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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, bevans}@ece.utexas.edu. Outline. Introduction

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tone dependent color error diffusion
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, bevans}@ece.utexas.edu

outline
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
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
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
BackgroundDirect 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 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

tone dependent color error diffusion7
Color TDEDTone 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
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
Color TDEDLinearized 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
Color TDEDHVS 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
Color TDEDTone 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

Input RGB Patch

FFT

Color Transformation

sRGB  Yy Cx Cz

(Linearized CIELab)

FFT

Halftone Pattern

Perceptual Error Metric
perceptual error metric13
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
Color TDEDResults

(a) Original Color Ramp Image

(b) Floyd-Steinberg Error Diffusion

slide15
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
Color TDED

Results …

  • Halftone Detail
    • Blue section of the color ramp

Floyd-Steinberg

Grayscale TDED

Color TDED

slide17
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
Original

House Image

slide26
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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