ece738 advanced image processing data hiding (1 of 3) curtsey of professor min wu electrical &...

ECE738 Advanced Image Processing

Data Hiding (1 of 3)

Curtsey of Professor Min Wu Electrical & Computer EngineeringUniv. of Maryland, College Park

Min Wu @ U. Maryland 2002 2ECE738 Advanced Image Processing

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


Quick Review on Image Compression, etc.


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.


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)


Examples of Sampling

256x256

64x64

16x16


Examples of Quantization

8 bits / pixel

4 bits / pixel

2 bits / pixel


Different Color Representations

• RGB• YIQ for NTSC transmission system

– National Television Systems Committee (NTSC)

– Receiver primary sys. (RN, GN, BN) 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)


Examples

HSV

YUV

RGB


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


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 = ai

*T y(i) ~ represented by basis vectors {ai*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(N4) computation– Separable: Y = A X AT = (A X) AT ~ O(N3) computation

• Apply 1-D transform to all columns, then apply 1-D transform to rows


Common Unitary Transforms– DFT, DCT, Haar

See also: Jain’s Fig.5.2 pp136


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


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)


Illustration of JPEG Baseline Algorithm

– Block diagram from Wallace’s JPEG tutorial paper– Flash demo by Dr. Ken Lam (Hong Kong PolyTech Univ.)


Additive Data Hiding


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


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


General Framework

marked media(w/ hidden data)

embedembeddata to be data to be hiddenhidden

host media

compresscompress

process / process / attackattack

extractextract

play/ record/…play/ record/…extracted extracted datadata

playerplayer

101101 …101101 …

““Hello, World”Hello, World”

101101 …101101 …

““Hello, World”Hello, World”test media


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


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

modulationmodulation

data to be hidden

Xoriginal source

X’ = X + marked copy

1011 …...1011 …...


Theoretical Foundations• Optimal detection for On-Off Keying (OOK)

– OOK under i.i.d. Gaussian noise {di}

• 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 {si}

• 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.

n~1ifor )1 (if :

)0 (if :

1

0

bdsyH

bdyH

iii

ii


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 = vi + vi wi = vi (1+ wi)

– Perform DCT on entire image and embed wmk in DCT coeff.

– Choose N=1000 largest AC coeff. and scale {vi} by a random factor

2D DCT sort v’=v (1+ w) IDCT & normalize

Original image

N largest coeff.

other coeff.

marked image

random vector generator

wmk

seed

1.0nceunit varia zeromean, iid,~iw


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

thresholdtest image

decision

wmk

DCT select N largest

original unmarked image

select N largest

preprocess

–

YY

WYWYsim

,

,),(

k watermar

watermarkno

:1

:0

NWYH

NYHXXY

–orig X

test X’

X’=X+W+N ?

X’=X+N ?

To think

To think


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(103) samples

• Comment– must store original unmarked image “private wmk”, “non-blind” detect.

– perform image registration if necessary

– adjustable parameters: N and

Distortion none scale25%

JPG10%

JPG 5% dither crop25%

print-xerox-scan

similarity 32.0 13.4 22.8 13.9 10.5 14.6 7.0 threshold = 6.0 (determined by setting false alarm probability)


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

)1(' iiii wvv


Compare Cox & Podilchuk Schemes

Original Cox Podilchuk

whole image DCT block-DCT

Embed in 1000 largest coeff. Embed to all “embeddables”


Compare Cox & Podilchuk Schemes (cont’d)

Cox Podilchuk


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)


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


Question for Today (QFT)

• [Hand-in] Optimal detection for OOK

– On-Off Keying under i.i.d. Gaussian noise {di}

– 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

n~1ifor )1 (if :

)0 (if :

1

0

bdsyH

bdyH

iii

ii


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

Up

per

L

ayer

s

Uneven capacity equalization

Error correction

Security

……

Low

er

Lay

ers

Imperceptible embeddingof one bit

Multiple-bit embedding

Coding of embedded data

Robustness

Capacity

Imperceptibility


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

modulationmodulation

data to be hidden

Xoriginal source

X’ = X + marked copy

10110100 ...10110100 ...

< X’ + noise, > = < + (X + noise), >

< X’ + noise - X, > = < + noise, >


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

mappingmapping{ bi }data tobe hidden X

original source

X’= f( b )marked copy

101101 ...101101 ...

even “0”odd “1”


Conveying One-bit Through Noisy Channel (cont’d)

• Optimal detection ~ minimize prob. of errorMAP ~ 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 yi si

• Prob. distribution under each hypothesis ~ N( ||s||2 , ||s||2 d 2

)

– [correlator with unit-variance] i yi si / [(i si 2) d

2 ]1/2 ~ N( ||s||/d ,1)

n~1ifor )1 (if :

)1 (if :

1

1

bdsyH

bdsyH

iii

iii


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


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

DEFENSEIntroduction to watermarking

PLANmagic ink

Do others …? know the data’sexistence?

know how todetect the data?

stegnography maybe not no (but may try)

cryptography yes no (but may try)

orig: watermarking

crypt: dzgvinziprmt

a b c … … x y zz y x … … c b a


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


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

visible/invisible

robust/fragile

private/public

verifyownership

detectalteration

imagequality

visible public easy possible degradeinvisible robust ? possible hard goodinvisible fragile public no yes good

inv.

rob.

pub.


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

w1w2w3

SellSell

DON’T

COPY

Titanic

Rec’ble DVD Player


Watermarking vs. Data Hiding

work for ... use orig. copy invisible robust

watermarking perceptualsource

either either either

data hiding any no usually yes generally no

• almost interchangable• some conventional distinctions

hiding

wmk

hiding

wmk


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– ...

ece738 advanced image processing data hiding (1 of 3) curtsey of professor min wu electrical &...

Documents

image plane

image compression

various image processing

image intensity value

inf color image

level grayscale image

real valued sampled

basis slide