Entropy as a measure of attractiveness in visual preference of images without content

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Entropy as a measure of attractiveness in visual preference of

images without content

Angelo C. Groot (11027118), Reitze L.H. Jansen (11045442),

Nina Leestemaker (11318228), Marnix Reemst (10817522)

January 20, 2019

University of Amsterdam Institute for Interdisciplinary Studies

Supervisors: Martijn Egas & Jelle Zandveld

Report Bachelor Project B`eta Gamma, 6 EC, conducted between September 5, 2018 and January 20, 2019

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Abstract

In this thesis the relation between visual preference and personality is further investigated in continuance of earlier research that found correlations between personality factors and art movement preference. It brings forward the issue of co-creation of style and content, which we refer to as ”artist bias”. This study aims to contribute to the research field of mapping prefer-ence in content-less imagery to Big Five personality aspects. To gain further understanding of the relation between preference and Big Five personality aspects, this study attempts to mini-mize artist bias. This is done through a novel method based on an evolutionary algorithm, the Pixel-Game. In order to classify structure in the content-less images throughout the study, entropy is used as a measuring method derived from statistical mechanics. With the help of 49 participants, we find correlations for each Big Five aspect but statistical significance has not been reached.

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1 Introduction

In 1994 two Russian artists, Vitaly Komar and Alex Melamid, asked polling company Marttila & Kiley to collect data of aesthetic preference of ten countries worldwide. Based on these results they listed the ‘most wanted’ and ‘least wanted’ paintings of the participating countries. The results were astonishing, almost all the ‘most wanted’ paintings were depicting a blue dominated landscape, with a large body of water, people and animals (Komar & Melamid, 1997).

Dutton (2009) explains the preference of these landscapes in art pieces, to be an inheritance from the Pleistocene, the time in which humans evolved. The sight of an open landscape, but with sufficient hiding place, water and preferably deer, still seems a beautiful and soothing thing to look at today, even though it is not what our habitat looks like nowadays. This suggests preference in art is related to evolutionary adaptations, and is therefore universal (Dutton, 2009). This study also suggests art preference is based on content rather than structure.

Other research has been done that investigates the correlations between aesthetic preferences and personality traits (Chamorro-Premuzic et al., 2010). The main results of this study are that both the factor Openness and the Unconventionality Index correlate with a liking for the art cate-gories ‘Geometric’, ‘Abstract’, and ‘Complex’1. This research, has been executed on the basis of art movements. The cited study had used twenty paintings, separated in five categories (Im-pressionist, Portrait, Geometric, Abstract, and Complex). Although this gives a holistic vision of aesthetic preferences, what exactly makes one prefer a certain art movement remains convoluted.

This is because both content and style in art-pieces are included within the genre. More specif-ically, content and style are not separated in this study, which is also the case in other studies which focus on art movements in general. Since in paintings, and other visual media, the content and style are always co-created, it is not possible to distinguish whether the preference is based on the medias content or style in man-made media. This principle, where content and style are conflated during the creation of a piece, is what we call ‘artist bias’.

This bias might be non-trivial, since research concerning the style-content dichotomy in similarity judgment, has found that in art perception, the processing of style happens later in the brain than the processing of content (Augustin et al., 2008). This is specifically the case after a longer time of exposure. This finding is in line with earlier research (Locher et al., 2007 in Augustin et al., 2008), according to which the processing of an art stimulus begins with a gist reaction that is followed by scrutiny of pictorial features. Furthermore, Augustin et al. (2008) note that the find-ing of style followfind-ing content seems, from a theoretical viewpoint of object perception, astonishfind-ing.

With the idea in mind that content might be a more immediate factor in perception, the assump-tion that content is a conflating factor in art preference might have some merit; to what extent do personality and image preference correlate, when artist bias is minimized? We will investigate this by minimizing the artist bias by using the Pixel-Game as described in section (2.2). For this we require an evolutionary algorithm, a measure of personality, for which we use the Big Five Aspect Scale, and a quantification of image structures with entropy of contrast. We explain these methods in section (2).

This research aims to give novel insights in our knowledge of human aesthetic preference. This is important, since there is little research done on human aesthetic preference where style and content have been separated.

