An Input-Level Dependent Approach To Color Error Diffusion

1. 2004 SPIE/IS&T Symposium on Electronic Imaging http://signal.ece.utexas.edu An Input-Level Dependent Approach To Color Error Diffusion 1Mr. Vishal Monga, 2Dr. Niranjan Damera-Venkata and 1Prof. Brian L. Evans 2Hewlett-Packard Laboratories1501 Page Mill RoadPalo Alto, CA 94304 USA damera@exch.hpl.hp.com 1Embedded Signal Processing LaboratoryThe University of Texas at AustinAustin, TX 78712-1084 USA {bevans,vishal}@ece.utexas.edu

2. 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

3. 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

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

5. 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

6. 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

7. 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 • Spatial filtering based on HVS characteristics & color space

8. 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/

9. 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

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 (a) Original Color Ramp Image (b) Floyd-Steinberg Error Diffusion

13. Color TDED Results … (c) Separable application of grayscale TDED (d) Color TDED

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

15. Original House Image

16. Floyd Steinberg Halftone

17. Color TDED Halftone

18. 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

19. Back Up Slides

20. Floyd Steinberg Yy component

21. Floyd Steinberg Cx component

22. TDED Yy component

23. TDED Cx component

24. 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.