  This paper is about authenticating genuine van Gogh paintings from forgeries.
The authentication process depends on two key steps: feature extraction and
outlier detection. In this paper, a geometric tight frame and some simple
statistics of the tight frame coefficients are used to extract features from
the paintings. Then a forward stage-wise rank boosting is used to select a
small set of features for more accurate classification so that van Gogh
paintings are highly concentrated towards some center point while forgeries are
spread out as outliers. Numerical results show that our method can achieve
86.08% classification accuracy under the leave-one-out cross-validation
procedure. Our method also identifies five features that are much more
predominant than other features. Using just these five features for
classification, our method can give 88.61% classification accuracy which is the
highest so far reported in literature. Evaluation of the five features is also
performed on two hundred datasets generated by bootstrap sampling with
replacement. The median and the mean are 88.61% and 87.77% respectively. Our
results show that a small set of statistics of the tight frame coefficients
along certain orientations can serve as discriminative features for van Gogh
paintings. It is more important to look at the tail distributions of such
directional coefficients than mean values and standard deviations. It reflects
a highly consistent style in van Gogh's brushstroke movements, where many
forgeries demonstrate a more diverse spread in these features.
