Histograms Analysis of the Microstructure of Halftone Images

Histograms Analysis of the Microstructure of Halftone Images J. S. Arney & Y. M. Wong Center for Imaging Science, RIT Given by Linh V. Tran ITN, Campus Norrköping, Linköping University In Digital Halftoning Course. Jan. 17, 2003

Linh V. Tran - Graduate course in Digital Halftoning Outline • J. S. Arney & Y. M. Wong. ”Histograms Analysis of the Microstructure of Halftone Images”. 1999 – Problem definition • Ideal case • More Complicated cases in Reality – Solution: Modeling the bimodal histogram – Experiments • Mat. Lab Halftoning Toolbox Developed in University of Texas at Austin, TX, USA • Comparison several halftoning methods Done by Michael Bruce de. Leon, Stanford, USA 2/36

Linh V. Tran - Graduate course in Digital Halftoning Problem • Estimate – The mean reflectance of the paper between the halftone dots, RP – The mean reflectance of the dots, RI and – The halftone dot area fraction, F of a given printed patch. 3/36

Linh V. Tran - Graduate course in Digital Halftoning 4/36 Ideal case Ink • Perfect ink drops • No dot gain Paper F 1 -F 0 Ri Rp A perfect frequency occurrence of gray levels of reflectance consists of 2 delta functions. 1

Linh V. Tran - Graduate course in Digital Halftoning Microdensitometry • CCD Camera: 1000 x 1000 pixels CCD Camera • Can measure also Microscope paper - Resolutions - Granularity - Micro-distribution of color in the image 5/36

Linh V. Tran - Graduate course in Digital Halftoning Experiments • Histogram of 65 LPI AM halftone printed by offset lithography, measured at 5 mm field of view (FOV) 6/36

Linh V. Tran - Graduate course in Digital Halftoning More Difficult • Histograms at 5 mm FOV of error diffusion dot pattern printed by thermal ink jet at 300 dpi with F = 0. 5 7/36

Linh V. Tran - Graduate course in Digital Halftoning More and More Difficult • Histograms at 5 mm FOV of error diffusion dot pattern printed by thermal ink jet at 300 dpi with F = 0. 05 8/36

Linh V. Tran - Graduate course in Digital Halftoning Modelling the Bimodal Histogram The edge modeled with Rmin = 0. 3, Rmax = 0. 7 a = 10, and b = 0. 5 9/36

Linh V. Tran - Graduate course in Digital Halftoning Frequency Occurence of R dx 10/36

Linh V. Tran - Graduate course in Digital Halftoning Add Gaussian Noise 11/36

Linh V. Tran - Graduate course in Digital Halftoning Five unknowns: Rmax Rmin a, b Curve Fitting 12/36

Linh V. Tran - Graduate course in Digital Halftoning Inverse Model 13/36

Linh V. Tran - Graduate course in Digital Halftoning Implementation • Main results published earlier in Wong’s B. Sc. Thesis: ”Modeling the Halftone Image to Determine the Area Fraction of Ink” CIS, RIT, 1998 • www. cis. rit. edu/research/thesis/bs/1998/wong • Simulations mainly done in Math. CAD 14/36

Linh V. Tran - Graduate course in Digital Halftoning Mat. Lab Toolbox Developed in University of Texas at Austin, TX, USA • Grayscale halftoning methods – – – Classical and user-defined screens Classical error diffusion methods Edge enhancement error diffusion Green noise error diffusion Block error diffusion • Figures of merit measures for grayscale halftones – – Peak signal-to-noise ratio (PSNR) Weighted signal-to-noise ratio (WSNR) Linear distortion measure (LDM) Universal quality index (UQI) 15/36

Linh V. Tran - Graduate course in Digital Halftoning 16/36 Figures of Merit • PSNR: Peak Signal to Noise Ratio of the output image with respect to the input image in d. B

Linh V. Tran - Graduate course in Digital Halftoning Figures of Merit • WSNR: Weighted Signal to Noise Ratio of output image with respect to the input image in d. B. A weighting appropriate to the human visual system is used. J. Mannos and D. Sakrison, "The effects of a visual fidelity criterion on the encoding of images", IEEE Trans. Inf. Theory, IT 20(4), pp. 525 -535, July 1974 • LDM: Linear Distortion Ratio. • UQI: Universal image Quality Index. Zhou Wang and Alan C. Bovik "A Universal Image Quality Index" IEEE Signal Processing Letters, 2001 17/36

