Recently, statistical techniques have been used to assist art historians in the analysis of works of art. We present a novel technique for the quantification of artistic style that utilizes a sparse coding model. Originally developed in vision research, sparse coding models can be trained to represent any image space by maximizing the kurtosis of a representation of an arbitrarily selected image from that space. We apply such an analysis to successfully distinguish a set of authentic drawings by Pieter Bruegel the Elder from another set of well-known Bruegel imitations. We show that our approach, which involves a direct comparison based on a single relevant statistic, offers a natural and potentially more germane alternative to wavelet-based classification techniques that rely on more complicated statistical frameworks. Specifically, we show that our model provides a method capable of discriminating between authentic and imitation Bruegel drawings that numerically outperforms well-known existing approaches. Finally, we discuss the applications and constraints of our technique. The statistical approaches that can be applied to the analysis of artistic style are varied, as are the potential applications of these approaches. Wavelet-based techniques are often used [e.g., (2)], as are fractals (3), as well as multiresolution hidden Markov methods (11). In this paper, we bring instead the adaptive technique of sparse coding to bear on the problem. Although originally developed for vision research (12), we show that the principle of sparse coding (finding a set of basis functions that is welladapted for the representation of a given class of images) is useful for accomplishing an image classification task important in the analysis of art. In particular, we show that a sparse coding model is appropriate for distinguishing the styles of different artists. This kind of discriminatory ability could be used to provide statistical evidence for, or against, a particular attribution, a task which is usually known as "authentication." In this paper, we consider the application of sparse coding to a particular authentication task, looking at a problem that has already been attacked by statistical techniques (2, 10): distinguishing a set of secure drawings by the great Flemish artist Pieter Bruegel the Elder (1525-1569) from a set of imitation Bruegels, each of whose attribution is generally accepted among art historians. The drawings in the group of imitations were long thought to be by Bruegel (13), so that their comparison to secure Bruegels is especially interesting. The sparse coding model attempts to create the sparsest possible representation of a given image (or set of images). Thus, a useful statistic for the attribution task is to compare the kurtosis of the representations of the authentic and imitation Bruegels in order to determine their similarity to a control set of authentic Bruegel drawings. Fig. 1 shows the steps involved in our analysis. We find that a sparse coding approach successfully distinguishes the secure Breugel drawings from the imitations. In addition, we compare our method to two other approaches: (i) the technique in refs. 2 and 10 that uses wavelets (quadrature mirror filters), and (ii) an approach similar to ref. 2 in which the wavelets are replaced by curvelets. Curvelets form a tight frame for the image space and are well adapted for generating sparse representations of curves, thus making them potentially appropriate for representing art images (14, 15). We find that sparse coding is superior (from a statistical point of view) for the task of discriminating imitations from secure Bruegels. These findings suggest that sparse coding could be of great use in visual stylometry. The sparse coding model attempts to describe a space of images by training an overcomplete set of not necessarily orthogonal basis functions that describe the space optimally according to a sparseness constraint (12). Although sparse coding is quite similar to independent component analysis (ICA), it differs in that in sparse coding the kurtosis of the resultant output distribution is maximized, whereas in ICA, the statistical independence of the outputs is maximized. However, if the sparseness constraint applied in a sparse coding model is the logarithm of a sparse probability density function, then the sparseness measure is essentially equivalent to entropy in an information-theoretic approach to ICA (16). The use of sparse coding in the 2D image domain was inspired by work in vision science related to natural scenes. Olshausen and Field showed that training a sparse coding model to represent the space of natural images resulted in basis functions that were similar to receptive fields in primate visual cortex (12). It is generally believed that these functions capture the localized orientation and spatial frequency information that exists in natural scenes (17). The success of sparse coding in the analysis of natural scenes indicates that it could be useful for modeling features in drawings and other 2D media. Indeed, it has been suggested that the sparseness of the statistical structure of works of art, which can only be detected via higher-order statistics, may contribute to the perception of similarity (6, 7, 18) . The sparse coding model, working with small local patches of images, learns functions that could capture the properties of a particular artist's style, to the extent that these properties are perceptible.
In other work REF , the tasks of artistic style recognition and authentication were successfully performed with sparse models to distinguish drawings by Pieter Bruegel the Elder from its imitations.
Quantification of artistic style through sparse coding analysis in the drawings of Pieter Bruegel the Elder.
Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America
Computer Science Medicine