Reversible Data Hiding
ECE643 Digital Image Processing (I) Course Project
Professor:Yun Q. Shi
Su Yu
12/02/2011
Contents
Introduction
 Applications
 Methods

◦ Histogram Pair
◦ Optimum Histogram Pair
Conclusion
 Simulation

Contents
Introduction
 Applications
 Methods

◦ Histogram Pair
◦ Optimum Histogram Pair
Conclusion
 Simulation

Introduction

What’s Data Hiding?
◦ A process to embed useful data (information)
into a cover media.
◦ Data invisibility is the major requirement.
Cover Media
Data
1
1 … … 1
0
+
Marked Media
=
Introduction

Distortion happens in embedding process:
Data
1
1 … … 1
0
+
=
Introduction

Distortion happens in embedding process:
Data
1
1 … … 1
0
+
=
First Requirement:
Minimize the distortion and maximize the data
payload

Introduction

What’s Reversible Data Hiding?
◦ A process to reverse the marked media back
to the original cover media after the hidden
data are extracted.
◦ Reversible or lossless ability is required.
Cover Media
Marked Media
Data
1
1 … … 1
0
+
Introduction

Errors in reverse process are not allowed:
Data
0
1 … … 1
1
+
Second Requirement:
No error in data and cover media

Contents
Introduction
 Applications
 Methods

◦ Histogram Pair
◦ Optimum Histogram Pair
Conclusion
 Simulation

Applications
Secure medical image data system
 Law enforcement
 E-government
 Image authentication
 Covert Communication

G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni;
Reversible Data Hiding Using Integer
Wavelet Transform and Companding
Technique
Contents
Introduction
 Applications
 Methods

◦ Histogram Pair
◦ Optimum Histogram Pair
Conclusion
 Simulation

Methods

Histogram Pair
◦ Based on Paper:
◦ Z. Ni, Y. Q. Shi, N. Ansari and W. Su, Reversible
Data Hiding

Optimum Histogram Pair
◦ Based on Papers:
◦ G. Xuan, C. Yang,Y. Zhen,Y. Q. Shi, and Z. Ni,
Reversible Data Hiding Using Integer Wavelet
Transform and Companding Technique
◦ G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and X.
Tong, Optimum Histogram Pair Based Image
Lossless Data Embedding
Contents
Introduction
 Applications
 Methods

◦ Histogram Pair
◦ Optimum Histogram Pair
Conclusion
 Simulation

Some Concepts

PSNR (Peak Signal-to-Noise Ratio)
◦ An engineering term for the ratio between
the maximum possible power of a signal and
the power of corrupting noise that affects the
fidelity of its representation
◦ The PSNR is most commonly used as a
measure of quality of reconstruction of lossy
compression (e.g., for image compression).
http://en.wikipedia.org/wiki/Peak_signal-tonoise_ratio
Some Concepts

PSNR (Peak Signal-to-Noise Ratio)
◦ Mathematical definition
◦ 𝑀𝑆𝐸 =
1
𝑚𝑛
◦ 𝑃𝑆𝑁𝑅 =
𝑚−1
𝑖=0
𝑛−1
𝑗=0 [𝐼
𝑀𝐴𝑋𝐼 2
10𝑙𝑜𝑔10
𝑀𝑆𝐸
𝑖, 𝑗 − 𝐾(𝑖, 𝑗)]2
, in dB
◦ I = cover image, K = marked image
◦ MAXI = maximum gray value 255

PSNR represent the distortion level
between marked image and cover image
http://en.wikipedia.org/wiki/Peak_signal-tonoise_ratio
Some Concepts

PSNR (Peak Signal-to-Noise Ratio)
◦ Typical values in lossy image and video
compression are between 30 and 50 dB,
where higher is better.
Original Image
PSNR=31.45dB
http://en.wikipedia.org/wiki/Peak_signal-tonoise_ratio
Some Concepts

Histogram Pair
◦ Histogram h(x) is the number of occurrence
as the variable X assumes value x, i.e. X is
number of pixels on one certain gray value in
an image.
◦ Only two consecutive integers a and b
assumed by X are considered, i.e. x ∈ a, b.
◦ Furthermore, let h(a) = m and h(b) = 0. We
call these two points as a histogram pair.
◦ And sometimes denote it by, h = [m, 0], or
simply [m, 0].
G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and
X. Tong, Optimum Histogram Pair Based
Image Lossless Data Embedding
Some Concepts

