Tone Dependent Color Error Diffusion

1. ICASSP 2004 http://signal.ece.utexas.edu Tone Dependent Color Error Diffusion Vishal Monga and Brian L. Evans May 20, 2004 Embedded Signal Processing LaboratoryThe University of Texas at AustinAustin, TX 78712-1084 USA {vishal, bevans}@ece.utexas.edu

2. Outline • Introduction • High Quality Halftoning Methods • ErrorDiffusion • 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. Introduction Original Image Threshold at Mid-Gray Dispersed Dot Screening Clustered DotScreening Floyd SteinbergError Diffusion, 1976 Digital Halftoning: Examples Direct Binary Search 1992

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

5. Background Direct Binary Search[Analoui, Allebach 1992] - Computationally too expensive for many real-time applications e.g. printing - Used in screen design - Practical upper bound for achievable halftone quality

6. Grayscale TDED Tone dependent threshold modulation b(m) x(m) _ + _ + Tone dependent error filter Midtone regions (21-234) e(m) FFT DBS pattern for graylevel x Halftone pattern for graylevel x FFT Tone Dependent Error Diffusion[Li & Allebach, 2002] • Train error diffusionweights and thresholdmodulation Highlights and shadows (0-20, 235-255) FFT Graylevel patch x Halftone pattern for graylevel x FFT

7. Color TDED Tone Dependent Color Error Diffusion • Goal: 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 • Two processing options • 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. Color HVS Model C1 C2 C3 Spatial filtering Perceptual color space Perceptual Model [Poirson, Wandell 1997] • Separate image into channels/visual pathways • Pixel based transformation of RGB  Linearized CIELab [Flohr, Kolpatzik, R.Balasubramanian, Carrara, Bouman, Allebach, 1993] • Spatial filtering based on HVS characteristics & color space [Näsänen and Sullivan, 1984], [Kolpatzik and Bouman, 1992]

9. 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

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

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

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

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

14. Color TDED Results III • Halftone Detail • Blue section of the color ramp Floyd-Steinberg Grayscale TDED Color TDED

15. 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

16. Back Up Slides

17. 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 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 + 16/116 0 ≤ x < 0.008856 f(x) = x1/3 0.008856 ≤ x ≤ 1 • Color Transformation • sRGB  CIEXYZ  YyCx Cz • sRGB CIEXYZ obtained from http://white.stanford.edu/~brian/scielab/

18. 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

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. 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.