1

DeepDream reveals the connection between art and mathematics

Stolyarevska Alla, Ukraine

The Preface

The presentation consists of two parts.

The first part consider some examples of connection between art and mathematics, and provides an overview of the methods that implement the algorithmic analysis of artworks:

– Authentication and Attribution;

– Stylometry;

– Dating of Works;

– Predicting the Effects of Conservation Treatment;

– Rejuvenating Faded Works;

– Inferring Artists’ Working Methods;

– Rendering New Views for Visualization.

The second part deals with the methods based on the work of neural networks: – the paintings classification;

– the neural algorithm of artistic style;

– the technique “Inceptionism”;

– the images generation.

The different points of view on whether is Google's Deep Dream art are also considered.

2

3

What is the connection between mathematics and art? Mathematics and art have a long historical relationship. Mathematics and art are related in a variety of ways. Artists have used mathematics since the 4th century BC. Mathematics has directly influenced art with conceptual tools such as linear perspective, the analysis of symmetry, and mathematical objects such as polyhedra and the Möbius strip. The Vitruvian Man, a drawing by Leonardo da Vinci; recursion and logical paradox in engraving by M.C. Escher and in painting by Rene Magritte; Dick Termes and his spheres. All of them are the examples of the relationship between mathematics and art.

3

M.C. Escher, Reptiles, 1943

R. Magritte,

Carte blanche, 1965

Leonardo da Vinci,

The Vitruvian Man, 1490

The golden ratio in art

4

The lines showing the

Divine proportion were

creating using PhiMatrix

golden ratio design and

analysis software.

5

M.C. Escher’s Print Gallery The “Print Gallery” shows a young man, who looks at the picture in the gallery, which recursively contains the image, and so on.

There is an effect of Droste - self-copying, as well as turning and decreasing. There is a mysterious white area in the center of the image.

An image transformation method, first used by the artist M.C. Escher, and described by Lenstra et al. (http://www.josleys.com/article_show.php?id=82)

was generalized for use in a graphics program.

M.K. Escher. «Print Gallery», 1956

5

6

The engravings of Albrecht Dürer

Melencolia: mathematical references include a compass for geometry, a magic square and a truncated rhombohedron, while measurement is indicated by the scales and hourglass.

St Jerome in his study (1514)

Melencolia (1514)

An artist drawing a seated man (1525)

Different techniques, refinement Measurement Mainly central perspective No notion of infinity, no vanishing point Spiritual notion of mathematical harmony 6

7

The tessellations of M.C. Escher

Circle Limit III (1959). Circular self-limiting tessellation art by M. C. Escher (fractals before Mandlebrot invented the term!)

Penrose 'Ghosts' tessellation by M.C. Escher, 1971

7

8

Fractals in art

Fractal sculpture: 3D Fraktal 03/H/dd by Hartmut Skerbisch, 2003

Left: Katsushika Hokusai, "In the Hollow of a Wave off the Coast of Kanagawa" (1830). Right: Fractal curve generated by three similarity transformations.

8

Another relationships between mathematics and art

D.G. Stork (2009) gave 7 problem areas in the history of art: • Authentication and Attribution • Stylometry • Dating of Works • Predicting the Effects of Conservation Treatment • Rejuvenating Faded Works • Inferring Artists’ Working Methods • Rendering New Views for Visualization All these include the algorithmic analysis of artworks.

Stork D.G. (2009) From digital imaging to computer image analysis of fine art. International. Conference on Arts and Technology.

https://pdfs.semanticscholar.org/b432/0020ff08e022345d0565a9385610910c580c.pdf

9

10

The application of Computer Vision in art

An expanding range of techniques from computer vision, pattern recognition, image analysis, and computer graphics are being applied to the art. These efforts are enabled by the growing corpus of high-resolution multi-spectral digital images of art (primarily paintings and drawings), sophisticated computer vision methods, and most importantly the engagement of some art scholars who bring questions that may be addressed through computer methods. The image interpretation relies in great part upon sophisticated algorithms from computer vision

Mathematical algorithms can provide clues about the artistic style of a painting. The composition of colors or certain aesthetic measurements can already be quantified by a computer.

