Invisible Digital Image Watermarking

Adam Day

Applications Classification Common watermarking methods Types of verification/detection Implementing watermarking using

wavelets

Overview

Applications Copyright Protection

◦ Invisibly mark products Manage distribution of assets

◦ Apply unique watermark key to each copy of a distributed video/image

Embed all necessary data in a single image Naturally expands to video watermarking

Simple◦ Spatial Domain – Modification made to the luminance

values Transformed Domain

◦ DCT◦ DWT◦ SVD

Product of 3 matrices A = UΣVT

U ,V are orthogonal matrices: UTU= I, VTV = I Σ = diag (λ1, λ2, ...). The diagonals of Σ are called the singular values of A The columns of U are called the left singular vectors of A and The columns of V are called the right singular vectors of A.

Common Watermarking Methods

An effective watermark should be:◦ Robust to common manipulations◦ Unobtrusive so that it does not affect visual

quality Categorize based on:

◦ Capacity◦ Complexity◦ Invertibility◦ Robustness◦ Security◦ Transparency◦ Verification

Classification

Fragile◦ Detection fails with even minor modification◦ Useful in tampering detection◦ Common in simple additive watermarking

Robust◦ Detection is accurate even under modification◦ Need for robustness dependent on use of data

Robustness

Verification / Detection Methods Non-blind

◦ The watermarking scheme requires the use of the original image

Semi-Blind◦ The watermarking scheme requires the

watermark data and/or the parameters used to embed the data

Blind◦ If the watermarking scheme does not require the

original image or any other data

The 2D-DWT Transform divides the image into 4 sub-bands◦ LL – Lower resolution version of image◦ LH – Horizontal edge data◦ HL – Vertical edge data◦ HH – Diagonal edge data

Most DWT watermarking algorithms embed only in the HL, LH and HH sub-bands

2D – Discrete Wavelet Transform

LL HL

LH HH

2D – Discrete Wavelet Transform

◦ Perform 2D-DWT to divide image into LL, HL, LH and HH sub-bands.

◦ Select coefficients from the LL, HL, LH and HH sub-bands that surpass a particular threshold T1

◦ Embed watermarking data via additive modificationt’i = ti + α|ti|xi xi = watermark α = weighting constant

◦ Perform 2D-IDWT to create “watermarked image”

Watermark Embedding Method

Modifications to edge data create the least visually perceptible changes

If using a hard threshold to select coefficients, the number of affected coefficients can vary greatly

Images with a greater number of edges will hold more watermarking data

Watermark Embedding Method (Cont)

Difference

Difference

Visual ResultsOriginal

Watermarked

Original Watermarked

Method◦ Perform 2D-DWT to divide image into LL, HL, LH

and HH sub-bands.◦ Select coefficients from each sub-band that

surpass a threshold T2>T1.◦ Compute the correlation z, between the

coefficients of the received image (ti*) > T2 and a

particular watermark (yi ).

Watermark Detection Scheme

Compute the threshold Tz. Detection Occurs when z>Tz. Comparison versus other incorrect

watermarks show that the correct watermark is the only one that surpasses the threshold

Watermark Detection Scheme (cont)

0 50 100 150 200 250-5

0

5

10

15

20

Threshold

Watermarks

DWT Watermarking schemes work well against most forms of image modification◦ Jpeg Compression◦ Downsampling -> Upsampling◦ Gaussian Noise◦ Median Filtering

Technique does not work well in cases of image rotation

Dependent on pixel location

Robustness of Scheme

Robustness of SchemeWatermarked - Med Filt Applied

0 50 100 150 200 250-20

0

20

40

60

80Median Filter Applied - T1 = 15, alpha = 0.4

0 50 100 150 200 250-20

0

20

40

60Gaussian Noise Applied - T1 = 15, alpha = 0.4

WatermarkedWatermarked

0 50 100 150 200 250-2

0

2

4

6Horizontally Flipped Image - T1 = 15, alpha = 0.4

DWT-Based watermarking methods are fast /robust and protect against most forms of manipulation

Schemes based on pixel dependency are robust in most forms of image manipulation, but fail when significant pixels are moved from their original location

Conclusion