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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
Data Embedding 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
Data Embedding 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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