10

11

Computer vision programs Humans use their eyes and their brains to see and visually sense the world around them. Computer vision is the science that aims to give a similar, if not better, capability to a machine or computer. Computer vision programs are concerned with the automatic extraction, analysis and understanding of useful information from a single image or a sequence of images. It involves the development of a theoretical and algorithmic basis to achieve automatic visual understanding. The goal of computer vision is to emulate human vision using digital images through three main processing components, executed one after the other:

Image acquisition; Image processing; Image analysis and understanding.

11

12

Computer vision goes to convolutional neural networks

Computer vision tries to do what a human brain does with the retinal input, it includes understanding and predicting the visual input. That could consist of segmentation, recognition, reconstruction (3D) and prediction (over video data). These give us the overall scene understanding. Classically, many Computer vision algorithms employed image processing and machine learning or sometimes other methods. Recently Convolutional Neural Networks (CNNs) do this purely through end-to-end machine learning. Szegedy C. et al. propose a deep convolutional neural network architecture codenamed Inception that achieves the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014. The main hallmark of this architecture is the improved utilization of the computing resources inside the network. By a carefully crafted design, Szegedy C. et al. increased the depth and width of the network while keeping the computational budget constant. To optimize quality, the architectural decisions were based on the Hebbian principle and the intuition of multi-scale processing. One particular incarnation was called GoogLeNet, a 22 layers deep network, the quality of which is assessed in the context of classification and detection.

https://www.quora.com/What-is-the-difference-between-image-processing-and-computer-vision Szegedy C. et al. (2015) Going Deeper with Convolutions https://www.cs.unc.edu/~wliu/papers/GoogLeNet.pdf

12

13

Basic Definitions for Deep Learning

Deep Learning: Algorithms attempting to model high level abstractions in data to determine a high level meaning.

Deep learning is part of a broader family of machine learning methods based on learning data representations, as opposed to task-specific algorithms.

Deep learning works with data, neural networks, and math.

Deep learning architectures such as deep neural networks have been applied to fields including computer vision.

DeepDream is a computer vision program that go deeper with convolutions.

13 https://www.researchgate.net/figure/Convolutional-network-of-the-GoogLeNet-team-5_fig4_319532211

The Stork’s problem areas in the history of art.

The problems 1-4 1. Authentication and Attribution. The task of authentication is to determine whether a particular,

candidate artist created a given work, and the task of attribution is to determine who among a candidate set of artists likely created the work.

2. Stylometry is a study of stylistics, usually involving statistical analysis and referring to a written text. This term can be applied to a similar study of painting. Stylometry is the discipline of quantifying artistic style, and has been applied to a range of works and creators in music, literature, dance, and other modes of artistic expression.

3. Dating. The expertize of visual analysis of style, brush strokes, colors, techniques, and so on. 4. The effect of conservation. The methods involve modeling the optical physics of varnish as well as

empirical statistical estimation from physical tests and small samples

14

The problems 5-7 and examples

5. Rejuvenating. Some pigments are fugitive, that is, they fade over time; thus, some old master paintings we see today are faded versions of what the artist intended.

6. Artists’ Working Methods. This is the understanding an artist’s marking tools and implements, for instance the nature of paint brushes, pencils, pastel sticks, conte crayons, or other markers.

7. Rendering New Views. Computer methods can provide new views into art works.

The examples are on the next slides:

– Restoration and technical study of The Death of Hyacinthus by Tiepolo

– Berns R. Rejuvenating Faded Works

– The analysis of Girl with a pearl earring by Jan Vermeer

– The analysis of the picture, made by D.Stork

– Rendering New Views for Visualization

– Pollock’s chaotic paintings

– Can mathematics explain the art of Jackson Pollock?

