Half Toning

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Half Toning
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Continuous Half Toning
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Color Half Toning
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Half toning and Colors
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Digital Half Toning
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Half Toning
Emulating 5 different levels
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Half Toning
10 levels
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Original
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Half Toning
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Original
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Dithering
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Dithering and Halftoning

• Trade spatial for intensity resolution
• (works well for printing where dot printing is
  very high)
• Thresholding.
• Random dither Roberts algorithm
• Ordered dither
• Error diffusion
• Your eye will average over an area
• - Spatial Integration

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Thresholding

• Assume we want to quantize a gray-level image to
  a binary colormap.
• Map the upper half of the gray-level scale to
  white, and the lower half to black a simple
  threshold operation, preformed independently at
  each pixel.

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Thresholding
Original image.
Simple threshold.
n 0.5
Errors are low spatial frequencies.
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Roberts Algorithm

• First add noise
• Then quantize

i
r 1
1
Quantized to 1
Quantized to 0
r
0
x
Moves errors to higher spatial frequencies. -gt
eye averages over an area.
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Threshold
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Threshold Noise
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Roberts Algorithm
Pink
Blue
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Roberts Algorithm

• Moves low frequency (average error) to high
  frequency
• Pink(low), Blue (high), White(all) frequency noise

Pink
Blue
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The trouble with noise

• Difficult to compute quickly.
• Not reproducible.
• Pre-compute pseudo-random function and store in
  table.
• Small tiled patterns sufficient

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Dithering

• It is possible to improve the quality of a
  quantized image by distributing the quantized
  error.
• Lets have a closer look.

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Dithering
Thresholding
Dithering
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Dithering
Each pixel produces a quatization error The
quality of the result may be improved by
adjusting the threshold locally, so that adjacent
pixels in small areas are quantized with
different thresholds. This reduces the average
local quantization error. Matrices of these
threshold are called dither matrices.
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Threshold Noise
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Dithering
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Ordered Dithering

• Trade off spatial resolution for intensity
  resolution.
• Use dither patterns.
• Can be represented as a matrix.

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Bayer Ordered Dither Patterns
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Other possibilities
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The dithering matrix (3x3)
For all Xpixels For all Ypixels v
approximate(x,y) i x mod 3 j
y mod 3 if v gt Mi,j then
Set_Pixel(x,y, BLACK) else
Set_Pixel(x,y, WHITE)
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Dithering
5
7
3
6
1
2
Dithering mask
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4
8
1
2
3
Image
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2
3
8
4
4
Binary image
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Original
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Dithering
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Dithering
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Error Diffusion
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Floyd-Steinberg Error Diffusion
With this method, the average quatization error
is reduced by propagating the error from each
pixel to some of its neighbors in the scan order.
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1D Error Diffusion
1
0
1
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1D Error Diffusion
1
0
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1D Error Diffusion
1
0
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1D Error Diffusion
1
0
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1D Error Diffusion
1
0
0
1
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1D Error Diffusion
1
0
0
1
1
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1D Error Diffusion
1
0
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1D Error Diffusion
1
0
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1D Error Diffusion
1
0
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Floyd-Steinberg Error Diffusion
With this method, the average quatization error
is reduced by propagating the error from each
pixel to some of its neighbors in the scan order.
Note that the error propagation weights must sum
to one
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Dither vs. Floyd-Steinberg
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Original Picture
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Dithering result
Error diffusion result
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Examples Continue
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Dithering
Dithering Note that each square ring is of
different brightness
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Error Diffusion
Error Diffusion Note that the error is
distributed across the layers
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Examples Continue
Original
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Dithering
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Error Diffusion
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Error Diffusion
Set AccErr to zero For each pixel in the image
scanning from left to right value
Pixel_value(x,y) AccErrx,y if (value gt
WHITE/2) Set_pixel(x,y, WHITE) Error value
- WHITE else Set_pixel(x,y,
BLACK) Error value - BLACK
if scanning from left to right
AccErrx1, y 3/8 Error AccErrx,
y1 3/8 Error AccErrx1,y1
2/8 Error
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Space Filling Curves

• order of scan

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Space Filling Curves
Hilbert curve (1-4)
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Space Filling Curves
Hilbert curve (1-4)
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Space Filling Curves
Hilbert curve (1-4)
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Space Filling Curves
Hilbert curve (1-4)
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Space Filling Curves
Peano curve
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Context Based SFC
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Original Image
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Threshholding
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Bayers Ordered Dithering
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Error Diffusion
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Median Cut (4 levels)
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Median Cut (8 levels)
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