1_{The highest correlations found are between Complex visual art and the factor Openness and the}

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1.1 Personality and preference

To investigate preferences on a personality trait basis, the Big Five personality model has often been used and has found results in widely differing contexts such as reading content, Facebook usage, physical exercise behavior and art and music preference (Schutte & Malouff, 2004; Ryan & Xenos, 2011; Courneya & Hellsten, 1998; Chamorro-Premuzic et al., 2009; Ferwerda et al., 2017). The Big Five personality model, also known as the five factor model (FFM), is an empirical gen-eralization of co-variants of personality traits (Pervin & John, 1999, p. 139). These five factors, which are commonly named Openness, Conscientiousness, Extraversion, Agreeableness, and Neu-rotiscism, were found in multiple areas of research. During years of research, this model has had substantive findings, pertaining to stability, heritability, consensual validation, cross-cultural in-variance and predictive validity (Pervin & John, 1999, p. 139).

A lot of research on the Big Five personality model has focused on a two-level hierarchy, with the five domains at the top subsuming narrower traits called ‘facets’ at a lower level which breaks each of the five domains down into six facets. However, a behavior genetic study in large Canadian and German samples has found that two genetic factors are responsible for the shared variance of the six facet scales that make up each of the Big Five personality model in the NEO-PI-R (Jang et al., 2002 in DeYoung et al., 2007). In this paper DeYoung et al. (2007) first lay out a couple of primary divisions of the domains that can be found in the literature. Then, they identify two factor loadings for each domain (for one of which they initially found three), which account for underlying facets. They name these underlying factors aspects, labeled them and selected 10 items from the IPIP2 _{for measurement of each aspect. The items selected for this measurement tool}

constitute the Big Five Aspect Scale which can be found in appendix (C).

Returning to preference, in their study on personality predictors of artistic preference Chamorro-Premuzic et al. (2009) noted that a wide range of studies have consistently found that more open individuals engage in more general art and visual art activities, identify more with art, and have greater preference for general visual arts. The other Big five traits factors have often been associ-ated in some form with art interests, but the results were often either not replicassoci-ated or inconsistent across studies (Chamorro-Premuzic et al., 2009).

A possible reason for found inconsistencies might be the subdivisions within the Big Five personal-ity model domains, the aspects. The aspects of a domain show high correlations with the domains themselves but might counteract each other in regard to third variables. As has been noted by DeYoung et al. (2007), when two positively correlated variables are related to a third variable in opposite directions, one or both of their associations with the third variable may be suppressed (DeYoung et al., 2007). This is exemplified by the aspects of Extraversion and Politeness. Whereas the aspect Enthousiasm (aspect one Extraversion) is positively correlated with Politeness, the as-pect Assertiveness (asas-pect two Extraversion) is negatively correlated with Politeness.

It might be possible that this phenomenon might play a role in the overall low magnitude of correlation of personality with art preference (Chamorro-Premuzic et al., 2010). This is the first reason we chose to investigate on the level of aspects, instead of factors which is commonly done. One of these aspects is the aspect Orderliness. Orderliness encompasses things like being bothered by disorder, keeping things tidy, and following a schedule. This aspect seems to us a prospective candidate that may correlate negatively with entropy as an analog for disorder. We define our entropy measures in section (2.6). Stated concretely we look to see whether the aspect Orderliness has a pronounced negative correlation with respect to entropy.

To investigate this in the content-minimized manner which was mentioned earlier, we use a new method for this study, the Pixel-Game, in which participants will make a selection between 9

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images. The selections and their corresponding entropy measures can then be statistically analyzed in order to test the above mentioned hypothesis.

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2 Theoretical framework & methods

Here we discuss the methods we use in this research to test our hypothesis. We describe what the Pixel-Game entails, we cover the VSR algorithm we use in the Pixel-Game, and what aspects of physics we use to measure the structures of images.

2.1 The Pixel-Game - gathering labeled samples

In order to gather labeled data representing visual preference, a game has been designed to label batches of 9 images by a human participant. This game, which will be referred to as ‘The Pixel-Game’, consists of 4 phases:

1. The participant is shown a batch of 9 images (which are randomly generated in the first instance) consisting of 8 × 8 pixels with varying colours in gray-scale.

2. The participant selects the image that the participant feels is the most appealing.

3. The image previously selected by the participant is then used to generate a new batch of 9 images that will slightly differ from the previously selected image.

4. This process repeats itself 49 times. The end result is the image selected in the 50th gener-ation.

The initial batch of images given to the participant will have randomly generated gray-scale values. For each batch of images, the predecessor will be linked to the batch in order to allow for measuring derivatives in entropy measures over multiple generations.

