Ph.D. Graduates: Dr. Niranjan Damera- Dr. Niranjan Damera- Venkata Venkata (HP Labs) (HP Labs) Dr. Thomas D. Kite Dr. Thomas D. Kite (Audio (Audio Precision) Precision) Ph.D. Student: Mr. Vishal Monga Mr. Vishal Monga (Intern, Xerox Labs) (Intern, Xerox Labs) Other Collaborators: Prof. Alan C. Bovik Prof. Alan C. Bovik (UT (UT Embedded Signal Processing Laboratory The University of Texas at Austin Austin, TX 78712-1084 USA http:://www.ece.utexas.edu/ ~bevans Prof. Brian L. Evans Prof. Brian L. Evans Error Diffusion Halftoning Error Diffusion Halftoning Methods for Methods for Printing and Display Printing and Display August 20, 2003 August 20, 2003
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Dr. Niranjan Damera-Venkata (HP Labs) Dr. Thomas D. Kite (Audio Precision) Ph.D. Graduates: Dr. Niranjan Damera-Venkata (HP Labs) Dr. Thomas D. Kite (Audio.
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Ph.D. Graduates: Dr. Niranjan Damera-Venkata Dr. Niranjan Damera-Venkata (HP Labs)(HP Labs) Dr. Thomas D. Kite Dr. Thomas D. Kite (Audio Precision)(Audio Precision)
Ph.D. Student: Mr. Vishal Monga Mr. Vishal Monga (Intern, Xerox Labs)(Intern, Xerox Labs)
Other Collaborators: Prof. Alan C. Bovik Prof. Alan C. Bovik (UT Austin)(UT Austin) Prof. Wilson S. Geisler Prof. Wilson S. Geisler (UT Austin)(UT Austin)
Embedded Signal Processing Laboratory
The University of Texas at Austin
Austin, TX 78712-1084 USA
http:://www.ece.utexas.edu/~bevans
Prof. Brian L. EvansProf. Brian L. Evans
Error Diffusion Halftoning Methods forError Diffusion Halftoning Methods forPrinting and DisplayPrinting and Display
Ph.D. graduates: Dong Wei (SBC Research) K. Clint Slatton (Univ. of Florida) Wade C. Schwartzkopf
Real-Time Imaging
Ph.D. graduates: Thomas D. Kite (Audio Precision) Niranjan Damera-Venkata (HP Labs)Ph.D. students: Gregory E. Allen (UT App. Res. Labs) Serene Banerjee Vishal MongaMS graduates: Young Cho (UCLA)
Ph.D. graduates: Güner Arslan (Silicon Labs) Biao Lu (Schlumberger) Milos Milosevic (Schlumberger)Ph.D. students: Dogu Arifler Ming Ding
magnitude
carrier
channel
ADSL/VDSL Transceiver Design
Wireless Communications Ph.D. graduates: Murat Torlak (UT Dallas)
Ph.D. students: Kyungtae Han Zukang Shen MS graduates: Srikanth K. Gummadi (TI) Amey A. Deosthali (TI)MS students: Ian Wong
http://signal.ece.utexas.edu
Wireless Networking and Comm. Group: http://www.wncg.org
Center for Perceptual Systems: http://www.cps.utexas.edu
3
OutlineOutline
• Introduction
• Grayscale error diffusion– Analysis and modeling– Enhancements
• Compression of error diffused halftones
• Color error diffusion halftoning – Vector quantization with separable filtering
– Matrix valued error filter methods
• Conclusion
4
Introduction
Dispersed Dot ScreeningThreshold at Mid-Gray
Clustered Dot
Screening
Floyd SteinbergError Diffusion
Stucki Error Diffusion
Original Image
Conversion to One Bit Per Pixel: Spatial DomainConversion to One Bit Per Pixel: Spatial Domain
5
Introduction
Original Image Threshold at Mid-Gray Dispersed Dot Screening
Stucki Error Diffusion
Clustered DotScreening
Floyd SteinbergError Diffusion
Conversion to One Bit Per Pixel: Magnitude SpectraConversion to One Bit Per Pixel: Magnitude Spectra
6
Human Visual System ModelingHuman Visual System Modeling
• Contrast at particular spatialfrequency for visibility– Bandpass: non-dim
backgrounds[Manos & Sakrison, 1974; 1978]
– Lowpass: high-luminance officesettings with low-contrast images[Georgeson & G. Sullivan, 1975]
