One of the first attempts to measure aesthetics in an image was published by Tong et al. (2004), who proposed a method to distinguish between photographs taken by professional photographers and photographs taken by non-expert (home) users. They used a set of low-level features that describe blur, contrast, colorfulness and saliency, and combined it with general purpose low-level features that capture texture, shape and energy in the frequency spectrum, by using difference-edge histograms. In total, they proposed 21 different features which added up to 846 dimensions. After reducing the dimensionality, they reported classification results comparing Boosting, an SVM and a Bayesian classifier, which performed best.

Using another set of low-level features, Datta et al. (2006) build a classifier for distinguishing images of high aesthetic appeal from other images, as rated by the community of the popular photo-sharing website Photo.net. Overall, the authors collected 3,581 different images and split them into two classes according to their aesthetic rating by the users of the site (low and high rating). They explicitly stated that their goal was not to build the best-performing classifier, but rather to be able to draw conclusions from the best performing features. Their choice of features was based on common intuition, rules of thumb in photography and trends that they observed for the ratings of the collected images. In total, they proposed a set of 56 different features, containing basic ones, such as colorfulness, saturation, hue, size and aspect ratio, as well as adherence to the rule of thirds. The features were selected as follows: First, the authors used a one-dimensional SVM to find the features with the most discriminative power and selected the top 30. Starting with an empty features set, they then iteratively added those features that improved the classification the most. As a result, they found that average hue, average pixel intensity as well as a saturation-based rule of thirds measure contributed the most to the aesthetic value of an image, as rated by human observers.

Ke et al. (2006) designed a system to distinguish between high-quality professional photographs and low-quality snapshots. They reference the work of Tong et al. (2004) but criticize their black-box approach, which prevents them from gaining any insight into why some photos are better than others, although the system by Tong and colleagues performed well for the task. Ke et al. (2006) therefore chose an approach similar to the one by Datta et al. (2006) and designed a set of features that capture image quality. They based their choice of the features on interviews conducted with photographers. Their feature set contained the spatial distribution of edges, color distribution, hue count and blur as well as contrast and brightness. For classification, they used a naive Bayes classifier and tested their system on images that were downloaded from a photo contest website. The blur feature turned out to be the most discriminative metric.

Luo and Tang (2008) extracted very simple features that captured lighting, simplicity, composition or color harmony, based on the subject region and the background of an image. They reported an improvement of classification upon Datta et al. (2006) and Ke et al. (2006) and contributed this success to the distinction of foreground and background, while the previous methods computed their features on the image as a whole.

Besides focusing on low-level features as provided by Ke et al. (2006) and Dhar et al. (2011) also integrate high-level attributes in their system in order to predict aesthetic value and interestingness. According to the authors, high-level attributes define characteristics of images as humans would describe them, and can be classified into compositional attributes (like the rule of thirds), content attributes (like the presence of people) and sky illumination attributes. Dhar et al. (2011) reported improved performance compared to the approach by Ke et al. (2006).

Although the general focus of aesthetic quality assessment in computational aesthetics is on the prediction of ratings of photographs, a few researchers have also proposed methods for quality assessment of paintings. Li and Chen (2009), for example, propose a total of 40 features that capture color, brightness and compositional characteristics of a paintings. Using these features, they use a Bayes classifier as well as AdaBoost on a binary task to predict whether a painting received high or low rating scores. In their work, they provide a detailed discussion of the importance of the individual features.

What all these approaches have in common is that a combination of multiple features is used to predict aesthetic ratings. While this has proven successful for automated aesthetic decision making, there are a number of problems that preclude a deeper understanding of the role of individual features in these decisions. First, because the features are not necessarily independent of each other, it would require more sophisticated statistical methods to extract the influence of each of them. Second, the experimental conditions, under which ratings are obtained in most of the above-mentioned studies, are unknown, unspecified or variable (for example, with regard to the size of the stimuli on the retina, the brightness of the stimuli, contrast settings of the monitors, background illumination, sequence of stimulus presentation etc.,). Third, the rating by users of internet platforms often remain anonymous which precludes any specification of their personal characteristics (sex, age, cultural background etc.,). All these factors might influence the results or introduce artifacts.