15

Restoration and technical study of The Death of Hyacinthus by Tiepolo

Museo Nacional Thyssen-Bornemisza, Madrid:

Following its recent cleaning, technical study and restoration the painting is exhibited in Room 17 between 23 June 2017 and 14 January 2018, alongside X-radiographs and infrared reflectographs that show all the work undertaken as well as revealing new discoveries and details. The subject of the painting comes from Ovid's Metamorphoses.

16

17

Berns R. Rejuvenating Faded Works

Some pigments of paintings fade over time; thus, some old master paintings have faded versions of what the artist intended. Berns R. developed computer models of such fading based on experimental colorimetric evidence and chemical analysis. He started with the painting as it appears today and runs the fading model “backward” in time, to the date of the painting’s creation. In this way the algorithms “rejuvenate” the colors. The example: the rejuvenating the colors in Georges Seurat’s Un dimanche apr`es-midi `a l’Ile de la Grande Jatte (1884–86), performed by R. Berns.

http://www.cis.rit.edu/people/faculty/berns/seurat/Rejuvenation_results_image.html 17

The analysis of Girl with a pearl earring by Jan Vermeer

Use of light

The use of camera obscura in this work enhances the lighting in the room and helps define starker shadows in the foreground the camera also dramatizes the reflective surfaces such as the pearl earring, the subject's eyes and lips in stark contrasts that intensify their gleam.

18

Use of color Vermeer use a blend of creamier colors for the girl's skin so that it reflect the glow of the light on her face with that dark background to direct the focus automatically be on her. The light coming from the frontal area help to define shadow around the girl, Vermeer uses brown to intense the shadow, so that the facial features look realistic as possible. Vermeer uses the Dutch custom of a dark background to manipulate the colors and techniques to create different contrasts of light around the girl.

http://www.jaffatelaqlam.com/posts/2014/6/24/formal-analysis-of-girl-with-a-pearl-earring-dina-rashid

The analysis of the picture, made by D.Stork

Art historians have long wondered whether Vermeer painted from a live model. To solve this art history mystery, Stork D. (2014) took advantage of the painting’s the soft, glowing light.

He modeled a reflection on a glassy pearl earring until it fit what he saw in the painting. He created a computerized eye with a catchlight that matched the girl’s, taking into account the eye’s natural corneal bump and the direction of the subject’s gaze. He measured the direction of the light washing over the occluding contour of the anonymous girl’s face. He even made a rotatable digital model of the figure as a whole. Then he analyzed the angles from which each part of the painting was illuminated.

The conclusion: Vermeer must have used a live model. It would have been nearly impossible for these light sources to match so closely if he had painted from his imagination.

Stork’s Computer Vision Revolutionizes the Study of Art.

19 http://community.bowdoin.edu/news/2014/05/storks-computer-vision-revolutionizes-the-study-of-art/

Rendering New Views for Visualization Computer methods can provide new views into art works. Criminisi developed uncalibrated methods to reconstruct three-dimensional models from two-dimensional artworks. The problem of reconstructing a three-dimensional scene from single or multiple views has been thoroughly studied in the computer vision literature, and recently has been applied to problems in the history of art. Criminisi pioneered the application of single-view metrology to reconstructing the fictive spaces in Renaissance paintings While the vast majority of realist paintings provide but a single view, some provide multiple views, through mirrors depicted within their tableaus. The contemporary American realist Scott Fraser’s Three way vanitas is a highly realistic still-life containing three mirrors; each mirror provides a new view of the objects in the tableau. Vanitas is a still-life painting of a 17th-century Dutch genre containing symbols of death or change as a reminder of their inevitability.

Criminisi A. (1999) Accurate Visual Metrology from Single and Multiple Uncalibrated Images

https://www.robots.ox.ac.uk/~vgg/publications/1999/Criminisi99b/criminisi99b.pdf

Smith B., Stork D., Zhanga Li. Three-dimensional reconstruction from multiple reflected views within a realist

painting: An application to Scott Fraser’s Three way vanitas

http://www.sfraser.com/pages/docs/SmithStorkZhang.pdf 20

21

Pollock’s chaotic paintings

An interesting modern case of art that broke traditional boundaries – and that has suggestive parallels with recent developments in mathematics – is that of the paintings of Jackson Pollock.

