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

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

Trainingdata

Selecttemplate

Design LUTInversehalftone

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

E16

7

E16

3 E

16

5 E

16

1

Floyd-Steinberg


Dot diffusion Process the pixel according to the table


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


Dot diffusion example


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.


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.


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


Optimized dot diffusion Optimized class matrix


Pros and Cons Ordered dithering

Advantage:

Parallel method, only comparisons Disadvantage:

Resulting halftones suffer from periodicity


Pros and Cons Error diffusion

Advantage:

Do not suffer from periodic patterns Disadvantage:

Waste Time


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


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


Algorithm Predict the continuous tone value of a pixel from its

surrounding neighborhoods

(“19pels” TEMPLATE)(“Rect” TEMPLATE)

Take N pixels (including the pixel being estimated) in the neighborhood P0,P1,……,PN-1

There are 2N different pattern



Target function T should return a value for each pattern:

: the number of occurrences of pattern

Corresponding continuous tone values:


LUT value for the pattern will be the weight mean of the corresponding continuous tone values:


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


Solutions of nonexistent pattern problem 1. Low pass filtering: the missing pattern is obtained

as a linear combination of the binary pixels Pi


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.


Solutions of nonexistent pattern problem 3. Best linear estimator:


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,


The PSNR values of these three solutions: Low pass filtering: 29.79dB Hamming distance: 28.91dB Best linear estimator: 29.92 dB


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:


The PSNR values of these templates:

(“19pels” TEMPLATE)(“Rect” TEMPLATE)(“x opt” TEMPLATE)


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


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


Result comparison (high frequency):

(LUT inverse halftone)(fast inverse halftone)


Result comparison (low frequency):

(LUT inverse halftone)(fast 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 …

(“x opt” TEMPLATE)

(pixel 0)

(pixel 1)

(pixel 2)

………

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

Documents

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

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