Linh V. Tran - Graduate course in Digital Halftoning Mat. Lab Toolbox • Color halftoning methods – – – Classical and user-defined (multilevel) screens (separable) Classical separable error diffusion methods (separable) Edge enhancement error diffusion (separable) Green noise error diffusion (separable) Block error diffusion (separable) Minimum brightness variation quadruple error diffusion (nonseparable design for separable implementation) – Vector error diffusion (non-separable) • Figures of merit measures for color – PSNR, WSNR, LDM, UQI as in grayscale halftoning – Noise gain in d. B over Floyd-Steinberg error diffusion (specific to Vector Error Diffusion) 18/36

Linh V. Tran - Graduate course in Digital Halftoning Demo • http: //www. ece. utexas. edu/~bevans/projects/ halftoning/toolbox/ 19/36

Linh V. Tran - Graduate course in Digital Halftoning 20/36 De. Leon’s Comparison • Done by Michael Bruce de. Leon, Stanford, USA http: //ise 0. stanford. edu/~mdeleon/ • Methods: 1. 2. 3. 4. Bayer Dither Matrix: 8 x 8 matrix Three Level Dither Error Diffusion: Floyd and Steinberg MBVQ Error Diffusion (Minimum Brightness Variation Quadrants) • Test images: Ramps, Trees, Lena, Chart

Linh V. Tran - Graduate course in Digital Halftoning • Original Image • Bayer Dither Matrix • 3 Level Dither • Error Diffusion • MBVQ Error Diffusion 21/36

Linh V. Tran - Graduate course in Digital Halftoning • Original Image • Bayer Dither Matrix • 3 Level Dither • Error Diffusion • MBVQ Error Diffusion 22/36

Linh V. Tran - Graduate course in Digital Halftoning Tree image Original Image Bayer Dither Matrix Three Level Dither Error Diffusion 23/36

Linh V. Tran - Graduate course in Digital Halftoning 24/36

Linh V. Tran - Graduate course in Digital Halftoning Tree Image MBQV Error Diffusion Bayer Dither Matrix Three Level Dither Error Diffusion 25/36

Linh V. Tran - Graduate course in Digital Halftoning 26/36

Linh V. Tran - Graduate course in Digital Halftoning Lena Image Original Image Bayer Dither Matrix Three Level Dither Error Diffusion 27/36

Linh V. Tran - Graduate course in Digital Halftoning 28/36

Linh V. Tran - Graduate course in Digital Halftoning Lena Image MBQV Error Diffusion Bayer Dither Matrix Three Level Dither Error Diffusion 29/36

Linh V. Tran - Graduate course in Digital Halftoning 30/36

Linh V. Tran - Graduate course in Digital Halftoning Chart Image Original Image Bayer Dither Matrix Three Level Dither Error Diffusion 31/36

Linh V. Tran - Graduate course in Digital Halftoning 32/36

Linh V. Tran - Graduate course in Digital Halftoning Chart Image MBQV Error Diffusion Bayer Dither Matrix Three Level Dither Error Diffusion 33/36

Linh V. Tran - Graduate course in Digital Halftoning 34/36

Linh V. Tran - Graduate course in Digital Halftoning 35/36 De. Leon’s Conclusions • Solid tones seem the most difficult to present smoothly with a halftoning pattern. Thus, simple computer graphics may be more of a challenge for a printer than complex photos. • The color error diffusion algorithm can effectively limit the number of colors used for a given region. Its execution time is only marginally longer than that of regular error diffusion. The pattern produced is slightly smoother than the regular error diffusion results, though unless closely examined in these monitor examples, the differences in dot brightness & color is easy to miss. Depending in its use with actual inks, tradeoffs might have to be made between the appearances of colors in grayscale images and this smoothing effect.

Linh V. Tran - Graduate course in Digital Halftoning De. Leon’s Conclusions • Multi-level halftoning seems to offer considerable image quality improvement without expensive algorithms. Although the expenses for realizing this functionality come from other areas (cost of extra inks, complexity of multi-drop or variable drop print head), the results would probably justify the extra overhead. • Model-based halftoning seems like an interesting way to make use of our understanding of the human visual system, but the complexity of these algorithms seems to limit their usefulness for the time being. 36/36

Linh V. Tran - Graduate course in Digital Halftoning 37/36