2.2 Participants of the Pixel-Game

Participants were primarily recruited through a flyer with a QR code3_{. To attract participants}

eight VVV coupons worth ten euros were offered as lottery prizes among the participants. This QR code led the participants to the website www.thepixelgame.nl. On this website both the BFAS survey and the Pixel-Game were conducted.

2.3 Big Five Aspect Scales

Although the formerly cited research of the influence of personality on preference, has exclusively used the Big Five personality model, either through NEO-PI-R or Big five Inventory, we choose to use the Big Five Aspect Scale. As mentioned before, we have used this scale for scoring according to both the domains and the subdivision into aspects. In this measurement tool each participant fills out a questionnaire with questions which were selected in the paper by (DeYoung et al., 2007).

2.4 The VSR algorithm

To generate the aesthetic preference of humans without an artist bias, the algorithm known from natural selection, the VSR (variation, selection and reproduction) algorithm is used in the Pixel-Game. This algorithm was first described in Darwin’s ‘The origin of species’ as the universal algorithm for speciation. In speciation ‘variation’ stands for random mutations in the genome of organisms, ‘selection’ for the fact that some of these mutations make the organism less or more fit to their environment and ‘reproduction’ the reproduction of surviving and viable individuals (Darwin, 2004).

Thirty six years later, Dennet (1995) describes the VSR algorithm as a ‘Universal Acid’ (Dennet, 1995). Because of substrate neutrality of the algorithm, it is possible to apply the algorithm to

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much more than the origin of species. Just like species are formed without the bias of a creator, this research strives to represent the preferences of the subjects as unbiased as possible.

In artificial intelligence, algorithms inspired on evolution in nature are often used, and are called Evolutionairy Algorithms or EA. An EA is described as an stochastic optimization technique (Tomassini, 1999). This research uses the method of aesthetic selection.

In this research the components of the VSR algorithm are:

1. Variation: In each generation’s images, random mutation will be simulated. 2. Selection: The participant of the Pixel-Game selects an image according to their

personal preference.

3. Reproduction: The selected image will be used as the ‘parent’ of the next generation pixel images.

2.5 Structure in images

With the Pixel-Game working, a method is needed to quantify structure in images so possible cor-relations between structure in images and personality traits can be interpreted. For this methods from statistical mechanics are used as described in (Schroeder, 1999).

Statistical mechanics is a sub-branch of thermodynamics. It is based upon probability theory and uses statistics to describe large systems containing many individual constituents (O (1023)), which are usually atoms or molecules. In our case the large system is an image and the constituents are the pixels. The specific way the individual constituents are ordered is called the microstate. The macrostate is the system and its properties as a whole. Generally speaking, there are lots of microstates which give the same macrostate. An important axiom of statistical mechanics is that each microstate is equally likely to occur. We ensure in the Pixel-Game that this is also the case so we can apply the methods we discuss here.

2.6 Classification of images and contrast entropy

Given that many microstates can lead to the same macrostate we can define a concept called entropy which is a property of the macrostate. Entropy is defined in the following way in statistical mechanics

S = kB log(Ω), (1)

where S is the entropy, kB is Boltzmann’s constant, and Ω is the number of different microstates

which lead to the same macrostate called the multiplicity (Schroeder, 1999). We will set kB = 1

since this constant is mostly to get the correct dimensions used in thermodynamics which are not important in this research.

The second law of thermodynamics states that the entropy tends to always increase or stay con-stant. This is just stating that the system will always find the macrostate which is provided by the most microstates, which is logical if each microstate is as likely to occur as any other. It is however possible for a non-isolated system to decrease its entropy, if the entropy of its surround-ings increases more than the entropy decrease of the system.

If we have an image of n × n pixels, and c is the number of colours a given pixel can have then the number of different pixel images N is given by

N = cn2. (2)

For instance, if we have an 8 by 8 image with 256 different colour possibilities for a given pixel then we can make 25664_{different pixel images. This of course is a huge number so what we want}

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is to be able to classify these images in some way. We will look at a classification based on the contrast of images. The contrast of an image in our case is determined by neighbouring pixels and their colours.

