Halftoning With Pre-Computed Maps

Objective Image Quality Measures

Halftoning and Objective Quality Measures for Halftoned Images

Halftoning With Pre-Computed Maps FM halftoning using threshold matrices

High computational speed Trade-off between quality of tints and quality of shades Optimization criteria can not be fulfilled for every tone value

PreCoM Meet both requirements for all tint levels Without any loss in speed

Pre-Computed Maps, PreCoM

Pre-computed maps, representing every tone value

Halftone volume Image value as index No comparison No information from

neighboring pixels

Computing the maps

Individually optimized- Full control of the dot pattern for each tone value

Dots in each map maximally dispersed- Avoid graininess

Correlation between adjacent maps- No discontinuity effects

Computing the maps

Arbitrary pattern Gaussian low-pass filter Locate tightest cluster

(maximum) and largest void (minimum)

Remove dot at tightest cluster

Move to largest void Continue until no further

change occur

Computing the maps

Gaussian low-pass filter

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Circular convolution

Change the width accordingto tone value

Creating the locally correlated volume

Optimize

Optimize, using the new filter

Add extra dots to create new tone value

Start with 20% tone value

Continue the iterative process until all maps are created

Results

PreCoM

Error diffusion

Summary, PreCoM Pre-computed maps Individually optimized Locally correlated

Tints without graininess Smoothly varying shades

No loss in computational speed

Objective Image Quality Measures

Image quality? A reproduced image’s resemblance to a digital

original Purpose: evaluate halftone images

Printed Observed by humans

Evaluate the perceived difference between the printed halftone and the original

Requirements

evaluate all kinds of halftones evaluate halftones for all kinds of printing techniques judge the quality of real images, not only synthetic test

patterns return measures for several aspects of quality that are

well correlated with results from subjective tests

An objective quality measure should be able to:

The Evaluation model Use printed images?

Uncontrolled variations Possible artifacts from scanning

Use models!

Print model Mechanical dot gain Optical dot gain

Observer model Contrast Sensitivity Function

Separation of information Two different types of errors will be mixed:

parts of the original that the halftone could not reproduce errors introduced by the halftone algorithm

Separate image information: Halftone carrier Reconstructed original

Reconstructing the original Extract as much as possible of the original

without including the carrier Use original as reference Fourier spectrum

Use an adaptive filter in the Fourier domain

Low-pass filter? No simple band limit!

The Adaptive filter Both magnitude and phase of the frequency

components are changed by the halftoning process The greater the phase difference, the less of the original

is described Take the vector in phase with the halftone that

minimizes the Euclidean distance to the original

The remainder of the halftone component is the halftone carrier, describing the halftone characteristics

Measuring quality Reconstructed original

The difference to the original shows information lost in the halftoning process

The capability for the halftone to reproduce the original

Halftone carrier Extra information introduced into the halftone May cause disturbances

Measuring quality Radial histogram in the Fourier domain

The average energy in each frequency band

Weight functions Numbers on certain aspects of quality Use weight functions to emphasize different

frequency bands

The Quality Measures Quality measures derived from the error

functions: Low Frequency deviation, LFDev Loss of Detail, Lod Loss of Fine Detail, LoFD

Quality measures derived from the carrier functions:

Low Frequency Disturbance, LFD Medium High Frequency Disturbance, MFD Very High Frequency Disturbance, VHFD

Summary Method for objective quality measures for

halftone images Evaluates the perceived printed image, using

models for the print and the observer Evaluates both the halftone’s truthfulness to

the original and the halftoned characteristics 6 Different quality measures, emphasizing on

different aspects of image quality Meets the requirements stated initially