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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 78712-1084 USA {vishal, bevans} Outline. Introduction

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Tone dependent color error diffusion l.jpg


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}

Outline l.jpg

  • 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

Slide3 l.jpg


Original Image

Threshold at Mid-Gray

Dispersed Dot Screening

Clustered DotScreening

Floyd SteinbergError Diffusion

Digital Halftoning: Examples

Direct Binary Search

Grayscale error diffusion halftoning l.jpg
















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



Direct binary search analoui allebach 1992 l.jpg


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 l.jpg

Grayscale TDED

Tone dependent threshold modulation







Tone dependent error filter

Midtone regions (21-234)



DBS pattern

for graylevel x

Halftone pattern

for graylevel x


Tone Dependent Error Diffusion[Li & Allebach, 2002]

  • Train error diffusionweights and thresholdmodulation

Highlights and shadows

(0-20, 235-255)


Graylevel patch x

Halftone pattern

for graylevel x


Tone dependent color error diffusion7 l.jpg

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

Slide8 l.jpg

Color HVS Model






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

Linearized cielab color space l.jpg

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 ) ]


    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

Hvs filtering l.jpg

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 diffusion11 l.jpg

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 l.jpg

Color TDED

Input RGB Patch


Color Transformation

sRGB  Yy Cx Cz

(Linearized CIELab)


Halftone Pattern

Perceptual Error Metric

Perceptual error metric13 l.jpg

Color TDED


HVS Luminance

Frequency Response

Total Squared Error (TSE)


HVS Chrominance

Frequency Response

HVS Chrominance

Frequency Response


Perceptual Error Metric

  • Find error filters that minimize TSE subject to diffusion and non-negativity constraints, m = r, g, b; a  (0, 255)


Results l.jpg

Color TDED


(a) Original Color Ramp Image

(b) Floyd-Steinberg Error Diffusion

Slide15 l.jpg

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

Slide16 l.jpg

Color TDED

Results …

  • Halftone Detail

    • Blue section of the color ramp


Grayscale TDED

Color TDED

Slide17 l.jpg

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

Slide19 l.jpg


House Image

Slide22 l.jpg

Floyd Steinberg Yy component

Slide23 l.jpg

Floyd Steinberg Cx component

Slide24 l.jpg

TDED Yy component

Slide25 l.jpg

TDED Cx component

Slide26 l.jpg

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.