To study neighbouring pixels we will treat the pixel images as square polyominoes (Golomb, 1954). A polyomino is a geometric figure which is made up out of squares or cells. The domino for instance is made up out of two cells. Polyominoes have interiors that are simply connected, i.e. there are no ‘holes’ in our images and no isolated ‘pixel islands’. The number of lines it takes to divide the cells (pixels in our case) of a n by n square polyomino is determined by

f (x) = 2 (x −√x), (3)

where f (x) is the number of lines, and x is the total number of pixels of the image which is always a square (0, 1, 4, 9, 16, ...) for square images so f (x) will always be integer ({f (x), x} ∈ N). Now, if we define a Contrast Score CS as the sum over the colour differences between neighbouring pixels we get the following expression

CS = n X j=1 n−1 X i=1 |ci,j− ci+1,j| + n X i=1 n−1 X j=1 |ci,j− ci,j+1| +√1 2 n,n X i,j=1,1

|ci,j− ci−1,j−1| + |ci,j− ci+1,j−1|

+|ci,j− ci−1,j+1| + |ci,j− ci+1,j+1|

. (4)

The index i indicates the counting of the horizontal pixels increasing to the right and j indicates the counting of the vertical pixels increasing downwards. ci,j is the colour code of the pixel at

position i, j which will be between 0 and 1.

The first double sum term accounts for all the horizontally neighbouring pixels where we first sum over the columns for a row j and then do the same for the next row until we had all rows.

The second double sum term accounts for all the vertically neighbouring pixels where we first sum over the rows for a column i and then do the same for next column until we had all columns.

The last four terms account for the diagonally neighbouring pixels which have a factor of 1/√2 in front of them since they are√2 times farther away to the pixel compared to the directly neigh-bouring pixels.

We can see that if an image has low contrast the sums over the difference |ci,j− ci+1,j| will give a

relatively small value of CS. Similarly if an image has high contrast the sums over the difference |ci,j−ci+1,j| will give a relatively large value of CS. For the maximum contrast case CSmax(which

would be an image like a chess board which is displayed in Appendix D) we simply get the number of lines it takes to divide the cells times 256 (expression (3)) since |ci,j− ci+1,j| = 256. For an

example for an image with very high CS ( 66609) see Appendix (D).

We can now talk about a measure of multiplicity of contrast (the analog of entropy). If the number of different images we can make is given by (2) then they will have different values for CS. The value of CS which has the highest number of images associated with it is the contrast with the highest ‘entropy’ since it has the most possible ways to achieve that contrast value. It will be between the highest contrast and the lowest contrast possible since those are only possible to

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achieve with one pixel configuration. Therefore we can determine the contrast entropy of an image by comparing its value for CS with the average. If we can count the number of different images which give a particular value of CS (which can become problematic if one has 25664 different number of images) and call it Ω which we define as the multiplicity then the analog of entropy will be

SC= log(Ω), (5)

which measures the so-called ‘contrast entropy’ of a particular value of CS. If we randomly gener-ate images and apply evolution for following generations we can test whether or not we also have an analog for the second law of thermodynamics, which states that entropy increases with time (Schroeder, 1999). Evolution between different generations would be the (discrete) analog of time evolution.

Now since the multiplicity in (5) is impossible to determine analytically, since the different number of images is 25664_{, we approximate the multiplicity with a probability density function (pdf). The}

pdf is a function which can be used to infer the probability that a certain data point occurs in the actual set which we want to approximate. In figure (1) below, the probability density for the multiplicity we use is displayed as a function of the Contrast Score CS.

Figure 1: The probability density for multiplicity we use which helps us to approximate the multiplicity plotted as a function of the Contrast Score.

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3 Results

Here we present the results from our research. After cleaning the data by removing all data points concerning participants involved with erroneous input, 49 of the initial 81 participants remained. In the following image, the course of the Pixel-Game has been visualized in terms of Contrast Scores:

Figure 2: Example overview of the development of contrast in the Pixel-Game, this figure depicts the evolution of Contrast Scores of the selected images throughout the Pixel-Game for one of the participants

In Figure (2) we see that for this particular participant, the Contrast Score appears to climb upwards as generations progress.

In order to gain more insight towards the course of evolution during the Pixel-Game, a histogram containing all starting and final Contrast Scores has been plotted together with the probability density from Figure (1).

Figure 3: Starting and Final CS values plotted together with the approximation of the probability density.

Here it can be seen that the starting CS values appear to be roughly following the same probability density distribution as the approximation of the density distribution, whereas the final CS appears to follow a different distribution towards a higher Contrast Score.

In the following table the correlations between the Big Five aspects and the Contrast Entropy are presented. All correlations have been individually computed using Pearson’s correlation coefficient.

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With an original critical p value of α0 = 0.05, the Bonferroni correction gives us a new critical

value of α = 4.17 × 10−4.

