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

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

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

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

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

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, 235-255) FFT Graylevel patch x Halftone pattern for graylevel x FFT

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

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

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 – 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/

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

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

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

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)

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

(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

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

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

Back Up Slides

Original House Image

Floyd Steinberg Halftone

Color TDED Halftone

Floyd Steinberg Yy component

Floyd Steinberg Cx component

TDED Yy component

TDED Cx component

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.