To those who first encountered them, the paintings of Pollock seemed chaotic and senseless. With time, however, the researchers have come to see that they have elements of order, though not a traditional sort. Their shapes are simultaneously predictable and unpredictable, in a fashion similar to the pattern of dripping water from a faucet. There’s no way to predict the exact effect of the next drip. But, if we chart the pattern of drips, it is found that they fall within a zone that has a clear shape and boundaries.

Adams H. (2017) Did artists lead the way in mathematics? https://theconversation.com/did-artists-lead-the-way-in-mathematics-75355

Convergence Reflection of the Big Dipper

21

22

Can mathematics explain the art of Jackson Pollock?

In 1999 the computer pattern analysis techniques were used by R.Taylor to show that Pollock’s paintings are as fractal as patterns found in natural scenery. Since then, more than 10 different groups have performed various forms of fractal analysis on his paintings.

Recent studies by others show that fractal analysis can help distinguish real from fake Pollocks with a 93 percent success rate. But the fractal authenticity of Pollock's paintings turned out to be doomed.

Nonetheless, Pollock’s simultaneously chaotic and orderly patterns have suggested a fruitful direction for mathematics. At some point, it may well be possible to describe what Pollock was doing with mathematical tools, and artists will have to move on and mark out a new frontier to explore.

Richard P. Taylor, Adam P. Micolich, David Jonas, Fractal analysis of Pollock's drip paintings, Nature 399, pp. 422, 1999. Stork D.G. (2009) Learning-based authentication of Jackson Pollock's paintings http://spie.org/newsroom/technical-articles-archive/1643-learning-based-authentication-of-jackson-pollocks-paintings Taylor R. (2017) Fractal patterns in nature and art are aesthetically pleasing and stress-reducing https://theconversation.com/fractal-patterns-in-nature-and-art-are-aesthetically-pleasing-and-stress-reducing-73255

22

23

Art scholars bring questions

Spratt E.L. and Elgammal A. aimed to begin to bridge the gap between computer science and art history, fostering research that will yield effective applications of computer vision in the analysis of art and theoretical reconsideration of aesthetic judgement given the newfound capabilities of machines.

They consider the degree to which computers can aid specialists within art history and examine whether computer vision can offer unique insights to art historians regarding iconographic and stylistic influence.

Spratt, Emily L.; Elgammal, Ahmed (2014). Computational Beauty: Aesthetic Judgment at the Intersection of Art and Science.

Emily L. Spratt is an American art historian. Spratt is considered an authority on the intersection of art, society, and artificial intelligence

Ahmed Elgammal is a Professor at the Department of Computer Science, Rutgers University, Director of the The Art & Artificial Intelligence Lab.

23

24

The algorithmic analysis of artworks

The deep learning techniques and technology help to create images in the style of the great masters like Van Gogh and Picasso.

Namely, the convolutional neural networks learn to separate the content of a painting from its style. The content of a painting consists of objects, shapes and their arrangements but usually does not depend upon the use of colors, textures and other aspects of artistic style.

A painting’s style, extracted in this manner, cannot be viewed on its own: it is purely mathematical in nature. But it can be visualized by applying the extracted style to the content of another painting or photo, making an image by one artist look like it’s by someone else.

24

The paintings classification

Babak Saleh and Ahmed Elgammal at Rutgers University have used new machine learning techniques to train algorithms to recognize the artist and style of a fine-art painting with an accuracy that has never been achieved before.

Saleh and Elgammal began with a database of images of more than 80,000 paintings by more than a 1,000 artists. These paintings cover 25 different styles, each with more than 1,500 examples. The researchers also classified the works by genre.

They took a subset of the images and use them to train various kinds of state-of-the-art machine-learning algorithms to pick out certain features. These include general, low-level features such as the overall color, as well as more advanced features that describe the objects in the image, such as a horse and a cross. The end result is a vector-like description of each painting that contains 400 different dimensions.

