Reversible Data Hiding by Su Yu

Reversible Data Hiding

Reversible Data HidingECE643 Digital Image Processing (I) Course Project

Professor: Yun Q. Shi

Su Yu12/02/2011ContentsIntroductionApplicationsMethodsHistogram PairOptimum Histogram PairConclusionSimulationContentsIntroductionApplicationsMethodsHistogram PairOptimum Histogram PairConclusionSimulationIntroductionWhats Data Hiding?A process to embed useful data (information) into a cover media.Data invisibility is the major requirement.1110Data+=

Cover Media

Marked Media

IntroductionDistortion happens in embedding process:So BadUnacceptable=1110Data+

IntroductionDistortion happens in embedding process:

First Requirement: Minimize the distortion and maximize the data payloadOKAcceptable1110Data+=

IntroductionWhats 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.1110Data+

Cover Media

Marked Media

IntroductionErrors in reverse process are not allowed:

Second Requirement: No error in data and cover media0111Data+Data ErrorUnacceptable

Not OriginalUnacceptableContentsIntroductionApplicationsMethodsHistogram PairOptimum Histogram PairConclusionSimulationApplicationsSecure medical image data systemLaw enforcementE-governmentImage authenticationCovert CommunicationG. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni; Reversible Data Hiding Using Integer Wavelet Transform and Companding Technique10ContentsIntroductionApplicationsMethodsHistogram PairOptimum Histogram PairConclusionSimulationMethodsHistogram PairBased on Paper:Z. Ni, Y. Q. Shi, N. Ansari and W. Su, Reversible Data HidingOptimum Histogram PairBased on Papers:G. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni, Reversible Data Hiding Using Integer Wavelet Transform and Companding TechniqueG. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and X. Tong, Optimum Histogram Pair Based Image Lossless Data EmbeddingContentsIntroductionApplicationsMethodsHistogram PairOptimum Histogram PairConclusionSimulationSome ConceptsPSNR (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 representationThe 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_ratioSome Conceptshttp://en.wikipedia.org/wiki/Peak_signal-to-noise_ratioSome ConceptsPSNR (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=31.45dBSome ConceptsHistogram PairHistogram 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 EmbeddingSome ConceptsHistogram PairExample: in a histogram of an image, a and b are adjacent integers, h = [m, 0] is a histogram pair.

mba0Gray ValueNumber of PixelsHistogram PairAdvantagesLarge data payload5k-60k bits for 512*512*8 grayscale imageHigh visual qualityPSNR > 48 dBMethodHistogram PairZ. Ni, Y. Q. Shi, N. Ansari and W. Su, Reversible Data HidingEmbedding AlgorithmUse Lena image as an exampleStep 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 HidingEmbedding AlgorithmStep 1:

Embedding AlgorithmStep 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 HidingEmbedding AlgorithmStep 2: h = [2785, 0] is a histogram pair

Embedding AlgorithmStep 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 HidingEmbedding AlgorithmStep 3: Embedded data

Embedding AlgorithmStep 3: Embedded dataPSNR = 53.8 dB

Retrieval algorithmStep 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 HidingRetrieval algorithmStep 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 HidingRetrieval algorithmResult: Data error rate=0, Image error rate=0Z. Ni, Y. Q. Shi, N. Ansari and W. Su, Reversible Data Hiding

PSNRZ. Ni, Y. Q. Shi, N. Ansari and W. Su, Reversible Data HidingContentsIntroductionApplicationsMethodsHistogram PairOptimum Histogram PairConclusionSimulationSome ConceptsCompandingThe process of signal compression and expansion.Compression and ExpansionCompression: 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 TechniqueSome ConceptsCompandingAssume 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 TechniqueSome ConceptsG. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni, Reversible Data Hiding Using Integer Wavelet Transform and Companding TechniqueSome ConceptsG. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni, Reversible Data Hiding Using Integer Wavelet Transform and Companding TechniqueSome ConceptsG. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni, Reversible Data Hiding Using Integer Wavelet Transform and Companding TechniqueSome ConceptsG. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni, Reversible Data Hiding Using Integer Wavelet Transform and Companding TechniqueSome ConceptsSub 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 EmbeddingSome ConceptsWavelet TransformLikes 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.C. Gonzalez and R. E. Woods, < Digital Image Processing >, Prentice Hall, 3rd (2007) editionG. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni, Reversible Data Hiding Using Integer Wavelet Transform and Companding TechniqueSome ConceptsG. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni, Reversible Data Hiding Using Integer Wavelet Transform and Companding TechniqueSome ConceptsG. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni, Reversible Data Hiding Using Integer Wavelet Transform and Companding TechniqueSome ConceptsHistogram ModificationAfter data embedded in coefficients, some pixels gray value may overflow (>255) or underflow (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 EmbeddingEmbedding AlgorithmG. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and X. Tong, Optimum Histogram Pair Based Image Lossless Data Embedding040-4102-23-14-302-3-1-20-10-212-11Embedding AlgorithmG. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and X. Tong, Optimum Histogram Pair Based Image Lossless Data Embedding-5-4-3-2-10123456Embedding AlgorithmStep1: expand image histogramFrom 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-5-4-3-2-10123456Embedding AlgorithmStep1: expand image histogramFrom 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-5-4-3-2-10123456Embedding AlgorithmStep1: expand image histogramFrom 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-5-4-3-2-10123456Embedding AlgorithmStep1: expand image histogramFrom 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-5-4-3-2-10123456Embedding AlgorithmG. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and X. Tong, Optimum Histogram Pair Based Image Lossless Data Embedding-5-4-3-2-10123456Embedding AlgorithmStep2: Embedding Datafrom right to left to center D=[110001];right [1,0], capacity=1, embedded 1 using histogram pair methodG. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and X. Tong, Optimum Histogram Pair Based Image Lossless Data Embedding-5-4-3-2-10123456Embedding AlgorithmStep2: Embedding Datafrom right to left to center D=[110001];left [0,2], capacity=2, embedded 10 using histogram pair methodG. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and X. Tong, Optimum Histogram Pair Based Image Lossless Data Embedding-5-4-3-2-10123456Embedding AlgorithmStep2: Embedding Datafrom 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-5-4-3-2-10123456Embedding AlgorithmG. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and X. Tong, Optimum Histogram Pair Based Image Lossless Data Embedding-5-4-3-2-10123456Embedding AlgorithmFor application in Lena image, for certain payload, PSNR is good.

Retrieval AlgorithmRetrieval 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 EmbeddingContentsIntroductionApplicationsMethodsHistogram PairOptimum Histogram PairConclusionSimulationConclusionComparison between two methods:

Histogram PairOptimum Histogram PairPayloadSmallLargePSNRLowHighComplexityLowHighContentsIntroductionApplicationsMethodsHistogram PairOptimum Histogram PairConclusionSimulationSimulationFor Histogram Pair method, to hiding data sentence:ECE 643 Digital Image Processing Course Project by Su YuIn Lena image.ReferencesZ. Ni, Y. Q. Shi, N. Ansari and W. Su, Reversible Data HidingG. Xuan, C. Yang, Y. Zhen, Y. Q. Shi, and Z. Ni, Reversible Data Hiding Using Integer Wavelet Transform and Companding TechniqueG. Xuan, Y. Q. Shi, P. Chai, X. Cui, Z. Ni, and X. Tong, Optimum Histogram Pair Based Image Lossless Data Embedding1. R. C. Gonzalez and R. E. Woods, < Digital Image Processing >, Prentice Hall, 3rd (2007) editionThank you!Questions?

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Reversible Data Hiding by Su Yu