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. 11……10 Data += Cover Media Marked Media

Introduction Distortion happens in embedding process: So Bad Unacceptable = 11……10 Data +

Introduction Distortion happens in embedding process: First Requirement: Minimize the distortion and maximize the data payload OK Acceptable 11……10 Data +=

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. 11……10 Data + Cover Media Marked Media

Introduction Errors in reverse process are not allowed: Second Requirement: No error in data and cover media 01……11 Data + Data Error Unacceptable Not Original Unacceptable

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). noise_ratio

Some Concepts noise_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. noise_ratio Original ImagePSNR=31.45dB

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. m ba 0 Gray Value Number of Pixels

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

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 G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni, Reversible Data Hiding Using Integer Wavelet Transform and Companding Technique

Some Concepts G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni, Reversible Data Hiding Using Integer Wavelet Transform and Companding Technique

Some Concepts G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni, Reversible Data Hiding Using Integer Wavelet Transform and Companding Technique

Some Concepts 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,, 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 G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni, Reversible Data Hiding Using Integer Wavelet Transform and Companding Technique

Some Concepts 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 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 > bpp ( bits) “Barbara”, if payload > bpp ( bits) “Baboon”, if payload > 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 G. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and X. Tong, Optimum Histogram Pair Based Image Lossless Data Embedding

Embedding Algorithm G. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and X. Tong, Optimum Histogram Pair Based Image Lossless Data Embedding

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

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

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

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

Embedding Algorithm G. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and X. Tong, Optimum Histogram Pair Based Image Lossless Data Embedding

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

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

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

Embedding Algorithm G. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and X. Tong, Optimum Histogram Pair Based Image Lossless Data Embedding

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 Optimum Histogram Pair PayloadSmallLarge PSNRLowHigh ComplexityLowHigh

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,, Prentice Hall, 3rd (2007) edition

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