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

2. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 2 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 http://www.ece.umd.edu/class/enee739m/lec/739S02_lec3.pdf Today –Quick review on image processing –Intro. to data hiding: additive embedding

3. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 3 Quick Review on Image Compression, etc.

4. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 4 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.

5. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 5 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)

6. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 6 Examples of Sampling 256x256 64x64 16x16

7. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 7 Examples of Quantization 8 bits / pixel 4 bits / pixel 2 bits / pixel

8. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 8 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)

9. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 9 Examples HSV YUV RGB

10. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 10 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

11. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 11 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

12. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 12 Common Unitary Transforms –DFT, DCT, Haar See also: Jain’s Fig.5.2 pp136

13. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 13 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

14. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 14 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)

15. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 15 Illustration of JPEG Baseline Algorithm –Block diagram from Wallace’s JPEG tutorial paper –Flash demo by Dr. Ken Lam (Hong Kong PolyTech Univ.)

16. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 16 Additive Data Hiding

17. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 17 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

18. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 18 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

19. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 19 General Framework marked media (w/ hidden data) embed data to be hidden host mediacompress process / attack extract play/ record/… extracted data player 101101 … “Hello, World” 101101 … “Hello, World” test media

20. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 20 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

21. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 21 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 …...

22. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 22 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.

23. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 23 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

24. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 24 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

25. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 25 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 

26. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 26 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

27. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 27 Compare Cox & Podilchuk Schemes OriginalCox Podilchuk whole image DCT block-DCT Embed in 1000 largest coeff. Embed to all “embeddables”

28. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 28 Compare Cox & Podilchuk Schemes (cont’d) CoxPodilchuk

29. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 29 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)

30. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 30 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.1673-1687, 1997. –Download from IEEE online journal, or http://www.neci.nj.nec.com/homepages/ingemar/papers/ip97.ps –C. Podilchuk and W. Zeng, “Image Adaptive Watermarking Using Visual Models,” IEEE Journal Selected Areas of Communications (JSAC), vol.16, no.4, May, 1998. –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

31. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 31 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

32. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 32 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

33. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 33 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 10110100... =

34. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 34 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 101101... even “0” odd “1”

35. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 35 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)

36. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 36 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

37. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 37 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

38. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 38 Categories of Watermarking digital media –speech/audio, image, video, 3D model @ @ perceptible / imperceptible @ @ robust / fragile @ @ –wrt. further compression, processing, and/or attack private / public –use original copy or not focused

39. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 39 Major Applications ownership protection @ @ –visible wmk … still visually annoying –invisible wmk … robustness preferred tradeoff between invisibility and robustness authentication @ @ –easy to edit digital media –detect (and locate) alteration  trustworthy dig.camera inv. rob. pub.

40. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 40 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

41. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 41 Watermarking vs. Data Hiding almost interchangable some conventional distinctions hiding wmk hiding wmk

42. ECE738 Advanced Image Processing Min Wu @ U. Maryland 2002 42 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 –...