Transcript Binarization of gray

Binarization of gray-scale
hologram
Fan Jiang
Fall 2006
Introduction
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Optics Diffraction theory and hologram
Motivation
Approach
Simple threshold
Random binarization
High-frequency binarizaion
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Result comparison
(The whole project is done on Mathematica)
Optics diffraction theory and
hologram
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Optics diffraction theory-Fraunhofer diffractionFourier Transform
Hologram-can be used to reconstruct the target
object.
Target
object
binarization
hologram
hologram
Gray-scale
binary
Gray-scale
Reconstruction
image
Motivation
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Computer-generated holograms are widely
used today.
However, during the lithography, we can only
write binary holograms on the mask.
Binarize the gray-scale hologram is important!
Approach 1
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Want to change a gray scale to binary?
Threshold!
Threshold = Median [hologram data]
Histogram of the gray-scale hologram
Binary hologram
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Approach 2
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Random Binarization
Create n (n< total pixel number) pseudorandom number as the
address of data, and use the median number for these data as
the threshold, then binary these part of numbers.
Repeat this process until all the numbers become 0 or 1.
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Process
No
Gray-scale
hologram
Binarize n
random pixels
All the
pixels are
binarized?
Yes
Binary
hologram
Approach 2
Binarization Result:
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The change of histogram:
Binary hologram:
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0.2
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0.5
10.5
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1
0.6
1.5
2 0.8 1 0.82
11.25
3 1.2
1
2.5
1.43
1.2
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0.25
0.2
0.5 0.4
0.4
1 0.6
0.75
1.5
0.6
20.8
2.51.5
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Approach 3
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High-frequency binarization
In this method, threshold is still needed. Median [hologram data]
is chosen as the threshold.
But after using threshold, pick up the max. intensity under the
threshold, and set it to 1. Similarly, pick up the min. intensity
above the threshold, set it to 0.
So, all the peaks are set to be 1, all the valleys are set to be 0,
independent on the threshold.
----- almost all the high frequency information has been saved.
Approach 3
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Example in 1-D:
Binary hologram:
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0
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Results
Now compare the reconstructions of the three binary
holograms.
Gray-scale
Method 1
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Method 2
Method 3
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Results
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We can also compare the mean-square error of the
results.
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Gray-scale: 0.01
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Method 1: 1.021
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Method 2: 1.019
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Method 3: 0.81
Conclusion
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As the result shown above. In my case, highfrequency binarization method is the best
one among the three of them.
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But all of them are much worse than the
result of gray-scale.
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Better binarization method is still needed! –
Future work.