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Optimum histogram pair based

image lossless data embeddingBy G. Xuan, Y. Q. Shi, etc.

Summarized By: Zhi Yong Li

Date: 11/22/2008


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Outline

Previous work

Overview

Theorem Algorithm

Experiment results

Conclusion

Comments

Acknowledgement


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Previous work

Prior this paper, people such as

Xuan and Dr. Shi has utilized the

thresholding method, IWT, histogram

modification for the data embedding

Into the images, but never reached

optimized measures talked about in

This paper.

Same process as in the left side,after IWT, in most case, histogram

will be modified, data was added in

HH, HL, LH region with a not

optimized threshold.


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Overview

The lossless data hiding scheme proposed

in this paper is based on optimum

histogram pairs. It is characterized byselection of optimum threshold T, most

suitable embedding region R, and

minimum possible amount of histogram

modification G, in order to achieve highestPSNR of the marked image for a given

data embedding capacity


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Theorem

Principle of Histogram Pair What is the histogram pair

In order to illustrate the concept of histogram

pair, we first consider a very simple case, Thatis, only two consecutive integers aand b

assumed byXare considered, i.e.xa, b.

Furthermore, let h(a) = mand h(b) = 0. We call

these two points as a histogram pair, andsometimes denote it by, h= [m,0], or simply [m,

0]. we assume m= 4. That is,Xactually

assumes integer value afour times, i.e.,X= [a,

a,a,a].


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Theorem

Principle of Histogram Pair

More restrictive definition

If for two consecutive non-negative integervalues a and b thatX

can assume, we have h(a) = mand h(b) = n,

where mand n are

the numbers of occurrence forx= aandx=

b, respectively. when a is positive integer, n =

0, we call h= [m, n] as a histogram pair. Ifa

is a negative integer, then h= [m, n] is a

histogram-pair as m= 0 and n not equal 0.


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Theorem

Principle of Histogram Pair Data embedding

Suppose the to-be embedded binary sequence is D= [1,0,0,1],

when a>0, h(4, 0) andX= [a,a,a,a] data embedding is:

X=D+X=[a+1, a, a, a+1],X= [b,a,a, b], and the new histogram

is h= [2,2]when a


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Theorem

Integer Wavelets and Histogram

Adjustment

Integer Wavelet Transform (IWT)In this proposed method, data is hidden into

IWT coefficients of high-frequency subbands.

The motivation of doing so is as follows.

1. Data embedding into high frequency subbands can leadto better imperceptibility of marked image.

2. High data embedding capacity.

3. Higher PSNR owing to the de-correlation property

among the wavelet subbands in the same

decomposition level than embedding into other


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Theorem

Integer Wavelets and HistogramAdjustment Histogram Modification

1. Why?

To avoid underflowand/oroverflowafter data embedding intosome IWT coefficients.

2. How?

Instead of doing the histogram adjustment at the beginning nomatter if necessary, do it in necessary. It is observed that it maynot need to do histogram modification for some images with some

payloads. When the embedding capacity increases, we may needhistogram modification.


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Algorithm

Optimum Thresholding Method Based

on Histogram Pairs

It is found that for a given data embeddingcapacity there does exist an optimum value for

T. Therefore the best threshold Tfor a given

data embedding capacity is searched with

computer program automatically and selected

to achieve the highest PSNR for the marked

image.


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Algorithm

Optimum Thresholding Method Based on

Histogram Pairs Optimum thresholding method

Divide the histogram into 3 parts:(1) the1stpart where data is to be embedded;

(2) the central part - no data embedded and the absolute value of

coefficients is smaller than that in the 1stpart;

(3) the end part - no data embedded and the absolute value of

coefficients is larger than that in the 1stpart. The whole embedding

and extraction procedure can be expressed by the formulae in

following table.


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Algorithm Optimum Thresholding Method Based on Histogram Pairs

Optimum thresholding method

Tis the selected threshold, i.e., start position for data embedding, Sis stop position,xis feature (wavelet coefficient) values beforeembedding,xis feature value after embedding, u(S) is unit step function(when S 0,u(S) = 1,when S < 0,u(S) = 0), xroundsxto the largestinteger not larger thanx.