In experimental aesthetics, some of the features used in the above combinatorial approaches have been isolated and studied in psychological experiments under well-defined experimental conditions (for a survey of such studies, see section 3).

Generic image features are features that are not explicitly designed for the prediction of image aesthetics, but rather for other popular research topics in computer vision, like object detection and classification, scene understanding, or image retrieval. An example of such features are the SIFT descriptors (scale-invariant feature transform; Lowe, 2004), which were originally designed for feature matching and image stitching. SIFT encodes edge orientations in gray-scale images as a vector (for more recent image descriptors, see Canclini et al., 2013).

The first study to model aesthetic ratings based on generic image features was published by Marchesotti et al. (2011). They used SIFT descriptors together with a color descriptor, motivated by the assumption that aesthetic properties, such as the presence of sharp edges or the saturation of colors, can be described implicitly by these kind of features. The authors chose a Bag-Of-Visual-Words and a Fisher-Vector representation in order to represent prototypical patches for aesthetic and non-aesthetic photographs. As a result, they reported an improvement in classification rates for high-quality and low-quality images, compared to the methods by Datta et al. (2006) and Ke et al. (2006) who used hand-crafted features (see section 2.1.1). While hand-crafted features allow to quantify which feature contributes the most to an aesthetic rating, this interpretability is lost with generic features. Here, conclusions can only be drawn by a comparison of the images that are rated high or low by the model because the features of the model are not deliberately designed to capture known properties of aesthetics, but they rather hide their relation to them. For example, Marchesotti et al. report that all blurry and low-resolution images were rated low in his model, whereas images that displayed foreground objects with sharp edges on out-of-focus backgrounds were rated highly. Moreover, highly-rated images had a dominant color or used complementary colors in their palette; if too many colors were present, images received low scores in general. On the same dataset, Murray (2012) used a low-level contrast model that was originally developed for saliency estimation and showed that it can also be applied to predict aesthetic preferences.

In recent years, deep learning models, in particular Convolutional Neural Networks (CNNs), have started to conquer many subareas in the field of computer vision and artificial intelligence. Although the basic idea of CNNs has already been proposed more than three decades ago (Fukushima, 1980; Lecun and Bengio, 1995), only recently, progress in computing technologies and the availability of huge datasets for training have helped to restore the interest in using CNNs for image processing (Krizhevsky et al., 2012; Simonyan and Zisserman, 2014; He et al., 2015; Huang et al., 2016). CNNs learn a hierarchy of filters, which are applied to an input image in order to extract meaningful information from the input. The training is done using backpropagation, a supervised training algorithm, in which the current output of a network is compared to a desired output. Filter parameters of the network are changed according to their contribution to the current error. When used on a large training set of images, CNNs tend to learn features that resemble Gabor-like edge detectors and color-opponent filters at lower layers of the CNNs. These features are akin to neural responses in the early mammalian visual system. On higher layers of the CNNs, features capture more abstract image content by integrating the lower-layer features (Yosinski et al., 2015). Different open-source implementations exist, which also include a variety of models that were pretrained for object or scene recognition. Their availability enables researchers to either retrain networks that already work well for recognition tasks (a process called fine-tuning), or to use features from pretrained models without any further modification.

CNNs have been applied to the task of rating image aesthetics. Lu et al. (2015) trained a two-column deep neural network simultaneously on global and local views of photographs in order to predict their aesthetic rating class (high or low). The authors motivated their architecture by the observation that the aesthetics of an image is influenced by local cues, such as sharpness, as well as global cues, which capture compositional aspects. They evaluated different cropping strategies for the local image view and report a higher accuracy in the prediction of image aesthetics than reported for previous approaches on the same dataset (Murray et al., 2012).

