Watermarking of Polygonal Lines

AIIA Lab, Department of InformaticsAIIA Lab, Department of InformaticsAristotle University of ThessalonikiAristotle University of Thessaloniki

V. R. Doncel, N. Nikolaidis and I. PitasV. R. Doncel, N. Nikolaidis and I. Pitas

Watermarking of Polygonal Watermarking of Polygonal LinesLines

Department of InformaticsDepartment of InformaticsAristotle University of ThessalonikiAristotle University of Thessaloniki

GREECEGREECE

e-mail: e-mail: {victor,nikos,pitas}@zeus.csd.auth.gr{victor,nikos,pitas}@zeus.csd.auth.gr

VISNETThessaloniki 25 June 2004


IntroductionIntroduction

Polygonal line: sequence of vertices defining a polygonPolygonal line: sequence of vertices defining a polygon

Polygonal lines in: GIS data, cartoons, segmented images (from Polygonal lines in: GIS data, cartoons, segmented images (from video), CAD, general vectorial graphicsvideo), CAD, general vectorial graphics

Robust watermark system using Fourier descriptorsRobust watermark system using Fourier descriptors


Fourier descriptors: Fourier coefficients of the polygon Fourier descriptors: Fourier coefficients of the polygon considered as a function in the complex planeconsidered as a function in the complex plane Sample: 1. USA 2. USA in the Fourier domainSample: 1. USA 2. USA in the Fourier domain

Watermark Embedding: 1Watermark Embedding: 1

-120 -115 -110 -105 -100 -95 -90 -85 -80 -75 -7015

20

25

30

35

40

45

50

55

60X(i) in the complex plane

-30 -20 -10 0 10 20 30-30

-25

-20

-15

-10

-5

0

5

10

15

20X(k) b> k > a


Watermark Embedding: 2Watermark Embedding: 2

Watermark:

Spread spectrum techniques

W(k) A pseudorandom signal, generated with an integer key

W(k) takes values of ±1 randomly, N length

Watermark is multiplicative: |X’(k)|=|X(k)| (1+pW(k)) Watermark is only embedded in medium frequencies


Correlation is calculated: C=Correlation is calculated: C=ΣΣ |X’(k)|W(k) |X’(k)|W(k)

Random variable with 0 mean if no key or wrong key providedRandom variable with 0 mean if no key or wrong key provided

Compared against a thresholdCompared against a threshold

For big N, it performs well (central limit theorem applies)For big N, it performs well (central limit theorem applies)

Watermark Detection: CorrelatorWatermark Detection: Correlator


Signal Im and Re parts considered to be independent gaussian Signal Im and Re parts considered to be independent gaussian processes: Modulus amplitudes follows a Rayleigh distributionprocesses: Modulus amplitudes follows a Rayleigh distribution

Every sample is expected to have a value according to the Every sample is expected to have a value according to the watermark for that point, different if watermark not present.watermark for that point, different if watermark not present.

Likelihood for every sample is considered. Likelihood for every sample is considered.

Better results than the correlator, but slowerBetter results than the correlator, but slower

Watermark Detection: OptimalWatermark Detection: Optimal


Correlator is faster but has higher error probabilityCorrelator is faster but has higher error probability Example for a very small embedding power (0.1)Example for a very small embedding power (0.1) In the ROC shown, correlator in green, optimal in redIn the ROC shown, correlator in green, optimal in red

Watermark Detection: ComparisonWatermark Detection: Comparison

10-3

10-2

10-1

100

10-3

10-2

10-1

100

P false detection

P w

ater

mar

k no

t det

ecte

d


Non-idealities happen in real life data.Non-idealities happen in real life data.

Variance is not stationary along the spectrum. Improvements Variance is not stationary along the spectrum. Improvements have to be done in the variance estimation.have to be done in the variance estimation.

Watermark Detection: Watermark Detection: ImprovementsImprovements


Reads ESRI’s shapefile format GIS dataReads ESRI’s shapefile format GIS data Extracts polygons and applies/read watermarksExtracts polygons and applies/read watermarks

Practical work: PolyWaterPractical work: PolyWater


1. Original and watermarked polygon: very small difference1. Original and watermarked polygon: very small difference 2. Rigth vs. wrong keys test: clear detection2. Rigth vs. wrong keys test: clear detection

Practical work: samplePractical work: sample


1. Slight differences are visible when zooming in. 1. Slight differences are visible when zooming in. Practical work: sample (2)Practical work: sample (2)


ConclusionConclusion

Watermark for polygons robust against attacksWatermark for polygons robust against attacks

Good performance for N > 1000 pointsGood performance for N > 1000 points

When multiple contours, fusion techniques have to be When multiple contours, fusion techniques have to be developed to avoid mismatching between bordersdeveloped to avoid mismatching between borders

Watermarking of Polygonal Lines

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