A Methodology for Automating the Classification of Works of Art Using Neural Networks

This abstract reports on a paper that describes a new methodology for building a software system capable of automatically classifying works of art according to certain characteristics chosen by a user [1]. The system is to be based on neural networks. The methodology allows a user to set up a neural network able to work with all the parameters that the user considers useful to the classification process. The proposed methodology makes use of well-consolidated algebraic work to build high-performance neural networks capable of processing many parameters chosen by the user, that is, neural networks with few neurons in both input and output. We also report on an experiment testing this methodology, performed on Mondrian's works. The significance of the experiment is in the small number of paintings considered and the great number of parameters chosen to perform the classification process. As is well known, such conditions discourage the use of neural networks for classification purposes. In our case, however, the results obtained by applying the methodology are very encouraging.

In this report we describe the methodology through its application to the classification of Mondrian's artworks.

From 1921 on Mondrian developed two standardized methods for subdividing the canvas: he called them the central one and the peripheral one. . . . In the central one Mondrian divides the plan into four parts with a horizontal and a vertical line, which cross near the center of the canvas. Different brief lines differentiate these quadrilateral subdivisions. In the peripheral system the lines are traced [so] as to obtain a square form, left without any color, in a slightly moved position related to the center of the canvas. The color planes are disposed along the edges [2].

These two systems, corresponding to a syntax, allow the assemblage of basic elements such as lines and areas according to a grammar, not expressly declared by the painter, but borne witness to by Mondrian's frequent references to the concepts of equilibrium and quietude.

The basic principle applied to the paintings we examined is that every line is ascribed a value, which we will call an order.

A line λ is:

• • of order 0 if it is one of the four sides of the painting;

• • of order n+1 if n = max (k, m) where k and m are the order of the lines on which the ends of • are leaning.

Therefore, all lines crossing the painting vertically or horizontally, without interruption, are of the first order. The lines of the second order will be supported at least at one end by a line of the first order, and so on.

We also introduced an analogous notion of order for the areas. The order of an area is the greater of the orders of the lines that constitute its perimeter.

When two or more rectangles of the same color share some common lines defining their perimeters, we consider as an area only the larger rectangle formed by their union. Once the concepts of order are defined for the lines and areas, we can proceed to the decomposition of Mondrian's neoplastic works. We consider, for each work of art, the number of lines of order n (for n = 1, . . . , 7) and the number of areas of color r (for r = red, yellow, blue, grey, black) of order n (for n = 1, . . . , 7).

The elements determined by the modeling constitute the input to the neural network. Note that if we associate every parameter considered (every order of lines and areas) to an input neuron, we would obtain a neural network with 42 neurons as input—not an efficient neural network. Our methodology, essentially based on a mathematical property [3] used in number theory for performing error-free arithmetic (i.e. large-size number calculations using only small-size numbers, as in the Chinese Remainder Algorithm) lets us build a neural network with only two neurons in input. The output constituted three periods of Mondrian's career: 1919-1921, 1921-1925, 1926-1944.

We have compared three models of neural network: the MLP [4], the RBF [5] and...