Dong et al. (2015) applied the AlexNet architecture presented by Krizhevsky et al. (2012), which was trained on 1.2 million images to discriminate between 1,000 different object categories. They used the features of the top convolutional layer, which are computed on the entire image, as well as on five local crops, and trained an SVM on the concatenated features. They improved upon the results by Marchesotti et al. (2011) by a margin of about 10%. Interestingly, their approach did not explicitly use features trained in the context of an aesthetic evaluation, but rather for object recognition, so that the decision whether an image was rated as highly aesthetic or not seemed to rely more on image content than on image form.

Denzler et al. (2016) proposed to use CNNs as model of perception for research in aesthetics. They trained the AlexNet model (Krizhevsky et al., 2012) on different datasets to experimentally evaluate how well pre-learned features of different layers are suited to distinguish art from non-art images using an SVM classifier. They report the highest discriminatory power with a Network trained on the ImageNet dataset, which outperforms a network solely trained on natural scenes.

Kao et al. (2016) proposed a multi-task learning approach, in which a CNN was trained to simultaneously assign semantic and aesthetic labels. They explored different network architectures and showed that a network trained to recognize semantic labels in addition to the aesthetic class outperforms a network trained solely to recognize the aesthetic class of an image. This finding is compatible with the role of both content and form in psychological models of aesthetic experience (see below).

Nowadays, deep neural networks have largely replaced the conventional approach of designing features deliberately in order to reflect aesthetic concepts that derive from human intuition. They outperform the conventional approach easily and have a number of additional advantages: (1) Deep neural networks learn features that are important for aesthetic evaluations automatically, provided that a dataset is big enough. (2) They can combine local image properties, such as sharpness or blur, with global properties, such as composition or color harmony. (3) They can even take into account abstract features, such as image content, without the explicit design of such features by humans. (4) Last but not least, deep neural networks are able to learn image properties that humans may not even be aware of. Such properties include unspecified compositional rules that are employed intuitively by photographers and painters (Bell, 1914; Arnheim, 1954; Redies, 2007, 2015).

While deep learning models are state-of-the-art in aesthetic image evaluation, their success comes at a cost. At present, the understanding of deep features and how they work in object or aesthetic recognition lacks behind. Although there have been attempts to analyze what deep neural networks actually encode at higher layers (Yosinski et al., 2015), we are far from understanding the success of deep learning in any significant detail. For applications in aesthetic image evaluation, it may be sufficient to simply build systems that closely match human perception in deciding whether an image is considered to be beautiful. However, for researchers who want to learn more about aesthetics per se, the limitations of deep learning models are particularly obvious. With handcrafted features, it is easy to draw conclusion about which features contribute to the aesthetic value of an image. Deep neural networks and generic features basically represent a black-box approach that lacks this kind of interpretability. Nevertheless, if we can develop tools to understand deep representations in the future, the drawback of deep learning approaches may eventually turn out into an asset for understanding aesthetics. Such a more profound understanding would also require that deep learning be better explainable in terms of actual neural mechanisms. Although some recent studies lead in this direction (for example, see Brachmann et al., 2017), an abundance of questions remains.