– Exponential decay [Näsäsen, 1984]
– Modified lowpass version[e.g. J. Sullivan, Ray & Miller, 1990]
– Angular dependence: cosinefunction [Sullivan, Miller & Pios, 1993]
– Promotes minority dot clustering• Linear gain model for quantizer
[Kite, Evans & Bovik, 2000]
– Models sharpening and noise shaping effects
Analysis and Modeling
Minority pixels
11
Linear Gain Model for QuantizerLinear Gain Model for Quantizer
• Extend sigma-delta modulation analysis to 2-D– Linear gain model for quantizer in 1-D [Ardalan and Paulos, 1988]
– Linear gain model for grayscale image [Kite, Evans, Bovik, 1997]
• Error diffusion is modeled as linear, shift-invariant– Signal transfer function (STF): quantizer acts as scalar gain– Noise transfer function (NTF): quantizer acts as additive
noise
Ks
us(m)
Signal Path
Ks us(m)
un(m)
n(m)
un(m) + n(m)
Noise Path
Q(.)u(m) b(m) {
Analysis and Modeling
12
Linear Gain Model for QuantizerLinear Gain Model for Quantizer
+ _
_+
e(m)
b(m)x(m) u(m)
)(mh
Ks
n(m)Quantizermodel
zz
z
HK
K
X
BSTF
s
ss
11)(
)(1
)(z
z
zH
N
BNTF n
Put noise in high frequencies
H(z) must be lowpass
)(H
Also, let Ks = 2
(Floyd-Steinberg)
1
STF2
Pass low frequencies
Enhance high frequencies
NTF
1
Highpass response(independent of Ks )
f(m)
Analysis and Modeling
13
Linear Gain Model for QuantizerLinear Gain Model for Quantizer
• Best linear fit for Ks between quantizer input u(m) and halftone b(m)
– Does not vary much for Floyd-Steinberg
– Can use average value to estimate Ks from only error filter
• Sharpening: proportional to Ks [Kite, Evans & Bovik, 2000]
Value of Ks: Floyd Steinberg < Stucki < Jarvis
• Weighted SNR using unsharpened halftoneFloyd-Steinberg > Stucki > Jarvis at all viewing distances
Color Monitor Display Example (Palettization)Color Monitor Display Example (Palettization)
• YUV color space– Luminance (Y) and chrominance (U,V) channels
– Widely used in video compression standards
– Contrast sensitivity functions available for Y, U, and V
• Display YUV on lower-resolution RGB monitor: use error diffusion on Y, U, V channels separably
Color Error Diffusion
+__
+
e(m)
b(m)x(m)
u(m)
)(mh
YUV to RGBConversion
RGB to YUVConversion
24-bitYUVvideo
12-bitRGBmonitor
h(m)
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Non-Separable Color Halftoning for DisplayNon-Separable Color Halftoning for Display
• Input image has a vector of values at each pixel (e.g. vector of red, green, and blue components)Error filter has matrix-valued coefficientsAlgorithm for adapting
matrix coefficientsbased on mean-squarederror in RGB space[Akarun, Yardimci & Cetin, 1997]
• Optimization problemGiven a human visual system model, find
color error filter that minimizes average visible noise power subject to diffusion constraints [Damera-Venkata & Evans, 2001]
Linearize color vector error diffusion, and use linear vision model in which Euclidean distance has perceptual meaning
vectormatrix
kmekhmtk
+ _
_
+e(m)
b(m)x(m)u(m)
)(mh
t(m)
Color Error Diffusion
28
Matrix Gain Model for the QuantizerMatrix Gain Model for the Quantizer
• Replace scalar gain w/ matrix [Damera-Venkata & Evans, 2001]
– Noise uncorrelated with signal component of quantizer input
– Convolution becomes matrix–vector multiplication in frequency domain
12minarg
uubu
A
CCmuAmbK
Es
IK
n
zNzHIzB
n
zXIKzHIKzB1
s
Noisecomponentof output
Signalcomponentof output
u(m) quantizer inputb(m) quantizer output
Color Error Diffusion
z
z
HK
XK
s
s
11
)(
)()(1 zz NH
Grayscale results
29