Histogram Pair
◦ Example: in a histogram of an image, a and b
are adjacent integers, h = [m, 0] is a histogram
pair.
Number of
Pixels
m
0
a
b
Gray Value
Histogram Pair

Advantages
◦
◦
◦
◦

Large data payload
5k-60k bits for 512*512*8 grayscale image
High visual quality
PSNR > 48 dB
Method
◦ Histogram Pair
Z. Ni, Y. Q. Shi, N. Ansari and W. Su,
Reversible Data Hiding
Embedding Algorithm
Use “Lena” image as an example
 Step 1:

◦ In the histogram find zero point (e.g. 255 no
pixel on the gray value of 255);
◦ Then find peak point (e.g. 155 maximum
number of pixels on the gray value of 155);
◦ The objective to find the peak point is to
increase the embedding capacity as large as
possible, which will be further explained.
Z. Ni, Y. Q. Shi, N. Ansari and W. Su,
Reversible Data Hiding
Embedding Algorithm

Step 1:
Embedding Algorithm

Step 2:
◦ The whole image is scanned;
◦ The gray value of pixel with gray value
between 156 and 254 is incremented by one;
◦ This step is equivalent to shifting the range of
histogram [156,254] one unit towards the
right hand side leaving the gray value 156
empty;
◦ Then a=155 and b=156 are adjacent integers,
h = [2785, 0] is a histogram pair.
Z. Ni, Y. Q. Shi, N. Ansari and W. Su,
Reversible Data Hiding
Embedding Algorithm

Step 2: h = [2785, 0] is a histogram pair
Embedding Algorithm

Step 3:
◦ The whole image is scanned once again;
◦ Once a pixel with gray value of 155 is
encountered, we check the data to be
embedded;
◦ If the to-be-embedded bit is “1”, the pixel
value is added by 1. Otherwise, the pixel value
is kept intact.
◦ The capacity of this algorithm equals to the
maximum number of pixels (2785 bits)
Z. Ni, Y. Q. Shi, N. Ansari and W. Su,
Reversible Data Hiding
Embedding Algorithm

Step 3: Embedded data
Embedding Algorithm
Step 3: Embedded data
 PSNR = 53.8 dB

Retrieval algorithm

Step 1:
◦ The whole marked image is scanned;
◦ The order must be same as embedding;
◦ Once the gray value of the maximum point is
met, if the value is intact, e.g., 155, the “0” is
retrieved;
◦ If the value is altered, e.g., 156, the “1” is
retrieved;
◦ In this way, the data embedded can be
retrieved.
Z. Ni, Y. Q. Shi, N. Ansari and W. Su,
Reversible Data Hiding
Retrieval algorithm

Step 2:
◦ The whole image is scanned once again;
◦ Once the pixels whose gray value is between
the peak point (e.g. 155) and the zero point
(e.g. 255) is met (e.g. interval [156,255]), the
gray value of those pixels will be subtracted
by 1;
◦ In this way, the original image can be
recovered without any distortion.
Z. Ni, Y. Q. Shi, N. Ansari and W. Su,
Reversible Data Hiding
Retrieval algorithm

Result: Data error rate=0, Image error rate=0
Z. Ni, Y. Q. Shi, N. Ansari and W. Su,
Reversible Data Hiding
PSNR
PSNR of all marked images is above 48 dB;
 Because the pixels whose gray value is between
the zero point and the peak point will add by 1
or minus by 1;
 In the worst case, all pixels of the image will add
or minus by 1. That means MSE=1;

1
𝑀𝑆𝐸 =
𝑚𝑛

𝑚−1 𝑛−1
[𝐼 𝑖, 𝑗 − 𝐾(𝑖, 𝑗)]2
𝑖=0 𝑗=0
Hence the
PSNR=10xLog10(255x255/MSE)=48.13 dB.
Z. Ni, Y. Q. Shi, N. Ansari and W. Su,
Reversible Data Hiding
Contents
Introduction
 Applications
 Methods

◦ Histogram Pair
◦ Optimum Histogram Pair
Conclusion
 Simulation

Some Concepts

Companding
◦ The process of signal compression and
expansion.