Using a Naive Bayes Classifier, Keren (2002) computed Discrete Cosine Transform (DCT) coefficients on an image and identified the painters of art images (Rembrandt, van Gogh, Picasso, Magritte, Dali) by using a voting scheme, where each 9 × 9 block of an image is assigned the style of an artist. A majority voting for an image yielded the final result and the authors reported an accuracy of 86% for choosing the correct painter. Widjaja et al. (2003) focused on nude paintings and used color of skin in order to identify the artist. They trained an SVM on color profiles of patches extracted from images of four different painters (Rubens, Michelangelo, Ingres, and Botticelli) and reported a rate of correct identifications of 85%. Li and Wang (2004) proposed a system for artist identification based on wavelets and a Multiresolution Hidden Markov Model and tested their approach on a dataset of grayscale Chinese ink images that contained works by five different Chinese artists. Besides the classification of paintings regarding their artist, they found that their modeling approach can also be used as a measure of similarity. To recognize the artist of an image, Lombardi (2005) proposed a system that used a set of low-level features for intensity, edge information, spatial frequency information, as well as a new feature that captured color. Shen (2009) combined a set of global visual features (color, textures, shape) and local visual features (Gabor wavelets) and reported an identification accuracy of 69.7% when distinguishing 25 classical Western painters in a dataset that included Caravaggio, Rubens, Vermeer, and van Gogh. For classification, they used an RBF neural network. Khan et al. (2010) automatically predicted painters (Ingres, Matisse, Monet, Picasso, Rembrandt, Rubens, Titian and van Gogh) by using a Bag-of-Visual-Words approach. They computed SIFT descriptors, as well as color name descriptors and trained an SVM on a dataset which consisted of 40 images each of the eight artist (320 images total). They report an accuracy of 62% for the combination of color and shape features. Condorovici et al. (2013) used a dataset of 1,896 paintings by 15 different artist (including Pollock, Rembrandt, Cezanne, and Magritte), from which they extracted low-level features like an RGB color histogram and edge information by Gabor filters. The authors experimented with eight different classifiers, among which multi-class logistic regression yielded the best results. Cetinic and Grgic (2013) extracted three types of features, namely image-intensity statistics, color-based features, and texture-based features and used a multi-layer perceptron with one hidden layer; they reported a 75.3% accuracy of identifying the correct one among 20 painters.

Overall, it is difficult to compare the performance of the different methods for artist identification because a common database, on which results could be reported and compared to others, is lacking to date. Condorovici et al. (2013) addressed this problem by comparing different methods to their guessing baseline. However, this approach may give an advantage to researcher who select painters who are more diverging to begin with. For example, it may be harder to distinguish an impressionist painting by Claude Monet from one by Paul Cezanne, than to distinguish an abstract drip painting by Jackson Pollock from a surrealist painting by René Magritte.

In summary, the most popular choices for features that are used for the classifiers include a measure to capture texture or spatial frequency, edge histograms for shape detection and histograms for color analysis; all these features are low-level and do not describe image content.

More recently, classification studies in other areas of research no longer rely on one classifier, but report results for a set of different classifiers that are studied in parallel. A popular choice for this type of analysis is the Weka data mining software (Hall et al., 2009).

To predict art styles in various sets of artworks, different approaches have been used. Gunsel et al. (2005) trained an SVM classifier in order to discriminate among five painting styles (Classicism, Impressionism, Cubism, Expressionism, and Surrealism) as well as between twelve different painters. They proposed a system that computes a 6-dimensional vector of low-level features including brightness and gradient information of an image as well as statistics of the gray-level histogram. This system allows a user to query the system for similar paintings of unknown style. For painter and art movement classification, the authors report a high accuracy with a low number false positive results. A different approach was taken by Jiang et al. (2006) who designed a way to retrieve traditional Chinese paintings and then classify them into one of the two styles, Gongbi (traditional Chinese realistic painting) or Xieyi (freehand style). For this task, they used low-level features, which captured color, texture and edges. With a classifier that combined a decision tree and SVMs, they obtained accuracies that are suitable for practical purposes.

