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 Paintings 1 / 15 Outline 1 Introduction 2 Methods Contourlets Hidden Markov Model 3 Results
Robert Jacobsen | Detecting Fake Paintings 2 / 15 Problem Statement: Which is Authentic?
Robert Jacobsen | Detecting Fake Paintings 3 / 15 Relevance The Art Newspaper:
Robert Jacobsen | Detecting Fake Paintings 4 / 15 Interest in this Subject 4 # publications 3 2 1 1998 2000 2002 2004 2006 2008 2010 2012
Robert Jacobsen | Detecting Fake Paintings 5 / 15 Brushstrokes
Robert Jacobsen | Detecting Fake Paintings 5 / 15 Brushstrokes
Robert Jacobsen | Detecting Fake Paintings 6 / 15 Divide and Conquer
Robert Jacobsen | Detecting Fake Paintings 6 / 15 Divide and Conquer
Robert Jacobsen | Detecting Fake Paintings 7 / 15 Details = High Frequencies
Robert Jacobsen | Detecting Fake Paintings 7 / 15 Details = High Frequencies
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
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
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
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
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
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)
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)
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)
Robert Jacobsen | Detecting Fake Paintings 11 / 15 Contourlet properties Directionality Frequency selection Made for digital images
Robert Jacobsen | Detecting Fake Paintings 12 / 15 Contourlet Transform
Robert Jacobsen | Detecting Fake Paintings 12 / 15 Contourlet Transform
Robert Jacobsen | Detecting Fake Paintings 13 / 15 Hidden Markov Model
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
Robert Jacobsen | Detecting Fake Paintings 15 / 15 Results: Pieter Bruegel the Elder 3 4 5 6 7 9 11 13 20 120 121 125
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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