The researchers then tested the algorithm on a set of paintings it has not yet seen. And the results are impressive. Their new approach can accurately identify the artist in over 60 percent of the paintings it sees and identify the style in 45 percent of them.

25

Saleh B., Elgammal A. (2015) Large-scale Classification of Fine-Art Paintings: Learning The Right Metric

on The Right Feature https://arxiv.org/abs/1505.00855

Map of artists

Saleh B. and Elgammal A. investigated the applicability of metric learning approaches and performance of different visual features for learning similarity in a collection of fine-art paintings. They implemented meaningful metrics for measuring similarity between paintings.

They used three concepts: Style, Genre and Artist.

These two figures represent graphic of artists’ names where proximity implies similarity.

The algorithm showed spikes in periods of creativity throughout history, with the 16th century high Renaissance period, the late 19th century, and the early 20th century rating highly.

Elgammal A. (2015) Which paintings were the most creative of their time? An algorithm may hold the answers

http://theconversation.com/which-paintings-were-the-most-creative-of-their-time-an-algorithm-may-hold-the-answers-43157 26

The progress in image classification

Artificial Neural Networks have spurred remarkable recent progress in image classification.

We train an artificial neural network by showing it millions of training examples and gradually adjusting the network parameters until it gives the classifications we want. The network typically consists of 10-30 stacked layers of artificial neurons. Each image is fed into the input layer, which then talks to the next layer, until eventually the “output” layer is reached. The network’s “answer” comes from this final output layer.

One of the challenges of neural networks is understanding what exactly goes on at each layer. We know that after training, each layer progressively extracts higher and higher-level features of the image, until the final layer essentially makes a decision on what the image shows. One way to visualize what goes on is to turn the network upside down and ask it to enhance an input image in such a way as to elicit a particular interpretation.

27

Neural networks have information to generate images

Instead of exactly prescribing which feature we want the network to amplify, we can also let the network make that decision.

In this case we simply feed the network an arbitrary image or photo and let the network analyze the picture.

We then pick a layer and ask the network to enhance whatever it detected.

Each layer of the network deals with features at a different level of abstraction, so the complexity of features we generate depends on which layer we choose to enhance.

28 https://adeshpande3.github.io/A-Beginner%27s-Guide-To-Understanding-Convolutional-Neural-Networks/

A feedback loop

If we choose higher-level layers, which identify more sophisticated features in images, complex features or even whole objects tend to emerge. Again, we just start with an existing image and give it to our neural net. We ask the network: “Whatever you see there, I want more of it!” This creates a feedback loop: if a cloud looks a little bit like a bird, the network will make it look more like a bird. This in turn will make the network recognize the bird even more strongly on the next pass and so forth, until a highly detailed bird appears, seemingly out of nowhere.

29

https://ai.googleblog.com/2015/06/inceptionism-going-deeper-into-neural.html

The technique “Inceptionism”

This technique gives us a qualitative sense of the level of abstraction that a particular layer has achieved in its understanding of images. We call this technique “Inceptionism” in reference to the neural net architecture used.

If we apply the algorithm iteratively on its own outputs and apply some zooming after each iteration, we get an endless stream of new impressions, exploring the set of things the network knows about. We can even start this process from a random-noise image, so that the result becomes purely the result of the neural network.

30

https://ai.googleblog.com/2015/06/inceptionism-going-deeper-into-neural.html

The original image influences what kind of objects form in the processed image

31

32

A Deep Convolutional Network for Fine-art Paintings Classification

The authors of the paper (Tan et al.) present a study on large-scale classification of fine-art paintings using the Deep Convolutional Network. At first they trained an end-to-end deep convolution model to investigate the capability of the deep model in fine-art painting classification problem. The argue that classification of fine-art collections is a more challenging problem in comparison to objects or face recognition. This is because some of the artworks are non-representational nor figurative, and might requires imagination to recognize them.