Wallraven et al. (2009) asked participants to group images from 11 different art periods (e.g., Gothic, Renaissance, Classicism, Surrealism and Postmodern Art) and different artists into self-selected categories. The resulting categories of artworks corresponded well with the canonical art periods. The authors then computed several low-level features of the images (e. g. raw pixel values, color histograms, frequency, or a GIST descriptor; Oliva and Torralba, 2006) and tested how well the features described the clustering into different art periods. The authors found a low correlation between their set of low-level features and the grouping into art periods and concluded that humans rely more on higher-layer properties. Siddiquie et al. (2009) used multiple kernel learning in their approach and chose texture, histograms of gradient orientations (HOGs), color, and saliency as their features to discriminate between seven different styles (Abstract Expressionism, Baroque, Cubism, Graffiti, Impressionism and Rennaissance). Zujovic et al. (2009) chose five different genres (Abstract Expressionism, Cubism, Impressionism, Pop Art, and Realism). As features, they used steerable filters as well as edge information extracted by a canny edge detector. For color, they calculated HSV histograms and used their bins as features. The classification was done with several different classifiers and the authors reported a best overall accuracy of 69.1% for the AdaBoost classifier. Shamir et al. (2010) classified paintings of nine artists of different genres (Impressionism, Surrealism and Abstract Expressionism) and reached an accuracy of 91.0% in style classification by using a set of features that contained frequency statistics, edge information and color information. Čuljak et al. (2011) focused on texture and color features, stating that such features are closely related to the way humans perceive artworks. As genres, they chose Realism, Impressionism, Cubism, Fauvism, Pointillism and Naïve Art. They tested a range of classifiers and reported best results for an SVM, reaching 60.2% accuracy. Ivanova et al. (2012) used various MPEG-7 descriptors in order to distinguish different art styles. In their experiment, they noted that color features were better suited than texture features for distinguishing between art styles and artists. Condorovici et al. (2015) reported that key to a better accuracy in style discrimination is to let features be inspired by human perception. Accordingly, they used luminance and features that detected shape, texture, edges and color. A total of eight genres was selected for style classification in their study. Like other authors, they tested a set of classifiers and reached best results with an SVM, outperforming their predecessors.

While all articles mentioned above used low-level features, which capture formal aspects of paintings, results from Arora and Elgammal (2012) first indicated that semantic features are also important for style classification. The author compared different features and reported the best results for an SVM trained on classeme feature vectors (Torresani et al., 2010), which represent an image as combined classification scores for many weak classifiers that were trained on low-level descriptors.

Beginning with the work of Krizhevsky et al. (2012) and due to the renewed interest in deep neural networks, these models have also been applied to style prediction. Karayev et al. (2013) used a relatively large dataset of 100K images together with color features, GIST descriptors, saliency, meta-class features (Bergamo and Torresani, 2012) for image content, as well as DeCAF features (Donahue et al., 2014), which are activations of higher layers of CNNs that encode image content rather than image form. They additionally trained a classifier for content features on the categories of animals, vehicles, indoor objects and people. For 25 different painting styles, they reached a mean accuracy of 47.3% with all features in combination. Other than painting style, they also reported results for photographic styles in their article. One of their main conclusions is that style is highly dependent on content. Another approach that also relied on DeCAF features can be found in Bar et al. (2014). These authors reported that a combination of DeCAF features and PiCoDes features (Bergamo et al., 2011), a binary descriptor, which incorporates several low-level descriptors, shows the best performance in style recognition.

Saleh and Elgammal (2015) used the object labels that were produced by the networks proposed in (Krizhevsky et al., 2012) as a feature to discriminate the artist, the style and the genre of roughly 80K paintings. They concluded that classemes (Torresani et al., 2010) are the best way to represent artist, genre, and style-specific properties for discrimination. Tan et al. (2016) conducted several experiments regarding painting style, genre, and artist discrimination and used the architecture proposed by Krizhevsky et al. (2012). They fine-tuned a model that was trained on the ImageNet (Deng et al., 2009) dataset for object recognition, trained a model from scratch, and also tested SVM classifiers on deep features. Interestingly, the fine-tuned model yielded the best results in all tasks and even outperformed the model that was trained from scratch.

Painter and style prediction go hand in hand. In the early days, hand-crafted features that captured the same type of image properties were equally suitable for both tasks. With more and more image data becoming available for training, style prediction can now be trained and tested on exceedingly large sets of images and collections of style categories can be expanded with ease. For painter identification, this is not necessarily the case because, for most artists, only a relatively limited number of paintings are available for training deep networks. As another complicating factor, many artists changed their style during their lifetime. For example, several abstract artists started their career with realistic paintings (for example, Wassily Kandinsky, Piet Mondrian, and Jackson Pollock). As a result, training deep neural networks for painter identification will likely remain more difficult than for style prediction.

For style prediction, the availability of huge collections of digitized artworks will open new possibilities for researchers who will use machine learning methods in the future. For example, popular and widely used datasets of paintings, such as the databases of the Google Art Project and WikiArt (formerly WikiPaintings), contains several thousands of annotated artworks.