Linear Color Vision ModelLinear Color Vision Model
• Undo gamma correction to map to sRGB
• Pattern-color separable model [Poirson & Wandell, 1993] – Forms the basis for Spatial CIELab [Zhang & Wandell, 1996]
– Pixel-based color transformation
B-W
R-G
B-YOpponentrepresentation
Spatialfiltering
E
Color Error Diffusion
30
Optimum vectorerror filter
SeparableFloyd-Steinberg
Color Error Diffusion
ExampleExample
Original
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Evaluating Linear Vision ModelsEvaluating Linear Vision Models[Monga, Geisler & Evans, 2003][Monga, Geisler & Evans, 2003]
• Objective measure: improvement in noise shaping over separable Floyd-Steinberg
• Subjective testing based on paired comparison taskOnline at www.ece.utexas.edu/~vishal/cgi-bin/test.html
UT Austin Halftoning Toolbox 1.1 for MATLABUT Austin Halftoning Toolbox 1.1 for MATLAB
Freely distributable software available atFreely distributable software available at http://ww.ece.utexas.edu/~bevans/projects/halftoning/toolboxhttp://ww.ece.utexas.edu/~bevans/projects/halftoning/toolbox
UT Austin Center for Perceptual Systems, www.cps.utexas.edu
Backup SlidesBackup Slides
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Need for Digital Image HalftoningNeed for Digital Image Halftoning
• Examples of reduced grayscale/color resolution– Laser and inkjet printers
– Facsimile machines
– Low-cost liquid crystal displays
• Halftoning is wordlength reduction for images– Grayscale: 8-bit to 1-bit (binary)
– Color displays: 24-bit RGB to 8-bit RGB
– Color printers: 24-bit RGB to CMY (each color binarized)
• Halftoning tries to reproduce full range of gray/ color while preserving quality & spatial resolution– Screening methods are pixel-parallel, fast, and simple– Error diffusion gives better results on some media
• Linearize the CIELab Color Space about D65 white pointDecouples incremental changes in Yy, Cx, Cz at white point on (L,a,b)
values
T is sRGB CIEXYZ Linearized CIELab
Color Error Diffusion
52
Plane Weights wi Spreads σi
Luminance 0.921 0.0283
0.105 0.133
-0.108 4.336
Red-green 0.531 0.0392
0.330 0.494
Blue-yellow 0.488 0.0536
0.371 0.386
Spatial FilteringSpatial Filtering
• Opponent [Wandell, Zhang 1997]
– Data in each plane filtered by 2-D separable spatial kernels
– Parameters for the three color planes are
Color Error Diffusion
53
Spatial FilteringSpatial Filtering
• Spatial Filters for Linearized CIELab and YUV,YIQ based on:
Luminance frequency Response [ Nasanen and Sullivan – 1984]
]~)(exp[)()~()( pLLKpWyY
dLcL
)ln(
1)(
L – average luminance of display, the radial spatial frequency andp~
K(L) = aLb
2
1)4cos(
2
1)(
wws
where p = (u2+v2)1/2 and
)arctan(u
v
)(~
s
pp
w – symmetry parameter = 0.7 and
)(s effectively reduces contrast sensitivity at odd multiples of 45 degrees which is equivalent to dumping the luminance error across the diagonals where the eye is least sensitive.
Color Error Diffusion
54
Spatial FilteringSpatial Filtering
Chrominance Frequency Response [Kolpatzik and Bouman – 1992]
]exp[)(),( pApWzx CC
Using this chrominance response as opposed to same for both luminance and chrominance allows more low frequency chromatic error not perceived by the human viewer.
• The problem hence is of designing 2D-FIR filters which most closely match the desired Luminance and Chrominance frequency responses.
• In addition we need zero phase as well.
The filters ( 5 x 5 and 15 x 15 were designed using the frequency sampling approach and were real and circularly symmetric).