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David Andrzejewski, Univ. of Wisconsin-Madison (USA) David G. Stork, Ricoh Innovations, Inc. and Stanford Univ. (USA) Xiaojin Zhu, Univ. of Wisconsin-Madison (USA) Ron Spronk, Queen's Univ. (Canada)

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inferring compositional style in the neo plastic paintings of piet mondrian by machine learning

David Andrzejewski, Univ. of Wisconsin-Madison (USA)

David G. Stork, Ricoh Innovations, Inc. and Stanford Univ. (USA)

Xiaojin Zhu, Univ. of Wisconsin-Madison (USA)

Ron Spronk, Queen's Univ. (Canada)

Inferring compositional style in the neo-plastic paintings of Piet Mondrian by machine learning

stylometry mathematics of style
Stylometry: mathematics of “style”
  • Visual arts
    • Digital authentication of Bruegel, Perugino (Lyu et al, 2004)
    • Jackson Pollock(Taylor, 1999)(Irfan and Stork, 2009)
  • Writings
    • Authorship of the Federalist Papers(Mosteller and Wallace, 1964)
    • Ronald Reagan’s radio addresses (Airoldi et al, 2007)
piet mondrian 1872 1944 avond evening red tree 1908
Piet Mondrian (1872-1944)Avond (Evening); Red Tree (1908)

http://www.artchive.comHaags Gemeentemuseum, The Hague

goal of this work
Goal of this work
  • Better understand compositional style
    • Develop a formal representation of the paintings
    • Extract these representations from paintings
    • Train a generative model
    • Learn relative visual weights of colors
    • Classify true Mondrians versus
      • “fakes” created by the generative model in step 3
      • “earlier states” of the Transatlantic paintings
simplified representation
Simplified representation
  • Vertical/horizontal lines
    • locations
    • extents
  • Rectangles
    • locations
    • sizes
    • colors
    • can span multiple lines
generative modeling
Generative modeling
  • Hypothesize an underlying probabilistic model that generates observed data
  • Many uses in machine learning
    • Make predictions (Naïve Bayes)
    • Generate new examples (Markov model)
    • Interpret parameter values (Linear regression)
  • Given data, learn/train model parameters
    • Our approach: Maximum likelihood estimation (MLE)
our generative model
Our generative model

Canvas aspect ratios (kernel density estimator)

our generative model11
Our generative model

Number of horiz/vert lines (Poisson)

Horiz/vert line spacing (Dirichlet)

our generative model12
Our generative model

Segments are deleted / invisible / left alone (Polya)

our generative model13
Our generative model

Rectangle colors (Multinomial)

additional constraints
Additional constraints

Don’t allow unrealistic “hanging” lines

Require ≥ 1 vertical line

learning color weights
Learning color weights
  • Calculate visual “center of mass”
  • Assume true Mondrians centered at [0.5,0.5]
  • Learn color weights via linear programming
the transatlantic paintings
The Transatlantic paintings
  • Completed in Europe, but then altered after Mondrian’s arrival in the United States
  • A variety of techniques (x-ray, UV, etc) were used to recover the earlier states (Cooper & Spronk, 2001 )
the transatlantic paintings18
The Transatlantic paintings

Composition with Red, Blue, and Yellow (1937-1942)

the transatlantic paintings19
The Transatlantic paintings

Composition with Red, Yellow, and Blue (1935-1942)

slide21

Decision tree classification

  • Very popular technique in machine learning
  • At each iteration, choose a rule to “split” on
  • Resulting partitions should be more “pure” with respect to target classification (true Mondrian or computer-generated fake?)
  • Key feature: resulting trees easy to interpret
  • Estimate accuracy with leave-one-out cross-validation
  • Control over-fitting with pruning
decision tree classification
Decision tree classification
  • 45 true Mondrians versus 45 generated “fakes”
  • 45 true Mondrians versus 11 “earlier states”
example learned decision tree
Example learned decision tree
  • Transatlantic dataset
    • < 1% pixels blue
    • # horiz / # vert < 0.9
    • Low visual “density”
    • THEN Transatlantic
  • Analysis of results
summary
Summary
  • Formal representation and feature extraction
  • Generative model
    • Fitting simple statistics of Mondrians cannot create realistic synthetic paintings
  • Color weights align well with our intuitions
  • Classification
    • Can reliably discriminate true Mondrians vs. computer-generated
    • Cannot do so for true Mondrians vs Transatlantic “earlier states”
      • Underlying images were “nearly complete” (!)