Hence, a question arose is that does a machine have or able to capture “imagination” in paintings? One way to find out is train a deep model and then visualize the low-level to high-level features learnt.

Tan et al. (2016) Ceci n’est pas une pipe: A Deep Convolutional Network for Fine-art Paintings Classification http://cs-chan.com/doc/ICIP2016.pdf

32

The visual art generation

In the domain of visual art generation, Gatys et al. (2015) were able to build a model of a specific painting style and then transfer it to non-artistic photographs. From a technical perspective, art generation is not very different from art style recognition: in both cases, the first step is to accurately model one or several artistic styles.

Gatys et al. (2015) started by training a deep VGG net (Simonyan and Zisserman, 2014) with a large number of pictures from a given artistic style. Then they generated an image that compromised the matching of the style with the matching of the original input image.

Gatys L.A., Ecker A.S., Bethge M. (2015) A Neural Algorithm of Artistic Style

https://www.robots.ox.ac.uk/~vgg/rg/papers/1508.06576v2.pdf 33

Google Deep Dream What the Deep Dream Generator brings to the table that classic Google Deep Dream style generators do not is the ability to train the neural network in a style image of your choosing. You can upload any image as the style image. And of course you can upload any image as the base image that the AI will apply the style to and create a new image from (the previous slide). The possibilities are limitless.

Google unveiled its "Deep Dream" software, a research experiment that converts everyday photos into bizarre, psychedelic images. Since then, the technology has become an internet sensation.

Many of the patterns that Deep Dream sees are animal faces, since the software has been "trained" on lots of pictures of animals. This means dog faces, in particular, show up a lot.

Sometimes when the software doesn't recognise dogs, it sees a lot of eyes. Here is Leonardo da Vinci's Mona Lisa run through Deep Dream.

Lots of eyes are in the background at Edvard Munch's The Scream run through Deep Dream.

34

The image before and after processing

The photograph depicting the Neckarfront in Tubingen, Germany

35

After processing

The Gray Area Exhibition, February 2016

In February 2016, Gray Area Foundation for the Arts and Research at Google held a benefit auction and art exhibition of artworks made using artificial neural networks followed by a day of open forums on machine learning. Let’s see some replicas from there.

Doug Eck, Google Research: “Art and computation are entering a new renaissance. People have  -  over the last 20, 30, 40 years  -  tried in different ways to do creative things with art and specifically with machine learning. I think we’re providing genuinely new tools for artists to work with and I want to be here to watch how it unfolds.” 

Blaise Agüera y Arcas, Google Research: “In addition to being a really cool art show, this is also the inaugural event of a collaboration that we are launching at Google between scientists, researchers, engineers, artists, thinkers  -  that we are calling ‘artists and machine intelligence.’ This is really a beginning and a seed, and something that that we hope is going to be going on for a long time.” 

36

37

Google Deep Dream: 19 of the best images from mesmerising photo software

37

A common theme with non-living subjects or long-range

vistas is that parts of the image are turned into building

domes or pagodas. Here's a view of New York

The code is based on Google's "machine learning"

artificial intelligence software, which looks for patterns it

has been trained to recognise in images fed to it. It then

repeatedly slightly changes the image to make it look like

that pattern, often beyond recognition, to create vivid, often

lucid, images.

38

Is Google's Deep Dream art?

38

And, in conclusion, several opinions.

Paddy Johnson, art critic: It's a tool, not the product.

Rich Oglesby, Creator and editor of Prosthetic Knowledge: The subject of Neural Network Art is still developing.

Anthony Antonellis, Artist: Google Deep Dream is a medium. On its own it's not art, but the images it’s being used to create can be art. Fugly art.

Ben Davis, Art critic: Of course it's art! There's no limit to what you can classify as "art." The question is only ever whether it's good art. And people seem to be very amused by it…. Maybe the smarter and more creative our computers get, the harder it gets for artists to find new strategies to symbolize "human creativity." Maybe the idea of celebrating exceptional "human creativity", in fact, is dated. But I'm pretty sure that's what the cult of "art" and the cult of the "artist" means, even today, so in that sense, Deep Dream just represents a modest new displacement, or challenge…

Conclusions

Let's consider some conclusions regarding the use of mathematical methods in art.

