Page 30 - AC-2-2

Arts & Communication Identification of Pollock Art

and unintuitive, and therefore, the classification of the test painting i and class c. The exponent is set to -5, which
images using these methods is largely considered a “black was determined through experiments. Unlike some other
30
box.” In UDAT, features were selected according to the distance-based methods, in which just the nearest samples
40
Fisher discriminant scores, which allow identification determine the predicted class, according to the WND that
and analysis of specific measurements that differentiate all paintings in the training set have impact on the predicted
between the classes. Equation II defines the Fisher class. The distance between painting i to class c is determined
discriminant score: by the minimum distance between i and any painting in class
c. Equation III computed the distance between tile i of the test
N ( f T −T , ) 2 painting and class c. Because each painting is separated into 16
W f = ∑ c =1 fc (II)
N σ 2 tiles, the distances from the 16 tiles are averaged, and the class
∑ c =1 , fc that has the training painting with the lowest average distance
to test painting i is predicted as the class of the painting.
Where W is the Fisher discriminant score, N is the
f
number of classes, T is the mean of the values of feature f As mentioned in section 2.1, 47 authentic Pollock
f
in the entire training set, and T and σ are the mean and paintings and 47 paintings that attempt to mimic Pollock’s
2
f,c
f,c
variance of the values of feature f among all training images style were used. The experiments were performed with a
of Class c, respectively. For the differentiation between leave-one-out strategy, such that in each run 46 paintings
authentic and faked Pollock paintings, N is set to 2, as just from each class were used for training, and one painting
two classes of paintings are used (authentic paintings and was used for testing. The steps were repeated until all
faked paintings). paintings were classified.
Since the set of numerical image content descriptors is 3. Results
a pre-defined set of general multipurpose features, many
numerical image content descriptors are not expected to be The results show that out of the 94 paintings, only three
paintings were misclassified. Table 1 shows the confusion
associated with Jackson Pollock’s artistic style. Therefore, matrix of the classification.
the 75% of the numerical image content descriptors with
the lowest Fisher discriminant score are rejected at that The authentic Jackson Pollock painting that was
point from the remainder of the analysis. incorrectly classified as a faked painting was “Number 3”
(1948), providing evidence that the anonymous artists were
As shown in Shamir, Shamir et al., Shamir et al. 23,28,29 able to mimic the artistic style of that painting, as reflected
each image is separated to a 4 × 4 grid of equal-sized tiles, by the numerical content descriptors measured in this
and the numerical image content descriptors are computed experiment. However, the anonymous painters were not
separately from each of the 16 tiles. Therefore, each painting able to mimic the artistic style of the other paintings, as the
is represented by 16 feature vectors. While the separation algorithm was able to classify between authentic and faked
to different tiles can increase the statistical signal, it is Pollock paintings with very high accuracy. Two paintings
required that no tiles of the same painting will be present that were not authentic Pollock paintings were classified
in both the training set and the test set. Therefore, when by the algorithm as authentic paintings. This provides
a painting is allocated to the test set, all of its 16 tiles are evidence that in some cases, anonymous painters are able
allocated to the test set, while allocation of the painting to to mimic the artistic style of Jackson Pollock sufficiently
the training set requires that all 16 tiles of the painting will well so that the mathematical visual content descriptors
be allocated to the training set. of their paintings are similar to the mathematical visual
For classification, UDAT provides distance-based content descriptors of authentic Jackson Pollock paintings.
classification. The distance metrics Table 2 shows the sum of the Fisher discriminant scores

26
used by UDAT is the weighted nearest distance, as of different image numerical content descriptors extracted
shown in Equation III.
∑ [ Wf ( f i − ) ]t f 2 p Table 1. The confusion matrix of the automatic classification
of authentic Jackson Pollock paintings and paintings by
d , ic = ∈ ∑ t Tc f (III)
|T c | anonymous painters who attempted to mimic Pollock’s
artistic style
Where T is the training set of class c, t is a feature vector
c
from T, W is the Fisher discriminant score of feature f, |T| Authentic Fake
c
f
c
is the number of training samples of class c, and p is the Authentic 46 1
exponent. The distance d is the computed distance between Fake 2 46
i,c
Volume 2 Issue 2 (2024) 4 doi: 10.36922/ac.1628