Jaroslaw Kutylowski 1

HEINZ NIXDORF INSTITUTEUniversity of Paderborn

Algorithms and Complexity

Robust Undetectable Interference Watermarks

Ryszard Grząślewicz (WUT)

Mirosław Kutyłowski (WUT)

Jarosław Kutyłowski (HNI)

Wojciech Pietkiewicz (WUT)

Jaroslaw Kutylowski 2

HEINZ NIXDORF INSTITUTEUniversity of Paderborn

Algorithms and ComplexityIntroduction

Motivation• undetectable watermarks cannot be detected in an image• only the owner can prove his rights to an image using

a secret private key• not suited for web crawlers

Key features of our scheme• watermarks encoded in spatial domain• resistant against attack preserving distance between points

(filtering, rotation, JPEG compression)• resistance against some attacks changing distance between points• watermark can be reconstructed from a small part of image• original image not needed for reconstruction• large computational effort for reconstruction needed

Jaroslaw Kutylowski 3

HEINZ NIXDORF INSTITUTEUniversity of Paderborn

Algorithms and ComplexityPhysical motivation

Interference – Young‘s experiment

Jaroslaw Kutylowski 4

HEINZ NIXDORF INSTITUTEUniversity of Paderborn

Algorithms and ComplexityScheme overview

Watermark image

Interference image

Watermarked image

Reconstructed watermark image

Cover image

Jaroslaw Kutylowski 5

HEINZ NIXDORF INSTITUTEUniversity of Paderborn

Algorithms and ComplexityConstruction of simple interference image

Watermark image• all black with some white points• white points are light source• set of white points

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Jaroslaw Kutylowski 6

HEINZ NIXDORF INSTITUTEUniversity of Paderborn

Algorithms and ComplexityConstruction of simple interference image

Interference image• interference image is placed at distance

on top of watermark image• each “light source” from influences

each point of interference image • distance and determine strength

of influence

• this is approximation of real physicalinterference image

• drawback: visible pattern

Jaroslaw Kutylowski 7

HEINZ NIXDORF INSTITUTEUniversity of Paderborn

Algorithms and ComplexityConstruction of encrypted interference image

Interference image• consider the influence of one point from• previously it influenced a point at distance with

• a ring at distance consists of cells of size • intensity of each cell defined by value of hash function• the angle is taken modulo – repetition of the same sequence• key is needed for computation of values

• interference image does not containvisible patterns

Jaroslaw Kutylowski 8

HEINZ NIXDORF INSTITUTEUniversity of Paderborn

Algorithms and ComplexityScheme overview

Watermark image

Interference image

Watermarked image

Reconstructed watermark image

Cover image

Jaroslaw Kutylowski 9

HEINZ NIXDORF INSTITUTEUniversity of Paderborn

Algorithms and ComplexityReconstruction of watermark

General idea• determine the intensity of each point of the watermark image

– take the watermarked image (cover image + interference image)

– generate interference image for point

– compare them

– if there is strong “similarity” – assign a high value

watermarked image interference image for

Low similarity

small pixel value

High similarity

large pixel valueExample with simple interference

image not with encrypted – usually the encrypted would be used

Jaroslaw Kutylowski 10

HEINZ NIXDORF INSTITUTEUniversity of Paderborn

Algorithms and ComplexityReconstruction of watermark

Idea (continued)• look for the highest valued points• check whether these points form a valid watermark

– use equilateral triangles

– certain number of triangles of specific edge length must be found to form a watermark

Properties• for the points actually in

– there will be a large similarity between the watermarked image and the interference image

• there are points to check• for each point operations are needed to compare the images• key is needed for reconstruction

Jaroslaw Kutylowski 11

HEINZ NIXDORF INSTITUTEUniversity of Paderborn

Algorithms and ComplexityReconstruction of watermark

Additional operations• the reconstruction must be repeated for all rotations with degree

– this yields resistance against rotations of the image

• the scale factor of the image must be determined– take a small part of the image

– there should be at least one “white point” from in this part

– check different scale factors and perform reconstruction of this image part for it

– determine scale factor with largest peak value – this peak corresponds to a white point from the watermark

– perform full reconstruction with this scale factor

Jaroslaw Kutylowski 12

HEINZ NIXDORF INSTITUTEUniversity of Paderborn

Algorithms and ComplexityExperimental results

Evaluation against StirMark 3• 77 of 89 tests passed• Cropping – all passed• Removing rows/columns – only lighter one passed• Flip – all passed• Scaling – all passed• Change aspect ratio – all passed• Rotation with cropping – for rotation smaller than 30% passed• Rotation with cropping and scalling – for rotation smaller than 30% passed• Shearing – only simple ones passed• Linear transformations – not passed• StirMark – not passed• Gaussian filtering – all passed• Sharpening – all passed• Median filtering – all passed• LRAttack – all passed• JPEG compression – all passed

Jaroslaw Kutylowski 13

HEINZ NIXDORF INSTITUTEUniversity of Paderborn

Algorithms and ComplexityConclusions

Results• robustness against attacks basing on filtering and local editions

of image shown• robustness against some linear transformations (rotating, scaling)

shown

Further work• methods for detection of general linear transformations needed• methods for detection of nonlinear transformations needed

Jaroslaw Kutylowski 14

HEINZ NIXDORF INSTITUTEUniversity of Paderborn

Algorithms and Complexity

Thank you for your attention!Thank you for your attention!