: Universal image Quality Index.
Zhou Wang and Alan C. Bovik "A Universal Image Quality Index"
IEEE Signal Processing Letters, 2001
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Halftoning MatLab Toolbox
• Color halftoning methods
–
–
–
–
–
–
Classical and user-defined (multilevel) screens (separable)
Classical separable error diffusion methods (separable)
Edge enhancement error diffusion (separable)
Green noise error diffusion (separable)
Block error diffusion (separable)
Minimum brightness variation quadruple error diffusion (nonseparable design for separable implementation)
– Vector error diffusion (non-separable)
• Figures of merit measures for color
– PSNR, WSNR, LDM, UQI as in grayscale halftoning
– Noise gain in dB over Floyd-Steinberg error diffusion
(specific to Vector Error Diffusion)
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Demo
• http://www.ece.utexas.edu/~bevans/projects/
halftoning/toolbox/
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DeLeon’s Comparison
• Done by Michael Bruce deLeon, Stanford, USA
http://ise0.stanford.edu/~mdeleon/
• Methods:
1.
2.
3.
4.
Bayer Dither Matrix: 8x8 matrix
Three Level Dither
Error Diffusion: Floyd and Steinberg
MBVQ Error Diffusion
(Minimum Brightness Variation Quadrants)
• Test images: Ramps, Trees, Lena, Chart
Linh V. Tran - Graduate course in Digital Halftoning
• Original Image
• Bayer Dither Matrix
• 3 Level Dither
• Error Diffusion
• MBVQ Error Diffusion
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• Original Image
• Bayer Dither Matrix
• 3 Level Dither
• Error Diffusion
• MBVQ Error Diffusion
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Tree image
Original Image
Bayer Dither Matrix
Three Level Dither
Error Diffusion
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Tree Image
MBQV Error Diffusion
Bayer Dither Matrix
Three Level Dither
Error Diffusion
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Lena Image
Original Image
Bayer Dither Matrix
Three Level Dither
Error Diffusion
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Lena Image
MBQV Error Diffusion
Bayer Dither Matrix
Three Level Dither
Error Diffusion
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Chart Image
Original Image
Bayer Dither Matrix
Three Level Dither
Error Diffusion
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Chart Image
MBQV Error Diffusion
Bayer Dither Matrix
Three Level Dither
Error Diffusion
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DeLeon’s Conclusions
• Solid tones seem the most difficult to present smoothly with
a halftoning pattern. Thus, simple computer graphics may
be more of a challenge for a printer than complex photos.
• The color error diffusion algorithm can effectively limit the
number of colors used for a given region. Its execution time
is only marginally longer than that of regular error diffusion.
The pattern produced is slightly smoother than the regular
error diffusion results, though unless closely examined in
these monitor examples, the differences in dot brightness &
color is easy to miss. Depending in its use with actual inks,
tradeoffs might have to be made between the appearances
of colors in grayscale images and this smoothing effect.
Linh V. Tran - Graduate course in Digital Halftoning
DeLeon’s Conclusions
• Multi-level halftoning seems to offer considerable
image quality improvement without expensive
algorithms. Although the expenses for realizing this
functionality come from other areas (cost of extra
inks, complexity of multi-drop or variable drop print
head), the results would probably justify the extra
overhead.
• Model-based halftoning seems like an interesting way
to make use of our understanding of the human
visual system, but the complexity of these algorithms
seems to limit their usefulness for the time being.
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