Introduction Whats Data Hiding? A process to embed useful data
(information) into a cover media. Data invisibility is the major
requirement. 1110 Data += Cover Media Marked Media
Slide 5
Introduction Distortion happens in embedding process: So Bad
Unacceptable = 1110 Data +
Slide 6
Introduction Distortion happens in embedding process: First
Requirement: Minimize the distortion and maximize the data payload
OK Acceptable 1110 Data +=
Slide 7
Introduction Whats 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.
1110 Data + Cover Media Marked Media
Slide 8
Introduction Errors in reverse process are not allowed: Second
Requirement: No error in data and cover media 0111 Data + Data
Error Unacceptable Not Original Unacceptable
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
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
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-to-
noise_ratio
Slide 15
Some Concepts http://en.wikipedia.org/wiki/Peak_signal-to-
noise_ratio
Slide 16
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.
http://en.wikipedia.org/wiki/Peak_signal-to- noise_ratio Original
ImagePSNR=31.45dB
Slide 17
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
Slide 18
Some Concepts Histogram Pair Example: in a histogram of an
image, a and b are adjacent integers, h = [m, 0] is a histogram
pair. m ba 0 Gray Value Number of Pixels
Slide 19
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
Slide 20
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
Slide 21
Embedding Algorithm Step 1:
Slide 22
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
Slide 23
Embedding Algorithm Step 2: h = [2785, 0] is a histogram
pair
Slide 24
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
Slide 25
Embedding Algorithm Step 3: Embedded data
Slide 26
Embedding Algorithm Step 3: Embedded data PSNR = 53.8 dB
Slide 27
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
Slide 28
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
Slide 29
Retrieval algorithm Result: Data error rate=0, Image error
rate=0 Z. Ni, Y. Q. Shi, N. Ansari and W. Su, Reversible Data
Hiding
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
Slide 33
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
Slide 34
Some Concepts G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni,
Reversible Data Hiding Using Integer Wavelet Transform and
Companding Technique
Slide 35
Some Concepts G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni,
Reversible Data Hiding Using Integer Wavelet Transform and
Companding Technique
Slide 36
Some Concepts G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni,
Reversible Data Hiding Using Integer Wavelet Transform and
Companding Technique
Slide 37
Some Concepts G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni,
Reversible Data Hiding Using Integer Wavelet Transform and
Companding Technique
Slide 38
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
Slide 39
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,, 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
Slide 40
Some Concepts G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni,
Reversible Data Hiding Using Integer Wavelet Transform and
Companding Technique
Slide 41
Some Concepts G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni,
Reversible Data Hiding Using Integer Wavelet Transform and
Companding Technique
Slide 42
Some Concepts Histogram Modification After data embedded in
coefficients, some pixels gray value may overflow (>255) or
underflow (
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
Slide 49
Embedding Algorithm G. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni,
and X. Tong, Optimum Histogram Pair Based Image Lossless Data
Embedding 040-41 02-23 4-302 -200 -2121
Slide 50
Embedding Algorithm G. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni,
and X. Tong, Optimum Histogram Pair Based Image Lossless Data
Embedding -5-4 -3 -2 0 123 456
Slide 51
Embedding Algorithm Step1: expand image histogram From right
side, h[4]=0, h[4] to h[5] G. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z.
Ni, and X. Tong, Optimum Histogram Pair Based Image Lossless Data
Embedding -5-4 -3 -2 0 123 456
Slide 52
Embedding Algorithm Step1: expand image histogram From right
side, h[5]=0, h[5] to h[6] G. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z.
Ni, and X. Tong, Optimum Histogram Pair Based Image Lossless Data
Embedding -5-4 -3 -2 0 123 456
Slide 53
Embedding Algorithm Step1: expand image histogram From left
side, h[-4]=0, h[-4] to h[-5] G. Xuan, Y. Q. Shi, P. Chai, X. Cui,
Z. Ni, and X. Tong, Optimum Histogram Pair Based Image Lossless
Data Embedding -5-4 -3 -2 0 123 456
Slide 54
Embedding Algorithm Step1: expand image histogram From center
h[3]=0, h[3] to h[4] G. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni,
and X. Tong, Optimum Histogram Pair Based Image Lossless Data
Embedding -5-4 -3 -2 0 123 456
Slide 55
Embedding Algorithm G. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni,
and X. Tong, Optimum Histogram Pair Based Image Lossless Data
Embedding -5-4 -3 -2 0 123 456
Slide 56
Embedding Algorithm Step2: Embedding Data from right to left to
center D=[110001]; right [1,0], capacity=1, embedded 1 using
histogram pair method G. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni,
and X. Tong, Optimum Histogram Pair Based Image Lossless Data
Embedding -5-4 -3 -2 0 123 456
Slide 57
Embedding Algorithm Step2: Embedding Data from right to left to
center D=[110001]; left [0,2], capacity=2, embedded 10 using
histogram pair method G. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni,
and X. Tong, Optimum Histogram Pair Based Image Lossless Data
Embedding -5-4 -3 -2 0 123 456
Slide 58
Embedding Algorithm Step2: Embedding Data from right to left to
center D=[110001]; Center [3,0], capacity=3, embedded 001 using
histogram pair method G. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni,
and X. Tong, Optimum Histogram Pair Based Image Lossless Data
Embedding -5-4 -3 -2 0 123 456
Slide 59
Embedding Algorithm G. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni,
and X. Tong, Optimum Histogram Pair Based Image Lossless Data
Embedding -5-4 -3 -2 0 123 456
Slide 60
Embedding Algorithm For application in Lena image, for certain
payload, PSNR is good.
Slide 61
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
Simulation For Histogram Pair method, to hiding data sentence:
ECE 643 Digital Image Processing Course Project by Su Yu In Lena
image.
Slide 66
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,, Prentice Hall, 3rd
(2007) edition