Compression and Expansion
◦ Compression: mapping large range of original
signals x, into narrower range, y=C(x).
◦ Expansion: reverse process of compression,
x=E(y).
◦ After expansion, the expanded signals are
close to the original ones.
G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni,
Reversible Data Hiding Using Integer
Wavelet Transform and Companding
Technique
Some Concepts

Companding
◦
◦
◦
◦
Assume the original signals are x,
If the compression function is y=C(x);
If the expansion function is x=E(y);
If the equation E[C(x)]=x is satisfied, then this
kind of companding could be applied into
reversible data hiding.
G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni,
Reversible Data Hiding Using Integer
Wavelet Transform and Companding
Technique
Some Concepts

Companding in Reversible Data Hiding
◦ Let y=C(x), y=P1P2P3…Pn, Pi ∈ {0,1};
◦ Let b ∈ {0,1}, y’=P1P2P3…Pnb, then
y’=P(y)=2y+b, b is the hiding data;
◦ If y’≈x, modification of signal will hardly be
perceived;
◦ By hiding data extraction, extract LSB of y’, i.e.
b=LSB(y’), recover signal y=(y’-b)/2;
◦ Recover original signal x by expansion x=E(y)
G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni,
Reversible Data Hiding Using Integer
Wavelet Transform and Companding
Technique
Some Concepts

Companding in Reversible Data Hiding
◦ So, two conditions must be satisfied:
 y=C(x), x=E[y], => E[C(x)]=x;
 Condition (1): E[C(x)]=x;
 y’=P(y)=2y+b≈x, => P[C(x)]≈x;
 Condition (2): P[C(x)]≈x
G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni,
Reversible Data Hiding Using Integer
Wavelet Transform and Companding
Technique
Some Concepts

For Condition (1), E[C(x)]=x
◦ Any one-to-one mapping function can be
used;
◦ For multiple x mapped to single y, still could
𝑓
be used, E.g. 𝑥0, 𝑥1 𝑦, use bit “0” to indicate
𝑥0 , and bit “1” to indicate 𝑥1 , these overhead
data also need to embedded into original
signal.

So, condition (1) is easy to satisfied.
G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni,
Reversible Data Hiding Using Integer
Wavelet Transform and Companding
Technique
Some Concepts

For Condition (2), P[C(x)]≈x
◦ On study of Human Visual System (HVS)
points out that slight modification on wavelet
high frequency sub band coefficients is hard to
be perceived by human eyes.
◦ The method to compand image is to slightly
change wavelet high frequency sub band
coefficients for hiding data.

So condition (2) could be satisfied.
G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni,
Reversible Data Hiding Using Integer
Wavelet Transform and Companding
Technique
Some Concepts
Sub bands (embedding region) for data
hiding in coefficients are three high
frequency sub bands HH, HL and LH.
 Question is: How to select the most
suitable embedding region?

G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and X.
Tong, Optimum Histogram Pair Based Image
Lossless Data Embedding
Some Concepts

Wavelet Transform
◦ Likes Fourier Transform, is used to analysis image
in frequency domain.
◦ Fourier Transform is based on sinusoid functions;
◦ Wavelet Transform is based on small waves
(wavelets) which are varying in frequency and
limited duration.

Integer Wavelet Transform (IWT) maps
integer to integer and can reconstruct the
original signal with out distortion.
R. C. Gonzalez and R. E. Woods, < Digital Image Processing >, Prentice Hall, 3rd (2007) edition
S.G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni, Reversible Data Hiding Using Integer Wavelet Transform and
Companding Technique
Some Concepts

IWT high frequency sub band coefficients
has two features:
◦ Most coefficients are small in magnitude, so it is
convenient to select compression function C(x),
could use linear functions to satisfy Condition (2),
P[C(x)]≈x;
◦ For coefficients are large in magnitude, linear
functions are difficult to satisfy Condition (2),
P[C(x)]≈x;
◦ A pre-defined threshold T is introduced to treat
these two kinds of coefficients differently.
G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni, Reversible Data Hiding Using Integer Wavelet Transform
and Companding Technique
Some Concepts

Threshold T
◦ For 𝑥 < 𝑇, use one to one mapping function;
◦ For 𝑥 ≥ 𝑇, x, x+1, or x-1… are compressed to
same y and the recording data need to be
embedded into wavelet coefficients as index for
distinguish different values mapped to the same y;
◦ If T is small, a good visual quality of marked image
is achieved;
◦ If T is large, a larger payload can be achieved.

