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Clustered-dot-ordered Dither

Clustered-dot-ordered Dither. Bui Hai Thanh. Introduction. Ordered dither Fixed pattern of number (halftone cell) Two approaches Dispersed: turn on the pixel individually Clustered: group pixels to clusters Dispersed/Clustered: Depends on devices capability of displaying dots.

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Clustered-dot-ordered Dither

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  1. Clustered-dot-ordered Dither Bui Hai Thanh

  2. Introduction • Ordered dither • Fixed pattern of number (halftone cell) • Two approaches • Dispersed: turn on the pixel individually • Clustered: group pixels to clusters • Dispersed/Clustered: Depends on devices capability of displaying dots

  3. Introduction • Clustered ordered • Described by • Screen angle • Screen frequency • Dot pattern • Level assignment

  4. Introduction • Screen angle • Printing industry: clockwise fr. vertical line • Fourfold symmetry: 0..90O • Color case: 45O K, 75O C, 15O M, 0O Y • Screen frequency:# of halftone cell in a unit of length (e.g.: lpi) • Dot pattern: fill-in order for dot growth sequence

  5. Introduction • Important development • Screen functions • Threshold array • Holladay algorithm • Rational/Irrational tangent screens • Supercell • Multicenter dot

  6. Threshold Array • Discrete representation • Dot pattern in the form of threshold values • 2D signal • Use threshold to decide if the pixel should be turned on • Goal • No moiré • No contour • Sharp and fine details

  7. Threshold Array

  8. Screen Functions • Guide for creating threshold array • Mathematical functions are used • Round dot: s(x,y)= 1-(x2+y2) 0 1

  9. Screen Functions • Within each ring, pixels have to be in sequence • Counter clockwise spiral • Classical spiral

  10. Clustered Dot Design • Minimize edge/area ratio • Minimize dot center migration • Dot join strategy • Boom dot • Kiss dot • Cell boundary: squared vs. round • Dot growth: make the dot asymmetric • Dot gain

  11. Some special requirements • Smooth transition: • The white area on black when coverage >50% should be the negative image of black area on white • s(x,y)=cxcos(2vxx)+ cycos(2vyy) • s(x,y)=0.5[1+sin(vxx)sin(vyy)] • vx,vy : are the scaling factors for screen size • cx, cy : aspect ratio without affecting screen frequency • The negative image has a shift from positive

  12. Tone level • With M x N screen: MN+1 level • Tone level assignment may have • Uniform (linear density function) • Non-uniform (non-linear density function)

  13. Threshold operation • The darkest element growths to the percentage of average intensity • Threshold by comparing with average value. Turn on pixel with threshold level > pixel value • Direct comparison

  14. Holladay Algorithm • Using general parallelogram • Width L • Height H • Shift S=L-D • Area: (x+u)(y+v)-xy-uv=xv+yu

  15. Holladay Algorithm • Halftone cell can be described by an equivalent rectangular cell • Width L • Height H • Shift S

  16. Postscript Halftone

  17. Partial Dotting • Mixture of full dots • Provide details and preserve edges

  18. Rational/Irrational Tangent Screens • Screen is rational if tangent angle is a ratio of integers • Have exactly the same size and shape • Limited # of angle/frequency combinations • Irrational tangent screen • Size and shape may vary • Can have more combinations

  19. Rational screen • Nishikawa

  20. Irrational screen • Can have non integer ratios • So can have any angle/frequency • One or more corners are not located on junctions of grid. • Cost: Different in size and shape • Dot pattern and # tone level vary from cell to cell • Select screen with frequency, rotate on the fly • If pixel in digital grid falls between points of the threshold array, interpolation is required

  21. Irrational • Rotation formula • x’=x cos  - y sin  • y’=y cos  + x sin  • General expression • x’=(x-x0) cos  - (y-y0) sin  +x0 • y’=(x-x0) sin  + (y-y0) cos  +y0

  22. Supercell • Integer tangent has limited number • Small cell provides less choice of angle • Large cell causes the low frequency • Divide large cell into small subcells give more choices of screen angle, with increased frequency and reduce tone level • Supercell is rational cell consist of subcells, which can be varied in size/shape

  23. Multicenter Dot • Similar to supercell • Cell is divided into equal parts • Each partial dot has nucleus growing also with clustered approach within larger dot • Increase frequency • Drawback: slight texture contouring, and tone jump in hightlight

  24. THANK YOU!!!

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