ECE738 Advanced Image Processing Data Hiding (1 of 3) Curtsey of Professor Min Wu Electrical & Computer Engineering Univ. of Maryland, College Park

ECE738 Advanced Image Processing Min U. Maryland Review of Last Class Wrap up optimal 1-bit detection –Performance is determined by SNR and signal length (# observations) –Detection under low SNR ~ use longer signal Cryptographic tools for secure communications –Building blocks: pseudo-random # generator, one-way func., hash –Encryption –Integrity verification (tampering detection) => 3rd lecture notes Today –Quick review on image processing –Intro. to data hiding: additive embedding

ECE738 Advanced Image Processing Min U. Maryland Quick Review on Image Compression, etc.

ECE738 Advanced Image Processing Min U. Maryland What is An Image? Grayscale image –A grayscale image is a function I(x,y) of the two spatial coordinates of the image plane. –I(x,y) is the intensity of the image at the point (x,y) on the image plane. –We can restrict the image to be bounded by some rectangle [0,a]  [0,b] I: [0, a]  [0, b]  [0, inf ) Color image –Can be represented by three functions, R(x,y) for red, G(x,y) for green, and B(x,y) for blue.

ECE738 Advanced Image Processing Min U. Maryland Sampling and Quantization Computer handles “discrete” data. Sampling –Sample the value of the image at the nodes of a regular grid on the image plane. –A pixel (picture element) at (i, j) is the image intensity value at grid point indexed by the integer coordinate (i, j). Quantization –Is a process of transforming a real valued sampled image to one taking only a finite number of distinct values. –Each sampled value in a 256-level grayscale image is represented by 8 bits. 0 (black) 255 (white)

ECE738 Advanced Image Processing Min U. Maryland Examples of Sampling 256x256 64x64 16x16

ECE738 Advanced Image Processing Min U. Maryland Examples of Quantization 8 bits / pixel 4 bits / pixel 2 bits / pixel

ECE738 Advanced Image Processing Min U. Maryland Different Color Representations RGB YIQ for NTSC transmission system –National Television Systems Committee (NTSC) –Receiver primary sys. (R N, G N, B N ) as TV receivers standard –Transmission system (Y, I, Q) facilitate transmission of color video via monochrome TV ch. YUV (YCbCr) for PAL and digital video HSV ~ Hue, Saturation, Value CMY for printing –Cyan, Magenta, Yellow (complement of RGB)

ECE738 Advanced Image Processing Min U. Maryland Examples HSV YUV RGB

ECE738 Advanced Image Processing Min U. Maryland Why Do Transforms? Fast computation –E.g., convolution vs. multiplication Conceptual insights for various image processing –E.g., spatial frequency info. (smooth, moderate change, fast change, etc.) Obtain transformed data as measurement –E.g., radiology images (medical and astrophysics) –Need inverse transform –May need to get assistance from other transforms For efficient storage and transmission –Pick a few “representatives” (basis) –Just store/send the “contribution” from each basis

ECE738 Advanced Image Processing Min U. Maryland Review of 1-D & 2-D Unitary Transforms Vector/matrix representation of 1-D & 2-D sampled signal –Representing an image as a matrix or sometimes as a long vector Basis functions/vectors and orthonormal basis –Used for representing the space via their linear combinations –Many possible sets of basis and orthonormal basis Unitary transform on input x ~ A -1 = A *T –y = A x  x = A -1 y = A *T y =  a i *T y(i) ~ represented by basis vectors {a i *T } –Rows (and columns) of a unitary matrix form an orthonormal basis General 2-D transform and separable unitary 2-D transform –2-D transform involves O(N 4 ) computation –Separable: Y = A X A T = (A X) A T ~ O(N 3 ) computation Apply 1-D transform to all columns, then apply 1-D transform to rows

ECE738 Advanced Image Processing Min U. Maryland Common Unitary Transforms –DFT, DCT, Haar See also: Jain’s Fig.5.2 pp136

ECE738 Advanced Image Processing Min U. Maryland Lossless Coding Tools PCM encoding –Fixed-length encoding of a sampled and quantized signal Entropy encoding –Basic ideas ~ why bring in probability distribution? Assign shorter codeword to commonly seen values –Limit of compression ~ Entropy –Huffman coding –Run-length coding Predictive coding –Basic ideas and DPCM

ECE738 Advanced Image Processing Min U. Maryland Transform Coding Basic ideas –Energy compaction via appropriate transform –Adaptive bit allocation allocate more bits to info.-rich coefficient bands General block-based transform coding –Tradeoff for block size –Ordering & Zonal/Threshold coding JPEG baseline algorithm (block DCT based)

ECE738 Advanced Image Processing Min U. Maryland Illustration of JPEG Baseline Algorithm –Block diagram from Wallace’s JPEG tutorial paper –Flash demo by Dr. Ken Lam (Hong Kong PolyTech Univ.)

