1. Halftoning With Pre- Computed Maps Objective Image Quality Measures Halftoning and Objective Quality Measures for Halftoned Images

2. 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

3. Pre-Computed Maps, PreCoM Pre-computed maps, representing every tone value Halftone volume Image value as index No comparison No information from neighboring pixels

4. 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

5. 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

6. Computing the maps Gaussian low-pass filter Circular convolution Change the width according to tone value

7. 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

8. Results PreCoM Error diffusion

9. Summary, PreCoM Pre-computed maps Individually optimized Locally correlated Tints without graininess Smoothly varying shades No loss in computational speed

10. 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

11. 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:

12. 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

13. 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

14. 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!

15. 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

17. 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

18. Measuring quality Radial histogram in the Fourier domain The average energy in each frequency band

19. Weight functions Numbers on certain aspects of quality Use weight functions to emphasize different frequency bands

20. 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

21. 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