1. Tone Dependent Color Error Diffusion
ICASSP 2004
Tone Dependent Color Error Diffusion
Vishal Monga and Brian L. Evans
May 20, 2004
Embedded Signal Processing Laboratory The University of Texas at Austin Austin, TX USA
{vishal,

2. Outline Introduction High Quality Halftoning Methods
Error Diffusion
Direct Binary Search (DBS)
Grayscale Tone Dependent Error Diffusion
Different error filter for each input gray-level
DBS halftone(s) used for filter design
Color Tone Dependent Error Diffusion
Perceptual Model
Error Filter Design
Conclusion & Future Work

3. Digital Halftoning: Examples
Introduction
Digital Halftoning: Examples
Original Image
Threshold at Mid-Gray
Dispersed Dot Screening
Clustered Dot Screening
Floyd Steinberg Error Diffusion
Direct Binary Search

4. Grayscale Error Diffusion Halftoning
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 + _
e(m)
b(m)
x(m)
difference
threshold
compute error
shape error
u(m)
Error Diffusion
current pixel
3/16
7/16
5/16
1/16
weights
Spectrum

5. Direct Binary Search [Analoui, Allebach 1992]
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

6. Tone Dependent Error Diffusion [Li & Allebach, 2002]
Grayscale TDED
Tone Dependent Error Diffusion [Li & Allebach, 2002]
Train error diffusion weights and threshold modulation
b(m) + _
e(m)
x(m)
Tone dependent error filter
Tone dependent threshold modulation
DBS pattern
for graylevel x
Halftone pattern
FFT
Midtone regions (21-234)
Highlights and shadows
(0-20, )
FFT
Graylevel patch x
Halftone pattern
for graylevel x
FFT

7. Tone Dependent Color Error Diffusion
Color TDED
Tone Dependent Color Error Diffusion
Extension of 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

8. Perceptual color space
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 C2 C3
Perceptual color space
Spatial
filtering

9. Linearized CIELab Color Space
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 – L = 116 f (Y/Yn) – 116
Cx = 200[X/Xn – Y/Yn] a* = 200[ f(X/Xn ) – f(Y/Yn ) ]
Cz = 500 [Y/Yn – Z/Zn] b* = 500 [ f(Y/Yn ) – f(Z/Zn ) ]
where
f(x) = 7.787x + 16/ ≤ x <
f(x) = x1/ ≤ x ≤ 1
Color Transformation
sRGB  CIEXYZ  YyCx Cz
sRGB CIEXYZ obtained from

10. HVS Filtering Filter chrominance channels more aggressively
Color TDED
HVS Filtering
Filter chrominance channels more aggressively
Luminance frequency response [Näsänen and Sullivan, 1984]
L average luminance of display
weighted radial spatial frequency
Chrominance frequency response [Kolpatzik and Bouman, 1992]
Chrominance response allows more low frequency chromatic error not to be perceived vs. luminance response

11. Tone Dependent Color Error Diffusion
Color TDED
Tone Dependent Color Error Diffusion
Design Issues
(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

12. Perceptual Error Metric
Color TDED
Perceptual Error Metric
Color Transformation
sRGB  Yy Cx Cz
(Linearized CIELab)
FFT
Input RGB Patch
Halftone Pattern 

13. Perceptual Error Metric
Color TDED
Perceptual Error Metric
HVS Chrominance
Frequency Response
HVS Luminance
Total Squared Error (TSE) 
Yy
Cx
Cz
Find error filters that minimize TSE subject to diffusion and non-negativity constraints, m = r, g, b; a  (0, 255)
(Floyd-Steinberg)

14. (a) Original Color Ramp Image (b) Floyd-Steinberg Error Diffusion
Color TDED
Results
(a) Original Color Ramp Image
(b) Floyd-Steinberg Error Diffusion

15. (c) *Separable application of grayscale TDED
Color TDED
Results …
(c) *Separable application of grayscale TDED
(d) Color TDED
*Halftone in (c) courtsey Prof. J. P. Allebach and T. Chang at Purdue University

16. Results … Halftone Detail Blue section of the color ramp
Color TDED
Results …
Halftone Detail
Blue section of the color ramp
Floyd-Steinberg
Grayscale TDED
Color TDED

17. Conclusion & Future Work
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

19. Original
House Image

20. Floyd Steinberg Halftone

21. Color TDED Halftone

22. Floyd Steinberg Yy component

23. Floyd Steinberg Cx component

24. TDED Yy component

25. TDED Cx component

26. HVS Filtering contd… frequency [Sullivan, Ray, Miller 1991]
Color TDED
HVS Filtering contd…
Role of frequency weighting
weighting by a function of angular spatial
frequency [Sullivan, Ray, Miller 1991]
where p = (u2+v2)1/2 and
w – symmetry parameter
reduces contrast sensitivity at odd multiples of 45 degrees
equivalent to dumping the luminance error across the diagonals
where the eye is least sensitive.