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#### Presentation Transcript

**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)

**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!!!