Question is: How to choose the best
threshold T?
G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni,
Reversible Data Hiding Using Integer
Wavelet Transform and Companding
Technique
Some Concepts

Histogram Modification
◦ After data embedded in coefficients, some pixel’s gray
value may overflow (>255) or underflow (<0);
◦ Histogram modification is needed to narrow the
histogram from both sides by GR and GL;
◦ Modification G=GR+GL.
G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and X. Tong, Optimum Histogram Pair Based Image Lossless Data
Embedding
Some Concepts

Histogram Modification
◦ This modification is needed to be recorded
and embedded as part of the overhead for
recovery the original cover image.

Question is: How to make adaptive
histogram modification?
G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni,
Reversible Data Hiding Using Integer
Wavelet Transform and Companding
Technique
Optimum Histogram Pair

Advantages
◦ Selection of most suitable embedding region
◦ Selection of best threshold T, leads highest
PSNR for a given payload
◦ Minimum amount of histogram modification

Method
◦ Optimum Histogram Pair
◦ Using Integer wavelet transformation
◦ Using adaptive histogram modification
G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and
X. Tong, Optimum Histogram Pair Based
Image Lossless Data Embedding
Optimum Histogram Pair

Selection of Optimum Parameters
◦
◦
◦
◦
◦
Suitable embedding region R
Best Threshold T
Adaptive histogram modification value G
𝑅, 𝑇, 𝐺 = 𝑎𝑟𝑔𝑅,𝑇,𝐺 max(𝑃𝑆𝑁𝑅)
The selection of three arguments is based on
generate maximum PSNR.
G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and
X. Tong, Optimum Histogram Pair Based
Image Lossless Data Embedding
Optimum Histogram Pair

Selection of Suitable embedding region R
◦ In order to improve PSNR,
◦ When the payload is small, R=HH, only embed
data into HH sub band;
◦ When the payload is large, R=HH,HL,LH all
three high frequency sub bands are used.
G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and
X. Tong, Optimum Histogram Pair Based
Image Lossless Data Embedding
Optimum Histogram Pair

Selection of Best Threshold T
◦ By experiment, for certain embedding capacity 0.02
bpp and three different cover image, the best
threshold T does exist.
Optimum Histogram Pair

Selection of Adaptive histogram modification
value G
◦ After data embedding into each coefficient,
underflow and overflow are checked;
◦ By experiment, only when the payload is larger
than certain level, it needs histogram modification
(G>0), otherwise, there is no need for histogram
modification.
“Lena”, if payload > 1.0873 bpp (285027 bits)
“Barbara”, if payload > 0.5734 bpp (150320 bits)
“Baboon”, if payload > 0.0080 bpp (2089 bits)
G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and
X. Tong, Optimum Histogram Pair Based
Image Lossless Data Embedding
Embedding Algorithm

Use as an example:
◦ Assume the to-be-embedded bit sequence
D=[110001];
◦ The image 5*5, has 12 gray values
◦ 𝑥 ∈ [−5, −4, −3, −2, −1,0,1,2,3,4,5,6]
0
4
0
-4
1
0
2
-2
3
-1
4
-3
0
2
-3
-1
-2
0
-1
0
-2
1
2
-1
1
G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and
X. Tong, Optimum Histogram Pair Based
Image Lossless Data Embedding
Embedding Algorithm

Use as an example:
◦ Histogram is ℎ0 = [0,1,2,3,4,6,3,3,1,2,0,0]
-5
-4
-3
-2
-1
0
1
2
3
4
5
G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and
X. Tong, Optimum Histogram Pair Based
Image Lossless Data Embedding
6
Embedding Algorithm

Step1: expand image histogram
◦ From right side, h[4]=0, h[4] to h[5]
-5
-4
-3
-2
-1
0
1
2
3
4
5
G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and
X. Tong, Optimum Histogram Pair Based
Image Lossless Data Embedding
6
Embedding Algorithm