ECE738 Advanced Image Processing Min U. Maryland Additive Data Hiding

ECE738 Advanced Image Processing Min U. Maryland Crypto is Useful, but Not Enough …… Encryption –Helps to protect confidentiality –Protection vanishes after decryption –Prefer a way to associate copyright info. with MM source even after decryption/compression/transmission/etc. Digital cryptographic signature –Helps to authenticate sender’s identity and data integrity –Need to attach a separate signature to the data source –Audio/image/video allows imperceptible changes –Opportunities for new and seamless ways of authentication

ECE738 Advanced Image Processing Min U. Maryland Multimedia Data Hiding / Digital Watermarking What? –Examples Picture in picture, words in words Silent message, invisible images –Secondary information in perceptual digital media data Why? –Seeing is believing? easy to modify --> authentication –Copy with a few mouse click easy to copy without degradation --> ownership –Convey other information without an additional channel

ECE738 Advanced Image Processing Min U. Maryland General Framework marked media (w/ hidden data) embed data to be hidden host mediacompress process / attack extract play/ record/… extracted data player … “Hello, World” … “Hello, World” test media

ECE738 Advanced Image Processing Min U. Maryland Issues and Challenges Tradeoff among conflicting requirements –Imperceptibility –Robustness & security –Capacity want to many bits and extract them with small prob. of errors Robustness Capacity Imperceptibility

ECE738 Advanced Image Processing Min U. Maryland Additive Embedding: Basic Ideas Add a weak signal representing ownership in host media –The weak signal (“watermark”) is known to detector –Detection by correlating a test copy with the watermark signal Achieving invisibility –Watermark signals with structural patterns can be easily perceived than random noisy signals Achieving robustness –Watermarks added to perceptually insignificant components can easily be distorted modulation data to be hidden  X original source X’ = X +  marked copy 1011 …...

ECE738 Advanced Image Processing Min U. Maryland Theoretical Foundations Optimal detection for On-Off Keying (OOK) –OOK under i.i.d. Gaussian noise {d i } b  {0,1} represents absence vs. presence of ownership mark Use a correlator-type detector (recall the review last week) –Need to determine how to choose {s i } Neyman-Pearson Detection [Poor’s book Sec.2.4] –False-alarm ~ claiming wmk existence when nothing embedded –Given max. allowed false-alarm, try to minimize prob. of miss detection Use likelihood ratio as detection statistic Determine threshold according to false-alarm prob.

ECE738 Advanced Image Processing Min U. Maryland Spread Spectrum Approach: Cox et al (NECI) Key points –Place wmk in perceptually significant spectrum (for robustness) Modify by a small amount below Just-noticeable-difference (JND) –Use long random vector as wmk to avoid artifacts (for imperceptibility & robustness) Embedding v’ i = v i +  v i w i = v i (1+  w i ) –Perform DCT on entire image and embed wmk in DCT coeff. –Choose N=1000 largest AC coeff. and scale {v i } by a random factor 2D DCTsort v’=v (1+  w) IDCT & normalize Original image N largest coeff. other coeff. marked image random vector generator wmk seed

ECE738 Advanced Image Processing Min U. Maryland Cox’s Scheme (cont’d) Detection –Subtract original image from the test one before running through detector –Original detection measure used by Cox et al. a correlator normalized by |Y| DCT compute similarity threshold test image decision wmk DCTselect N largest original unmarked image select N largest preprocess – – orig X test X’ X’=X+W+N ? X’=X+N ? To think

ECE738 Advanced Image Processing Min U. Maryland Cox’s Scheme (cont’d) Robustness –(claimed) scaling, JPEG, dithering, cropping, “printing-xeroxing-scanning”, multiple watermarking –No surprise with high robustness Equiv. to conveying just 1-bit {0,1} with O(10 3 ) samples Comment –must store original unmarked image  “private wmk”, “non-blind” detect. –perform image registration if necessary –adjustable parameters: N and 

ECE738 Advanced Image Processing Min U. Maryland Invisible Robust Wmk: Improved Schemes Apply better Human-Perceptual-Model –Global scaling factor is not suitable for all coeff. –More explicitly compute Just-noticeable-difference (JND) JND ~ max amount each freq. coeff. can be modified imperceptibly Use  i for each coeff.  finely tune wmk strength –Better tradeoff between imperceptibility and robustness Try to add a watermark as strong as possible Block-DCT based schemes: –Podichuk-Zeng & Swanson et al. –Existing visual model for block DCT: JPEG

ECE738 Advanced Image Processing Min U. Maryland Compare Cox & Podilchuk Schemes OriginalCox Podilchuk whole image DCT block-DCT Embed in 1000 largest coeff. Embed to all “embeddables”

ECE738 Advanced Image Processing Min U. Maryland Compare Cox & Podilchuk Schemes (cont’d) CoxPodilchuk

ECE738 Advanced Image Processing Min U. Maryland Summary Quick review of image processing basics Introduction to data hiding: Additive Embedding –Use hypothesis testing as foundations –Determine embedding domains and watermark sig. –Cox approach –Improvement (Podilchuk approach)

