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Detecting Fake Paintings Robert Jacobsen Centre for Stochastic - - PowerPoint PPT Presentation
Detecting Fake Paintings Robert Jacobsen Centre for Stochastic - - PowerPoint PPT Presentation
Detecting Fake Paintings Robert Jacobsen Centre for Stochastic Geometry and Advanced Bioimaging Department of Mathematical Sciences Aalborg University 9th SSIAB Workshop, 2012 Joint work with Morten Nielsen Robert Jacobsen | Detecting Fake
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Problem Statement: Which is Authentic?
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Relevance
The Art Newspaper:
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Interest in this Subject
1998 2000 2002 2004 2006 2008 2010 2012 1 2 3 4 # publications
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Brushstrokes
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Brushstrokes
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Divide and Conquer
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Divide and Conquer
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Details = High Frequencies
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Details = High Frequencies
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Fourier Fails
Fourier: One frequency, lots of pixels Heisenberg: One frequency, one pixel is impossible Realistic: Few frequencies, few pixels. spatial frequency
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Fourier Fails
Fourier: One frequency, lots of pixels Heisenberg: One frequency, one pixel is impossible Realistic: Few frequencies, few pixels. spatial frequency
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Fourier Fails
Fourier: One frequency, lots of pixels Heisenberg: One frequency, one pixel is impossible Realistic: Few frequencies, few pixels. spatial frequency
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Multiresolution Analysis: Digital image
digital image =
- k∈❩2
akφ(x − k), φ(x) = ✶[0,1)2(x).
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Multiresolution Analysis: Digital image
digital image =
- k∈❩2
akφ(2x − k), φ(2x) = ✶[0,1/2)2(x).
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Multiresolution Analysis: Contourlets
digital image =
D
- d=0
- k∈❩2
akψd(x − k).
a(1,1) a(1,2) a(2,1) a(2,2)
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Robert Jacobsen | Detecting Fake Paintings 10 / 15
Multiresolution Analysis: Contourlets
digital image =
D
- d=0
- k∈❩2
akψd(x − k).
a(1,1) a(1,2) a(2,1) a(2,2)
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Robert Jacobsen | Detecting Fake Paintings 10 / 15
Multiresolution Analysis: Contourlets
digital image =
D
- d=0
- k∈❩2
akψd(2x − k).
a(1,1) a(1,2) a(1,3) a(1,4) a(2,1) a(2,2) a(2,3) a(2,4) a(3,1) a(3,2) a(3,3) a(3,4) a(4,1) a(4,2) a(4,3) a(4,4)
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Contourlet properties
Directionality Frequency selection Made for digital images
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Contourlet Transform
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Contourlet Transform
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Hidden Markov Model
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Distances: Multidimensional Scaling
imagei imagej d( HMMi , HMMj ) = dij xi xj xi − xj ≈ dij
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Results: Pieter Bruegel the Elder
3 4 5 6 7 9 11 13 20 120 121 125
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