Step1: expand image histogram
◦ From right side, h[5]=0, h[5] to h[6]
-5
-4
-3
-2
-1
0
1
2
3
4
5
G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and
X. Tong, Optimum Histogram Pair Based
Image Lossless Data Embedding
6
Embedding Algorithm

Step1: expand image histogram
◦ From left side, h[-4]=0, h[-4] to h[-5]
-5
-4
-3
-2
-1
0
1
2
3
4
5
G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and
X. Tong, Optimum Histogram Pair Based
Image Lossless Data Embedding
6
Embedding Algorithm

Step1: expand image histogram
◦ From center h[3]=0, h[3] to h[4]
-5
-4
-3
-2
-1
0
1
2
3
4
5
G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and
X. Tong, Optimum Histogram Pair Based
Image Lossless Data Embedding
6
Embedding Algorithm

Step1: expand image histogram
◦ Histogram is ℎ2 = 1, 𝟎, 𝟐, 3,4,6,3, 𝟑, 𝟎, 𝟏, 𝟎, 2
◦ Three histogram pairs: from right to left to center
◦ right [1,0], left [0,2], center [3,0]
-5
-4
-3
-2
-1
0
1
2
3
4
5
G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and
X. Tong, Optimum Histogram Pair Based
Image Lossless Data Embedding
6
Embedding Algorithm

Step2: Embedding Data
◦ from right to left to center D=[110001];
◦ right [1,0], capacity=1, embedded 1 using histogram
pair method
-5
-4
-3
-2
-1
0
1
2
3
4
5
G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and
X. Tong, Optimum Histogram Pair Based
Image Lossless Data Embedding
6
Embedding Algorithm

Step2: Embedding Data
◦ from right to left to center D=[110001];
◦ left [0,2], capacity=2, embedded 10 using histogram
pair method
-5
-4
-3
-2
-1
0
1
2
3
4
5
G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and
X. Tong, Optimum Histogram Pair Based
Image Lossless Data Embedding
6
Embedding Algorithm

Step2: Embedding Data
◦ from right to left to center D=[110001];
◦ Center [3,0], capacity=3, embedded 001 using
histogram pair method
-5
-4
-3
-2
-1
0
1
2
3
4
5
G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and
X. Tong, Optimum Histogram Pair Based
Image Lossless Data Embedding
6
Embedding Algorithm

Step2: Embedding Data
◦ Histogram is ℎ3 = 1,1,1,3,4,6,3,2,1,0,1,2
-5
-4
-3
-2
-1
0
1
2
3
4
5
G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and
X. Tong, Optimum Histogram Pair Based
Image Lossless Data Embedding
6
Embedding Algorithm

For application in “Lena” image, for
certain payload, PSNR is good.
Retrieval Algorithm

Retrieval Algorithm is inverse to the
embedding process;
To retrieval data, the order is still from right to
left to center, to check number of pixels on gray
value (4,5), (-3,-4), (2,3) because those pairs are
embedded data;
 Using the expansion function to get original
cover image.

G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and
X. Tong, Optimum Histogram Pair Based
Image Lossless Data Embedding
Contents
Introduction
 Applications
 Methods

◦ Histogram Pair
◦ Optimum Histogram Pair
Conclusion
 Simulation

Conclusion

Comparison between two methods:
Histogram
Pair
Payload
Small
Optimum
Histogram
Pair
Large
PSNR
Low
High
Complexity
Low
High
Contents
Introduction
 Applications
 Methods

◦ Histogram Pair
◦ Optimum Histogram Pair
Conclusion
 Simulation

Simulation
For Histogram Pair method, to hiding data
sentence:
 “ECE 643 Digital Image Processing
Course Project by Su Yu”
 In “Lena” image.

References




Z. Ni, Y. Q. Shi, N. Ansari and W. Su,
Reversible Data Hiding
G. Xuan, C.Yang,Y. Zhen, Y. Q. Shi, and Z. Ni,
Reversible Data Hiding Using Integer
Wavelet Transform and Companding
Technique
G. Xuan,Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and X.
Tong, Optimum Histogram Pair Based Image
Lossless Data Embedding
1. R. C. Gonzalez and R. E. Woods, <
Digital Image Processing >, Prentice Hall,
3rd (2007) edition
Thank you!
Questions?