As outlined for rating prediction (section 2.1), deep features are getting more and more popular for style prediction and increasingly replace hand-crafted features because they are capable of representing semantic information also. For example, Chiaroscuro style paintings often depict indoor scenes and people, while Impressionist paintings frequently display landscapes. Therefore, deep features do well on style prediction and prove to be more powerful than low-level features that focus on image form only. On the other hand, as with the prediction of ratings, interpretability is not as high as it has been with purposely designed features.

Although the vast area of computer-generated artistic images is beyond the scope of the present review, we would like to point out that deep models have boosted recent developments in this area that harbor a large potential for understanding aesthetics. Gatys et al. (2016) proposed an algorithm that can transfer the style of any image to another, by matching the statistics of the gram matrix of lower-layer features, as well as image content that is represented at higher layers. They demonstrated that arbitrary images can be redrawn in the style of famous paintings from Van Gogh or Picasso. More recent generative models (Generative Adversarial Networks [GANs]; Goodfellow et al., 2014) are even capable of matching the style of entire collections of artworks, as shown by Zhu et al. (2017), who used collections of paintings by Monet, Cezanne and Van Gogh to redraw landscape photographs to match the respective painter's style. While GANs are advanced methods that originate in Machine Learning, other methods like the approach by Malo and Simoncelli (2015) focus more on using physiologically plausible architectures to generate images with similar textures. This latter approach is likely to have more explanatory power because it makes use of mathematical tools that are more directly related to findings from vision science.

Among the methods that address art historical questions, we can discern two areas of interest. First, some researchers have developed computational methods to study artistic technique. Second, the influence of a painter on the style of other artists has been studied.

Criminisi et al. (2002) developed methods for investigating the perspective and the reconstruction of the 3-dimensional space from realistic paintings. This information can help art historians to answer spatial questions like, for example, to determine the height of people or objects that are depicted in paintings. In another study, Criminisi and Stork (2004) analyzed inaccuracies in the perspective cues in a painting by Jan van Eyck and demonstrated that is it unlikely that the painter used optical aids like mirrors during the creation of the painting “Portrait of Arnolfini and his wife.” Stork and Johnson (2006) applied a technique that was originally designed for detection of tampering in photographs, in order to localize light sources in paintings. They presented such an analysis for Georges de La Tour's painting “Christ in the carpenter's studio.” Based on their findings, they rebutted the claim that the light source of the depicted scene lays outside the painting, which could have been an indication of the use of optical aids as well. Papaodysseus et al. (2006) investigated the use of stencils in late Bronze Age wall paintings by applying a Hough Transform (a method for finding instances of mathematically defined shapes in images), and identified a set of stencils that were likely used during creation of the wall paintings. Kim et al. (2014) propose statistical measures to quantify the usage of individual colors, their variety in a painting, and the roughness of the brightness of a painting and report significant differences for different art periods. Berezhnoy et al. (2005) studied color and texture features in paintings by van Gogh. They confirmed that the painter increasingly made use of opponent colors later in his lifetime. Later, Berezhnoy et al. (2009) proposed a method for aiding art experts in automatically extracting the orientations of brushstrokes in a painting.

The study of a painter's influence on other artists, which can be investigated by detecting similarities between images, is a popular topic of research in computational aesthetics. Bressan et al. (2008) used SIFT features and local color statistics to compute similarities between images based on a Fisher Kernel representation of the images. Shamir and Tarakhovsky (2012) used a set of 4,027 features that represented many different aspects of visual appearance (e.g., shape, texture, color) and computed a phylogeny, which shows distinct clusters for classic artists like Vermeer or Rembrandt and for modern artists like Jackson Pollock, Marc Rothko, or Wassily Kandinsky. Wang and Takatsuka (2012) extracted color and composition features, which allowed them to classify Renaissance, Impressionist and Postimpressionist paintings. Furthermore, they applied hierarchical clustering in order to identify relationships among artists and demonstrated that they can detect influences of preceding art periods on Picasso's works. Abe et al. (2013) proposed a framework for determining artistic influences based on the semantics of images. By using classeme features to compute distances between images (Torresani et al., 2010), they succeeded in identifying novel cases where one artist influenced another, which had not been considered by art historians before. Elgammal and Saleh (2015) approached the problem of assessing creativity in terms of the originality of an artwork and represented influences and originality as a graph. Relying on classemes for subject matter and GIST features for compositional aspects, they computed a creativity score for each painting in comparison to contemporary artworks.

