lut method for inverse halftone 資工四 林丞蔚 林耿賢. outline introduction methods for...
TRANSCRIPT
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LUT Method For Inverse Halftone
資工四 林丞蔚 林耿賢
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Outline
Introduction Methods for Halftoning LUT Inverse Halftone Tree Structured LUT Conclusion
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Introduction
halftoning Inverse halftoning
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Introduction (cont.)
Traditional inverse halftoning method The contone value of a pixel is a linear
combination of the surrounding halftone pixels
LUT inverse halftoning method
Trainingdata
Selecttemplate
Design LUTInversehalftone
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Methods for halftoning
Ordered dithering Error diffusion Dot diffusion
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Methods for halftoning (cont.)
Ordered dithering Pairwise comparison between gray level image
and repeated dither matrix
Error diffusion Separate the quantization
error over neighboring pixels
E16
7
E16
3 E
16
5 E
16
1
Floyd-Steinberg
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Methods for halftoning (cont.)
Dot diffusion Process the pixel according to the table
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Methods for halftoning (cont.)
Dot diffusion Just like error diffusion But separate error to only 3 * 3 neighbors
Orthogonal: origin + 2 * e (i, j) / w Diagonal: origin + e (i, j) / w
1 2 1
2 O 2
1 2 1
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Methods for halftoning (cont.)
Dot diffusion example
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Methods for halftoning (cont.)
Optimized dot diffusion Baron: a pixel has only low-class neighbor Near baron: a pixel has one high-class neighbor Traditional dot diffusion try to minimum the
number of baron and near-baron.
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Methods for halftoning (cont.)
Optimized dot diffusion But the result is still not good enough. Take human visual system into account. Target function:
The average number of dark pixel should be equal to the original gray level.
The dark pixel are spatially distributed with the same average frequency.
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Methods for halftoning (cont.)
Pairwise exchange algorithm Randomly order the class matrix List all possible exchange If exchange reduce the value of target function
exchange it and restart Repeat above steps a fixed time
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Methods for halftoning (cont.)
Optimized dot diffusion Optimized class matrix
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Methods for halftoning (cont.)
Pros and Cons Ordered dithering
Advantage:
Parallel method, only comparisons Disadvantage:
Resulting halftones suffer from periodicity
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Methods for halftoning (cont.)
Pros and Cons Error diffusion
Advantage:
Do not suffer from periodic patterns Disadvantage:
Waste Time
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Methods for halftoning (cont.)
Pros and Cons Dot diffusion
Advantage:
Parallel method Disadvantage:
Periodic structures in the halftones
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LUT Inverse Halftone
A novel method for inverse halftone
LUT method is extremely fast and do not need any computation
LUT is obtained from histogram gather from a few sample images
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LUT Inverse Halftone (cont.)
LUT method can be applied to any halftoning method
Image quality achieved is comparable to best methods
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LUT Inverse Halftone (cont.)
Training set Use some images with its halftoning and
original image for the base to build the LUT
A good training set should have enough images representing both smooth and nonsmooth images
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LUT Inverse Halftone (cont.)
Algorithm Predict the continuous tone value of a pixel from its
surrounding neighborhoods
(“19pels” TEMPLATE)(“Rect” TEMPLATE)
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Take N pixels (including the pixel being estimated) in the neighborhood P0,P1,……,PN-1
There are 2N different pattern
LUT Inverse Halftone (cont.)
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LUT Inverse Halftone (cont.)
Target function T should return a value for each pattern:
: the number of occurrences of pattern
Corresponding continuous tone values:
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LUT Inverse Halftone (cont.)
LUT value for the pattern will be the weight mean of the corresponding continuous tone values:
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LUT Inverse Halftone (cont.)
Problems of nonexistent pattern Some rows of LUT may not be used
Memory waste
Some patterns may not exists in the training set Has no corresponding continuous tone value
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LUT Inverse Halftone (cont.)
Solutions of nonexistent pattern problem 1. Low pass filtering: the missing pattern is obtained
as a linear combination of the binary pixels Pi
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LUT Inverse Halftone (cont.)
Solutions of nonexistent pattern problem 2. Hamming distance:
Examples:The Hamming distance between 1011101 and 1001001 is 2.
The Hamming distance between 2143896 and 2233796 is 3.
The Hamming distance between "toned" and "roses" is 3.
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LUT Inverse Halftone (cont.)
Solutions of nonexistent pattern problem 3. Best linear estimator:
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LUT Inverse Halftone (cont.)
Solutions of nonexistent pattern problem 3. Best linear estimator:
For each nonexistent pattern (p0,p1……pN-1), we obtain the continuous tone value, T(p0,……,pN-1), as follows: Define y = [p0,p1……,pN-1]x. Then,
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LUT Inverse Halftone (cont.)
The PSNR values of these three solutions: Low pass filtering: 29.79dB Hamming distance: 28.91dB Best linear estimator: 29.92 dB
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LUT Inverse Halftone (cont.)
Template selection Assume we have P images, both continuous tone
images Dl(n1,n2) and halftone images Hl(n1,n2) for
l = 1,2,3,……,P.
Define the mean square error between two image sets:
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LUT Inverse Halftone (cont.) Template selection algorithm:
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LUT Inverse Halftone (cont.)
The PSNR values of these templates:
(“19pels” TEMPLATE)(“Rect” TEMPLATE)(“x opt” TEMPLATE)
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LUT Inverse Halftone (cont.)
The PSNR values of these templates:
16 pixel 19 pixel
template 16pel Rect 16opt 19pel 19opt
Avg. PSNR
26.43 26.50 26.43 26.61 26.76
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LUT Inverse Halftone (cont.)
The PSNR values of LUT and tradition IH:
Image LUT with Rect fastiht2
Lena 30.41dB 31.37dB
mandrill 24.42dB 22.59dB
Halftone by error diffusion
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LUT Inverse Halftone (cont.)
Result comparison (high frequency):
(LUT inverse halftone)(fast inverse halftone)
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LUT Inverse Halftone (cont.)
Result comparison (low frequency):
(LUT inverse halftone)(fast inverse halftone)
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Tree Structured LUT
Reduce storage requirements of LUT Can be thought as ‘comparison’ of LUT
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Tree Structured LUT
Roots contain their patterns (i ,j) stand for the template position of the
additional pixel. Halftone value = 0(1), go to left (right).
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Tree Structured LUT
1. Denote the size of template a. 2. Define 2a binary tree corresponding to
different patterns.
2a
Contone value.If it’s root, included its pattern
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Tree Structured LUT
3. for each leaf t, find a pixel p that MSE is minimum.
4. split leaf t, and add p to the tree
2a
(-3, 0)
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Tree Structured LUT
Compute the new contone value: Average the actual value form current tree.
2a
(-3, 0)
(2, -1)
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Tree Structured LUT
Improve method for tree structured LUT: Directly build from LUT Built only one binary tree Start from pixel 0 as the root …
(“x opt” TEMPLATE)
(pixel 0)
(pixel 1)
(pixel 2)
………
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Conclusion
LUT based method can be improved by Better halftone method The way predict the contone value in LUT More efficiency tree structure
Tree structured LUT inverse halftone could be applied to color halftone of RGB
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Conclusion (cont.)
LUT inverse halftone is extremely fast
Image quality achieved the best methods known for inverse haltoning
Requires much less storage than LUT halftoning