LUT Method For Inverse Halftone
資工四 林丞蔚 林耿賢
Outline
Introduction
 Methods for Halftoning
 LUT Inverse Halftone
 Tree Structured LUT
 Conclusion

Introduction
halftoning
Inverse halftoning
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
Training
data
Select
template
Design LUT
Inverse
halftone
Methods for halftoning
Ordered dithering
 Error diffusion
 Dot diffusion

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

7
 E
16
1
3
5
 E  E  E
16
16
16
Floyd-Steinberg
Methods for halftoning (cont.)

Dot diffusion

Process the pixel according to the table
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 1
O 2
2 1
Methods for halftoning (cont.)

Dot diffusion

example
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.

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.
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

Methods for halftoning (cont.)

Optimized dot diffusion

Optimized class matrix
Methods for halftoning (cont.)

Pros and Cons

Ordered dithering


Advantage:
Parallel method, only comparisons
Disadvantage:
Resulting halftones suffer from periodicity
Methods for halftoning (cont.)

Pros and Cons

Error diffusion
 Advantage:

Do not suffer from periodic patterns
Disadvantage:
Waste Time
Methods for halftoning (cont.)

Pros and Cons

Dot diffusion
 Advantage:
Parallel method
 Disadvantage:
Periodic structures in the halftones
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
LUT Inverse Halftone (cont.)

LUT method can be applied to any
halftoning method

Image quality achieved is comparable to
best methods
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
LUT Inverse Halftone (cont.)

Algorithm

Predict the continuous tone value of a pixel from its
surrounding neighborhoods
(“Rect” TEMPLATE)
(“19pels” TEMPLATE)
LUT Inverse Halftone (cont.)

Take N pixels (including the pixel being estimated)
in the neighborhood


P0,P1,……,PN-1
There are 2N different pattern
LUT Inverse Halftone (cont.)



Target function T should return a value for each
pattern:
: the number of occurrences of pattern
Corresponding continuous tone values:
LUT Inverse Halftone (cont.)

LUT value for the pattern will be the weight mean
of the corresponding continuous tone values:
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
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
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.
LUT Inverse Halftone (cont.)

Solutions of nonexistent pattern problem

3. Best linear estimator:
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,
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

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:
LUT Inverse Halftone (cont.)

Template selection algorithm:
LUT Inverse Halftone (cont.)

The PSNR values of these templates:
(“x opt” TEMPLATE)
(“Rect” TEMPLATE)
(“19pels” TEMPLATE)
LUT Inverse Halftone (cont.)

The PSNR values of these templates:
16 pixel
19 pixel
template
16pel Rect
Avg.
PSNR
26.43 26.50 26.43 26.61 26.76
16opt 19pel 19opt
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
LUT Inverse Halftone (cont.)

Result comparison (high frequency):
(fast inverse halftone)
(LUT inverse halftone)
LUT Inverse Halftone (cont.)

Result comparison (low frequency):
(fast inverse halftone)
(LUT inverse halftone)
Tree Structured LUT
Reduce storage requirements of LUT
 Can be thought as ‘comparison’ of LUT

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).

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
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)
Tree Structured LUT

Compute the new contone value:

Average the actual value form current tree.
2a
(-3, 0)
(2, -1)
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
…

(pixel 0)
(pixel 1)
(pixel 2)
(“x opt” TEMPLATE)
………
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
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