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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


  1. 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

  2. Robert Jacobsen | Detecting Fake Paintings 1 / 15 Outline 1 Introduction 2 Methods Contourlets Hidden Markov Model 3 Results

  3. Robert Jacobsen | Detecting Fake Paintings 2 / 15 Problem Statement: Which is Authentic?

  4. Robert Jacobsen | Detecting Fake Paintings 3 / 15 Relevance The Art Newspaper:

  5. Robert Jacobsen | Detecting Fake Paintings 4 / 15 Interest in this Subject 4 # publications 3 2 1 1998 2000 2002 2004 2006 2008 2010 2012

  6. Robert Jacobsen | Detecting Fake Paintings 5 / 15 Brushstrokes

  7. Robert Jacobsen | Detecting Fake Paintings 5 / 15 Brushstrokes

  8. Robert Jacobsen | Detecting Fake Paintings 6 / 15 Divide and Conquer

  9. Robert Jacobsen | Detecting Fake Paintings 6 / 15 Divide and Conquer

  10. Robert Jacobsen | Detecting Fake Paintings 7 / 15 Details = High Frequencies

  11. Robert Jacobsen | Detecting Fake Paintings 7 / 15 Details = High Frequencies

  12. Robert Jacobsen | Detecting Fake Paintings 8 / 15 Fourier Fails Fourier: One frequency, lots of pixels Heisenberg: One frequency, one pixel is impossible Realistic: Few frequencies, few pixels. spatial frequency

  13. Robert Jacobsen | Detecting Fake Paintings 8 / 15 Fourier Fails Fourier: One frequency, lots of pixels Heisenberg: One frequency, one pixel is impossible Realistic: Few frequencies, few pixels. spatial frequency

  14. Robert Jacobsen | Detecting Fake Paintings 8 / 15 Fourier Fails Fourier: One frequency, lots of pixels Heisenberg: One frequency, one pixel is impossible Realistic: Few frequencies, few pixels. spatial frequency

  15. Robert Jacobsen | Detecting Fake Paintings 9 / 15 Multiresolution Analysis: Digital image � digital image = a k φ ( x − k ) , φ ( x ) = ✶ [0 , 1) 2 ( x ) . k ∈ ❩ 2

  16. Robert Jacobsen | Detecting Fake Paintings 9 / 15 Multiresolution Analysis: Digital image � digital image = a k φ (2 x − k ) , φ (2 x ) = ✶ [0 , 1 / 2) 2 ( x ) . k ∈ ❩ 2

  17. Robert Jacobsen | Detecting Fake Paintings 10 / 15 Multiresolution Analysis: Contourlets D � � digital image = a k ψ d ( x − k ) . d =0 k ∈ ❩ 2 a (2 , 1) a (2 , 2) a (1 , 1) a (1 , 2)

  18. Robert Jacobsen | Detecting Fake Paintings 10 / 15 Multiresolution Analysis: Contourlets D � � digital image = a k ψ d ( x − k ) . d =0 k ∈ ❩ 2 a (2 , 1) a (2 , 2) a (1 , 1) a (1 , 2)

  19. Robert Jacobsen | Detecting Fake Paintings 10 / 15 Multiresolution Analysis: Contourlets D � � digital image = a k ψ d (2 x − k ) . d =0 k ∈ ❩ 2 a (4 , 1) a (4 , 2) a (4 , 3) a (4 , 4) a (3 , 1) a (3 , 2) a (3 , 3) a (3 , 4) a (2 , 1) a (2 , 2) a (2 , 3) a (2 , 4) a (1 , 1) a (1 , 2) a (1 , 3) a (1 , 4)

  20. Robert Jacobsen | Detecting Fake Paintings 11 / 15 Contourlet properties Directionality Frequency selection Made for digital images

  21. Robert Jacobsen | Detecting Fake Paintings 12 / 15 Contourlet Transform

  22. Robert Jacobsen | Detecting Fake Paintings 12 / 15 Contourlet Transform

  23. Robert Jacobsen | Detecting Fake Paintings 13 / 15 Hidden Markov Model

  24. Robert Jacobsen | Detecting Fake Paintings 14 / 15 Distances: Multidimensional Scaling image j image i d ( HMM i , HMM j ) = d ij x j x i � x i − x j � ≈ d ij

  25. Robert Jacobsen | Detecting Fake Paintings 15 / 15 Results: Pieter Bruegel the Elder 3 4 5 6 7 9 11 13 20 120 121 125

  26. Robert Jacobsen | Detecting Fake Paintings 15 / 15 Results: Pieter Bruegel the Elder 3 125 authentic forgery 2 121 3 4 5 6 1 4 5 20 0 120 13 7 9 11 13 3 9 11 7 −1 127 6 20 120 121 125 −2 −4 −3 −2 −1 0 1 2 3 4

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