Another example where computational methods can help art historians is in the detection of forgeries, which is a problem closely related to artist identification. In artist identification, the works of an artist are identified among many others that usually possess rather different characteristics, which are often obvious even to laymen. However, when detecting forgeries, any differences may no longer be as easy to spot so that the task may be difficult even for art experts. Both approaches aim at identifying unique features of an artist, but an algorithm, which works well for artist identification, may not work as well for authentication and vice versa.

For example, Lyu et al. (2004) performed a wavelet decomposition of eight works attributed to the Renaissance painter Pieter Bruegel the Elder and five imitations of his work. From the wavelet statistics, they extracted a feature vector for subimages of each image and performed authentication by measuring distances between these high-dimensional points. They found that imitations of Bruegel's works differ significantly from authentic paintings. In another application of their technique, they solved the problem of “many hands.” Here, art historians are interested in how many different painters contributed to one particular painting. Using their method, they were able to identify at least four different painters for face depictions in an image attributed to Pietro Perugino, a notion that is shared by art historians. Polatkan et al. (2009) introduced a new dataset of images that included originals and purposely copied paintings. Using the parameters of a Hidden Markov Model trained on wavelet coefficients, they succeeded in discriminating the copies from the originals. Li et al. (2012) studied the brushstrokes of paintings by Vincent van Gogh and used them for comparison with contemporaries and forgeries, as well as for dating different periods of van Gogh's work. Johnson et al. (2008) summarize different approaches by three research groups for discriminating between 82 original van Gogh paintings, 6 non-original works, and 13 paintings of questionable authorship. All approaches are based on a wavelet decomposition of the images.

The work of American painter Jackson Pollock has received particular interest from the scientific community. Taylor et al. (1999) performed a fractal analysis of the artist's drip paintings and found that the fractal dimension, computed using a box-counting approach, increased over the artist's lifetime. The authors suggested that this method could be used for authenticating or dating individual works by the artist. Taylor's approach was criticized by Jones-Smith and Mathur (2006), who showed that they could easily generate images that had the same fractal properties albeit not being similar to Pollock's paintings in their aesthetic value. Stork (2009b) later defended Taylor and colleagues and argued that, while one feature in isolation may not be sufficient for the analysis, a combination of multiple fractal measures can provide useful information. Shamir (2015) used a set of features from biological image analysis (Shamir et al., 2008) and reported an accuracy of 93.0% in discriminating between original and non-original drip paintings.

Hughes et al. (2010) applied a sparse coding scheme in order to compare authentic Bruegel paintings with works by imitators. They demonstrated that their technique can be used to discriminate between authentic and non-authentic Bruegel drawings. Olshausen and DeWeese (2010) suggested that the methods of detecting forgeries brought forward by Hughes et al. (2010) could be useful not only in learning styles of particular artists but also for using these statistics to generate novel images. Montagner et al. (2016) proposed a system for forgery detection of paintings by the Portuguese painter Amadeo Souza-Cardoso. In their approach, they combined a brushstroke analysis using SIFT features on RGB images and an analysis of the pigments in the painting by hyperspectral imaging. Using a dataset of 12 images, among which one was not painted by the artist, they successfully determined the authenticity of the original paintings.

In summary, computational methods can provide support for art historians who study individual paintings or artists. Computational methods have aided art historians in multiple ways, for example by enabling them to detect the use of practical aids like stencils or projectors in the creation of an artwork. Furthermore, telling forgeries from originals as well as the dating of an artist's work can be improved with the help of algorithmic approaches. Other applications are the exploration of hitherto unknown influences between artists.