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ICASSP 2004. http://signal.ece.utexas.edu. 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, [email protected] Outline. Introduction

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Tone dependent color error diffusion l.jpg

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, [email protected]


Outline l.jpg

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


Slide3 l.jpg

Introduction

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

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


Direct binary search analoui allebach 1992 l.jpg

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 l.jpg

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


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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


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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


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 ) ]

    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 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

FFT

Color Transformation

sRGB  Yy Cx Cz

(Linearized CIELab)

FFT

Halftone Pattern

Perceptual Error Metric


Perceptual error metric13 l.jpg

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)


Results l.jpg

Color TDED

Results

(a) Original Color Ramp Image

(b) Floyd-Steinberg Error Diffusion


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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


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Color TDED

Results …

  • Halftone Detail

    • Blue section of the color ramp

Floyd-Steinberg

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


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Back Up Slides


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Original

House Image


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Floyd Steinberg Halftone


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Color TDED Halftone


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Floyd Steinberg Yy component


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Floyd Steinberg Cx component


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TDED Yy component


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TDED Cx component


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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.


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