ECE738 Advanced Image Processing Min U. Maryland Suggested reading –I. Cox, J. Kilian, T. Leighton, T. Shamoon: “Secure Spread Spectrum Watermarking for Multimedia'', IEEE Transaction on Image Processing, vol.6, no.12, pp , –Download from IEEE online journal, or –C. Podilchuk and W. Zeng, “Image Adaptive Watermarking Using Visual Models,” IEEE Journal Selected Areas of Communications (JSAC), vol.16, no.4, May, –Download from IEEE online journal –Logistics No class on Tue. 2/12/02 This week’s office hour will be Fri. (tomorrow) 10-11am Assignment on additive watermark will be announced

ECE738 Advanced Image Processing Min U. Maryland Question for Today (QFT) [Hand-in] Optimal detection for OOK –On-Off Keying under i.i.d. Gaussian noise {d i } –Determine the detection statistic, threshold, and Pe (assume equal prior probability) [Food-for-thought] –How to detect additive watermark without using the original? –Attacks on additive embedding ~ making it undetectable

ECE738 Advanced Image Processing Min U. Maryland Issues and Challenges Tradeoff among conflicting requirements –Imperceptibility –Robustness & security –Capacity Key elements of data hiding –Perceptual model –Embedding one bit –Multiple bits –Uneven embedding capacity –Robustness and security –What data to embed Upper Layers Uneven capacity equalization Error correction Security …… Lower Layers Imperceptible embedding of one bit Multiple-bit embedding Coding of embedded data Robustness Capacity Imperceptibility

ECE738 Advanced Image Processing Min U. Maryland Type-I Additive Embedding Add secondary signal in host media Representative: spread spectrum embedding –add a noise-like signal and detection via correlation –good tradeoff between imperceptibility and robustness –limited capacity host signal serves as major interferer modulation data to be hidden  X original source X’ = X +  marked copy =

ECE738 Advanced Image Processing Min U. Maryland Type-II Relationship Enforcement Embedding Deterministically enforcing relationship –Secondary info. carried solely in X’ Representative: odd-even embedding –No interference from host signal –High capacity but limited robustness –Robustness achieved by quantization or tolerance zone –Odd-even enforcing blackpixel# per block to hide data in binary image mapping { b i } data to be hidden X original source X’= f( b ) marked copy even “0” odd “1”

ECE738 Advanced Image Processing Min U. Maryland Conveying One-bit Through Noisy Channel (cont’d) Optimal detection ~ minimize prob. of error MAP ~ maximize posterior probability => ML ~ maximum likelihood detector [for equal prior] => Minimum distance detector [for iid Gaussian noise] => Maximum correlation detector [for equal-energy sig.] Detection statistics –[correlator]  i y i s i Prob. distribution under each hypothesis ~ N(  ||s|| 2, ||s|| 2  d 2 ) –[correlator with unit-variance]  i y i s i / [(  i s i 2 )  d 2 ] 1/2 ~ N(  ||s||/  d,1)

ECE738 Advanced Image Processing Min U. Maryland Performance of Optimal Detector Probability of detection error = Q ( ||s||/  d ) –Q (x) is monotonically decreasing for non-negative x –Signal-to-noise ratio (SNR) ~ ( ||s|| 2 /n) /  d 2 Communications under very low SNR –Choose large n collect info. (energy) from many signal components a basic idea behind “spread spectrum communications” Useful in invisible watermarking (data hiding) –Adding or subtracting a weak signal to convey one-bit hidden info. –Will go into more details next time Extension for non-i.i.d. Gaussian noise

ECE738 Advanced Image Processing Min U. Maryland Related Terminology stegnography: the art/science of communicating in a hidden way –“covered writing” (Greek) cryptography: the study/application of secret writing techniques –encipher and decipher messages in secret code DEFENSE Introduction to watermarking PLAN magic ink orig: watermarking  crypt: dzgvinziprmt a b c … … x y z z y x … … c b a

ECE738 Advanced Image Processing Min U. Maryland Categories of Watermarking digital media –speech/audio, image, video, perceptible robust –wrt. further compression, processing, and/or attack private / public –use original copy or not focused

ECE738 Advanced Image Processing Min U. Maryland Major Applications –visible wmk … still visually annoying –invisible wmk … robustness preferred tradeoff between invisibility and –easy to edit digital media –detect (and locate) alteration  trustworthy dig.camera inv. rob. pub.

ECE738 Advanced Image Processing Min U. Maryland Major Applications (cont’d) copy control –identify recipients –permission control on hardware convey other info. –data hiding cable co. Shakespeare in Love Alice Bob Carl w1w1 w2w2 w3w3 Sell DON’T COPY Titanic Rec’ble DVD Player

ECE738 Advanced Image Processing Min U. Maryland Watermarking vs. Data Hiding almost interchangable some conventional distinctions hiding wmk hiding wmk

ECE738 Advanced Image Processing Min U. Maryland Verify Ownership: Invisible Robust Wmk Encryption no longer protects decrypted image Visible watermark:... still visually annoying Invisible watermark:... robustness is necessary –robust wrt. common image processing techniques, distortions, and attacks –tradeoff between invisibility and robustness Existing work –spread spectrum approach [ Cox et al (NECI) ] –visual model based approaches –...