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# Watermarking of Polygonal Lines

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An Optimal Detector Structure for the Fourier Descriptors Domain Watermarking of 2D Vector Graphics, V. Rodríguez-Doncel, N. Nikolaidis, I. Pitas, IEEE Transactions on Visualization and Computer Graphics, ISSN: 1077-2626, vol. 13(5), pp. 851-863, Sept./Oct. 2007

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### Watermarking of Polygonal Lines

1. 1. AIIA Lab, Department of Informatics V. R. Doncel, N. Nikolaidis and I. PitasV. R. Doncel, N. Nikolaidis and I. Pitas Watermarking of Polygonal LinesWatermarking of Polygonal Lines Department of InformaticsDepartment of Informatics Aristotle 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 VISNET Thessaloniki 25 June 2004
2. 2. AIIA Lab, Department of Informatics IntroductionIntroduction  Polygonal line: sequence of vertices defining a polygonPolygonal line: sequence of vertices defining a polygon Polygonal lines in: GIS data, cartoons, segmented images (fromPolygonal 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
3. 3. AIIA Lab, Department of Informatics  Fourier descriptors: Fourier coefficients of the polygonFourier 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 -70 15 20 25 30 35 40 45 50 55 60 X(i) in the complex plane -30 -20 -10 0 10 20 30 -30 -25 -20 -15 -10 -5 0 5 10 15 20 X(k) b> k > a
4. 4. AIIA Lab, Department of Informatics 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
5. 5. AIIA Lab, Department of Informatics  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
6. 6. AIIA Lab, Department of Informatics  Signal Im and Re parts considered to be independent gaussianSignal 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 theEvery 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
7. 7. AIIA Lab, Department of Informatics  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 10 0 10 -3 10 -2 10 -1 10 0 P false detection Pwatermarknotdetected
8. 8. AIIA Lab, Department of Informatics  Non-idealities happen in real life data.Non-idealities happen in real life data.  Variance is not stationary along the spectrum. ImprovementsVariance 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
9. 9. AIIA Lab, Department of Informatics  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
10. 10. AIIA Lab, Department of Informatics  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
11. 11. AIIA Lab, Department of Informatics  1. Slight differences are visible when zooming in.1. Slight differences are visible when zooming in. Practical work: sample (2)Practical work: sample (2)
12. 12. AIIA Lab, Department of Informatics 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 beWhen multiple contours, fusion techniques have to be developed to avoid mismatching between bordersdeveloped to avoid mismatching between borders