1 Embedded Signal Processing Laboratory The University of Texas at Austin Austin, TX USA 1 Mr. Vishal Monga, 2 Dr. Niranjan Damera-Venkata and 1 Prof. Brian L. Evans An Input-Level Dependent Approach To Color Error Diffusion 2 Hewlett-Packard Laboratories 1501 Page Mill Road Palo Alto, CA USA SPIE/IS&T Symposium on Electronic Imaging

2 current pixel weights 3/16 7/16 5/161/16 + _ _ + e(m)e(m) b(m)b(m)x(m)x(m) differencethreshold compute error shape error u(m)u(m) Error Diffusion Spectrum 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 Background

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

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

5 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 Color TDED

6 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 Input-Level Dependent Color Error Diffusion Color TDED

7 C1C1 C2C2 C3C3 Perceptual color space Spatial filtering 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 Color HVS Model

8 Linearized CIELab Color Space Linearize CIELab space about D65 white point [Flohr, Kolpatzik, R.Balasubramanian, Carrara, Bouman, Allebach, 1993] Y y = 116 Y/Yn – 116 L = 116 f (Y/Yn) – 116 C x = 200[X/Xn – Y/Yn] a* = 200[ f(X/Xn ) – f(Y/Yn ) ] C z = 500 [Y/Yn – Z/Zn] b* = 500 [ f(Y/Yn ) – f(Z/Zn ) ] where f(x) = 7.787x + 16/116 0 ≤ x < f(x) = x 1/ ≤ x ≤ 1 Color Transformation –sRGB  CIEXYZ  Y y C x C z –sRGB  CIEXYZ obtained from Color TDED

9 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 Color TDED

10 Color Transformation sRGB  Y y C x C z (Linearized CIELab) FFT Input RGB Patch Halftone Pattern  Perceptual Error Metric Color TDED

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

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

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

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

15 Original House Image

16 Floyd Steinberg Halftone

17 Color TDED Halftone

18 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 Conclusion & Future Work Color TDED

Back Up Slides

20 Floyd Steinberg Y y component

21 Floyd Steinberg C x component

22 TDED Y y component

23 TDED C x component

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