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 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