2004 SPIE/IS&T Symposium on Electronic Imaging
An Input-Level Dependent Approach To
Color Error Diffusion
1Mr.
Vishal Monga, 2Dr. Niranjan Damera-Venkata
and 1Prof. Brian L. Evans
1Embedded
Signal Processing Laboratory
The University of Texas at Austin
Austin, TX 78712-1084 USA
{bevans,vishal}@ece.utexas.edu
2Hewlett-Packard
Laboratories
1501 Page Mill Road
Palo Alto, CA 94304 USA
damera@exch.hpl.hp.com
http://signal.ece.utexas.edu
Background
Grayscale Error Diffusion Halftoning
• 2- D sigma delta modulation [Anastassiou, 1989]
– Shape quantization noise into high freq.
• Several Enhancements
– Variable thresholds, weights and scan paths
difference
threshold
current pixel
u(m)
x(m)
+
Error Diffusion
b(m)
_
_
h(m)
7/16
+
3/16 5/16 1/16
e(m)
shape error
compute
error
weights
Spectrum
2
Background
Direct Binary Search
[Analoui, Allebach 1992]
- Computationally
too expensive for
real-time
applications e.g.
printing
- Used in screen
design
- Practical upper
bound for achievable
halftone quality
3
Grayscale TDED
Tone Dependent Error Diffusion
• Train error diffusion
weights and threshold
modulation
Tone dependent threshold
modulation
x(m)
[Li & Allebach, 2002]
h 
x m  , Qx m  
Halftone pattern
for graylevel x
_
_
Tone
dependent
error filter
Midtone regions
DBS pattern
for graylevel x
+
Q x m 
hx  m 
b(m)
+
e(m)
FFT

FFT
Highlights and shadows
Graylevel patch x
FFT

h 
x m
, Qx m  
Halftone pattern
for graylevel x
FFT
HVS
4
Color TDED
Input-Level Dependent Color Error Diffusion
• Extend TDED to color?
– Goal: e.g. for RGB images obtain optimal (in visual
quality) error filters with filter weights dependent on
input RGB triplet (or 3-tuple)
– Applying grayscale TDED independently to the 3 (or 4)
color channels ignores the correlation amongst them
• Processing: channel-separable or vectorized
– Error filters for each color channel (e.g. R, G, B)
– Matrix valued error filters [Damera-Venkata, Evans 2001]
• Design of error filter key to quality
– Take human visual system (HVS) response into account
5
Color TDED
Input-Level Dependent Color Error Diffusion
• Problem(s):
– (256)3 possible input RGB tuples
– Criterion for error filter design?
• Solution
– Design error filters along the diagonal line of the color
cube i.e. (R,G,B) = {(0,0,0) ; (1,1,1) …(255,255,255)}
– 256 error filters for each of the 3 color planes
– Color screens are designed in this manner
– Train error filters to minimize the visually weighted
squared error between the magnitude spectra of a
“constant” RGB image and its halftone pattern
6
Color HVS Model
Perceptual Model
[Poirson, Wandell 1997]
• Separate image into channels/visual pathways
– Pixel based transformation of RGB  Linearized CIELab
– Spatial filtering based on HVS characteristics & color space
C1
E
C2
C3
Perceptual color space
Spatial
filtering
7
Color TDED
Linearized CIELab Color Space
• Linearize CIELab space about D65 white point
[Flohr, Kolpatzik, R.Balasubramanian, Carrara, Bouman, Allebach, 1993]
Yy = 116 Y/Yn – 116
Cx = 200[X/Xn – Y/Yn]
Cz = 500 [Y/Yn – Z/Zn]
where
f(x) = 7.787x + 16/116
f(x) = x1/3
L = 116 f (Y/Yn) – 116
a* = 200[ f(X/Xn ) – f(Y/Yn ) ]
b* = 500 [ f(Y/Yn ) – f(Z/Zn ) ]
0 ≤ x < 0.008856
0.008856 ≤ x ≤ 1
• Color Transformation
– sRGB  CIEXYZ  YyCx Cz
– sRGB CIEXYZ obtained from
http://white.stanford.edu/~brian/scielab/
8
Color TDED
HVS Filtering
• Filter chrominance channels more aggressively
– Luminance frequency response [Näsänen and Sullivan, 1984]
W(Yy )
 ( L ) ~
~
(  )  K ( L) e
L average luminance of display
~ weighted radial spatial frequency
– Chrominance frequency response [Kolpatzik and Bouman, 1992]
W(Cx ,Cz ) (  )  Ae 
– Chrominance response allows more low frequency
chromatic error not to be perceived vs. luminance response
9
Color TDED
Perceptual Error Metric
Input RGB Patch
FFT
Color Transformation

sRGB  Yy Cx Cz
(Linearized CIELab)
FFT
Halftone Pattern
10
Color TDED
Perceptual Error Metric
Yy
Cx

Cz
HVS Luminance
Frequency Response

HVS Chrominance
Frequency Response

HVS Chrominance
Frequency Response

Total Squared Error
(TSE)
• Find error filters that minimize TSE subject to diffusion
and non-negativity constraints, m = r, g, b; a  (0, 255)
 h k; a   1
m
k
h m k; a   0
 k S
(Floyd-Steinberg)
11
Color TDED
Results
(a) Original Color Ramp Image
(b) Floyd-Steinberg Error Diffusion
12
Color TDED
Results …
(c) Separable application of grayscale TDED
(d) Color TDED
13
Color TDED
Results …
• Halftone Detail
– Blue section of the color ramp
Floyd-Steinberg
Grayscale TDED
Color TDED
14
Original
House
Image
15
Floyd
Steinberg
Halftone
16
Color
TDED
Halftone
17
Color TDED
Conclusion & Future Work
• Color TDED
–
–
–
–
Worms and other directional artifacts removed
False textures eliminated
Visibility of “halftone-pattern” minimized (HVS model)
More accurate color rendering (than separable application)
• Future Work
– Incorporate Color DBS in error filter design to enhance
homogenity of halftone textures
– Design visually optimum matrix valued filters
18
Back Up Slides
Floyd
Steinberg Yy
component
20
Floyd
Steinberg Cx
component
21
TDED Yy
component
22
TDED Cx
component
23
Color TDED
HVS Filtering contd…
• Role of frequency weighting
– weighting by a function of angular spatial
frequency [Sullivan, Ray, Miller 1991]
v
  arctan( )
u
s ( ) 
p
~
p
s( )
where p = (u2+v2)1/2 and
1 w
1 w
cos( 4 ) 
2
2
w – symmetry parameter
s ( ) reduces contrast sensitivity at odd multiples of 45 degrees
equivalent to dumping the luminance error across the diagonals
where the eye is least sensitive.
24