Nowadays with the vast expansion of digital contemporary painting collections, automatic theme stylization has grown in demand in both academic and commercial fields.

The deep neural networks has provided powerful visual features that achieve state-of-the-art results in various visual classification tasks.

Automatic art identification and classification support the expert’s mission of painting analysis, assist in organizing large collections of paintings and can be used for art recommendation systems.

39 Elgammal A. (2014). Computer science can only help – not hurt – art historians http://theconversation.com/computer-science-

can-only-help-not-hurt-art-historians-33780

40

The list of references • Adams H. (2017) Did artists lead the way in mathematics? https://theconversation.com/did-artists-lead-the-way-in-mathematics-75355

• Elgammal A. (2014). Computer science can only help – not hurt – art historians. http://theconversation.com/computer-science-can-only-help-not-hurt-art-historians-33780

• Elgammal A. (2015) Which paintings were the most creative of their time? An algorithm may hold the answers http://theconversation.com/which-paintings-were-the-most-creative-of-their-time-an-algorithm-may-hold-the-answers-43157

• Elgammal A. (2017) Picasso, Matisse, or a Fake? A.I. for Attribution and Authentication of Art at the Stroke Level https://medium.com/@ahmed_elgammal/picasso-matisse-or-a-fake-a-i-for-attribution-and-autehntication-of-art-at-the-stroke-level-f4ec329c8c26

• Gatys L.A., Ecker A.S., Bethge M. A Neural Algorithm of Artistic Style (2015) https://www.robots.ox.ac.uk/~vgg/rg/papers/1508.06576v2.pdf

• Jafarpour S. et al. (2009) Stylistic analysis of paintings using wavelets and machine learning https://services.math.duke.edu/~ingrid/publications/dating.pdf

• Lecoutre A., Negrevergne B., Yger F. Recognizing Art Style Automatically in painting with deep learning. http://www.lamsade.dauphine.fr/~bnegrevergne/webpage/documents/2017_rasta.pdf

• Leone G. The Best Explanation: Machine Learning vs Deep Learning. May 3, 2017 https://www.kairos.com/blog/the-best-explanation-machine-learning-vs-deep-learning

• Leone G. What is Computer Vision and Why Is It Important? May 16, 2017 https://www.linkedin.com/pulse/what-computer-vision-why-important-gabriella-leone/

• Spratt, Emily L. (2017). "Dream Formulations and Deep Neural Networks: Humanistic Themes in the Iconology of the Machine-Learned Image" (PDF). Kunsttexte. Humboldt-Universität zu Berlin. 4

• Spratt, Emily L.; Elgammal, Ahmed (2014). "Computational Beauty: Aesthetic Judgment at the Intersection of Art and Science". ECCV 2014: Computer Vision - ECCV 2014 Workshops. Springer Verlag: 35–53. arXiv:1410.2488  .

• Spratt, Emily L.; Elgammal, Ahmed (November 2014). "The Digital Humanities Unveiled: Perceptions Held by Art Historians and Computer Scientists about Computer Vision Technology". arXiv:1411.6714  .

• Stork D.G. (2009) From digital imaging to computer image analysis of fine art. International Conference on Arts and Technology. https://pdfs.semanticscholar.org/b432/0020ff08e022345d0565a9385610910c580c.pdf

• Stork D.G. (2009) Learning-based authentication of Jackson Pollock's paintings http://spie.org/newsroom/technical-articles-archive/1643-learning-based-authentication-of-jackson-pollocks-paintings

• Tan et al. Ceci n’est pas une pipe: A Deep Convolutional Network for Fine-art Paintings Classification https://www.researchgate.net/publication/305402238_Ceci_n'est_pas_une_pipe_A_Deep_Convolutional_Network_for_Fine-art_Paintings_Classification

40

Thank You for Attention!

41