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Algorithm Optimum

ThresholdingMethod Based onHistogram Pairs Selection ofOptimum

Parameters

For a given required dataembedding capacity, theproposed method selects theoptimum parameter toachieve the highest possiblePSNR.

[T,G,R] = argT,G,Rmax(PSNR)

1. Best threshold T

Threshold varies accordingto images. See left sideFigure.


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Algorithm

Data Embedding Algorithm

The high frequency subbands (HH,HL,LH) coefficients ofIWT are used for data embedding in this proposed method.

Assume the number of bits to be embedded is L.

4 steps as follows.

(1)For a given data embedding capacity, apply our

algorithm to the given image to search for an optimum

threshold T. And set the P T, where Tis a starting

value for data embedding.


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Algorithm


(2) In the histogram of high frequency wavelet coefficients, move all the portion of

histogram with the coefficient values greater than Pto the right-hand side by

one unit to make the histogram at P+1 equal to zero (call P+1 as a zero-point).Then embed data in this point.

(3) If some of the to-be-embedded bits have not been embedded yet, let P (P),

and move all the histogram (less than P) to the left-hand side by 1 unit to

leave a zero-point at the value (P 1). And embed data in this point.

(4) If all the data have been embedded, then stop embedding and record the P

value as the stop value, S. Otherwise, P (P 1), go back to (2) to continue

to embed the remaining to-be-embedded data, where Sis a stop value. If the

sum of histogram forx [T,T] is equal L, the Swill be zero.


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Algorithm

Data Extraction Algorithm

The data extraction is the reverse of data embedding.


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Algorithm



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Algorithm

ExampleT= 3, S= 2,x [5,4,3,2,1,0,1,2,3,4,5,6]. h0 = [0,1,2,3,4,6,3,3,1,

2,0,0], h1 = [1,0,2,3,4,6,3,3,0,1,0.2], D= [110001], after embedded, h2 =

[1,1,1,2,4,6,3,2,1,0,1,2]

D=[1 10 001],marked in solid (orange) line squares shows how the last 3 bits are embedded.


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Algorithm

Example (continue)

(a) original one, (b) after 3 expanding, (c) after6-bit

embedding (what marked is how the last 3 bits are embedded)


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Experiment results

Experimental Results and

Performance Comparison

(a) Comparison on Barbara (b) Comparison on Baboon


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Experiment results

Experimental Results andPerformance Comparison

same image with different methods, Proposed method show

the better PSNR results.

(a) Performance comparison on Lena (b)

Comparison of multiple-time data

embedding into Lena image among [2],[8] and the

proposed method


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Experiment results

Experimental Results andPerformance Comparison

GL and GR adjusted according to bpp. Proposed method

shows the better result.

(a) Original and marked Lena image with three different

payloads by the proposed method (b) Performance on

Lena image reported in Coltuc, D.: Improved capacityreversible watermarking


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Experiment results

Comparison by Using Integer (5,3)and Haar Wavelets

Integer(5.3) wavelet shows the better result.


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Conclusion

Superior performance in terms of the visual

quality of marked image measured by PSNR

versus data embedding capacity over, to

authors best knowledge, all of the prior arts.

The proposed method uses integer (5,3) and

Haar wavelet transforms in our experiments

show that integer (5,3) wavelet is better than that

by using integer Haar wavelet transform.


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Conclusion

The new method has more flexibility and

simplicity in the implementation because of

using adaptive histogram modification

and selecting suitable region . Thecomputational complexity, is shown affordable

for possible real applications.

Specifically, for data embedding ranging from 0.01 bpp to 1.0 bpp into Lena,

Barbara and Baboon, the execution time varies from 0.25 sec. to 2.68 sec. Ifthe data embedding rate is not high, the amount of histogram

modification G = 0, meaning that the histogram shrinkage is not needed,

which is more simple to be implemented.


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Acknowledgement

The Summary also referred to the

following Cox et al., Secure spread spectrum watermarking for

multimedia, IEEE Transactions on Image Processing, 6(12):

1673-1687, 1997.

Fundamentals ofWatermarkingandData Hidingby Perrie

Moulin

http://en.wikipedia.org

Integer transform by WenWen -- Chih HongChih Hong

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