Fittest Lowest Highest Range Start Final Gen Fittestr

Withdrawal -0.01 -0.10 0.15 0.00 -0.18 0.10 0.09 0.17 Volatility -0.02 -0.10 -0.12 0.16 -0.16 -0.01 0.17 0.14 Neurotiscism -0.02 -0.11 0.02 0.08 -0.19 0.05 0.15 0.17 Compassion -0.02 -0.16 -0.05 0.18 -0.17 -0.03 0.12 0.16 Politeness 0.04 0.13 0.01 -0.14 -0.03 0.16 0.01 0.05 Agreeableness 0.02 -0.03 -0.02 0.03 -0.12 0.07 0.08 0.13 Industriousness -0.03 -0.04 -0.08 0.11 0.07 -0.14 -0.06 -0.08 Orderliness -0.02 -0.13 0.01 0.12 -0.12 0.02 0.05 0.10 Conscientiousness -0.03 -0.11 -0.04 0.15 -0.03 -0.08 -0.01 0.01 Enthusiasm -0.02 -0.23 0.20 0.15 -0.15 -0.15 0.04 0.13 Assertiveness *-0.08 -0.10 -0.23 0.18 -0.07 -0.22 -0.02 0.03 Extraversion -0.07 -0.22 -0.02 0.21 -0.14 -0.24 0.01 0.10 Intellect -0.03 -0.12 0.12 0.03 -0.16 -0.21 0.00 0.14 Openness -0.05 -0.21 -0.04 0.19 -0.15 -0.11 0.02 0.13 Openness\Intellect -0.05 -0.21 0.05 0.14 -0.19 -0.20 0.01 0.17

Table 1: The correlation table for entropy values acquired through equation (5). ‘Fittest’ describes the entropy value of the chosen individual at each generation. ‘Lowest’ and ‘Highest’ refer to to the lowest and highest Entropy of the individuals chosen by single participant respectively throughout a single game. ‘Range’ indicates the difference between ‘Lowest’ and ‘Highest’ per participant. ‘Start’ and ‘Final’ describe the entropy value of the chosen individual from the first and the last generation. ‘Gen’ is measured as the chronological order of generations such that different participants can be compared at the same stage in the game. ‘Fittestr’ is the entropy value of a

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4 Discussion

In this discussion we will first we discuss some assumptions we made, as well as important decisions in the research process. Then we offer an interpretation of our results as well as a suggestion for future research. We also discuss the Founder effect and the effects of it on our research, as well as the balance between mutation and selection in the Pixel-Game.

4.1 Assumptions and the research process

During this research a number of assumptions were made. Firstly, we assumed that gray-scale is perceived in the same manner as the rgb gray-scale works, such that the difference between two low-value gray-scale codes is perceived similarly as between two high-value gray-scale codes.

Secondly, although two pilots were used create the Pixel-Game in order to ensure that partici-pants both felt like they had as much choice as possible as well as as much control over their choice as possible, we still encountered multiple difficulties. During the first pilot one of these was that pilot-participants reported a too high mutation rate. The difficulty of high mutation can be concluded from the fact that it was hard for them to retain images which they liked as well as selecting images they liked more, while retaining likeness of previous choice. Another difficulty was that participants felt overwhelmed by the sheer amount of different colours.

To counteract the high mutation rate, we opted to offer more choices (twelve 8 × 8 images instead of nine) to participants during a second pilot. To lessen overwhelming we also decided to do our experiment in gray-scale.

During our second pilot, though, participants still reported being overwhelmed. This time it was by the amount of options presented. The participants also still reported some dissatisfaction, with regard to their selection being contested by the mutation.

Also, due to the technical nature of the website, if participants refreshed the page while playing the Pixel-Game, it would effectively cause a participant to return to the founder phase, thus leading for multiple data points in identical generations. We have removed these datapoints.

Although a goal of the study is investigation of preference, with content removed, it seems content is a vital part of preference based selection. Both during our Pixel-Game pilot as well as after several Pixel-Game series where we have spoken to the subject afterwards, we have often been told by the participants they were trying to make some object with their choices.

Another discussion point is that, in the calculation of the contrast, white was used for the edges of the image, since it was white in the game environment. This results in a bias where images with dark edges have a higher contrast value.

Because the sample size is quite small the distribution of scores might be skewed, in following research a bigger sample size will be needed.

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5 Interpretation of results

Contrary to what was hypothesized, Orderliness does not have the most pronounced correlation with any Entropy measure, but as the results can be seen to not have reached statistical signifi-cance, it is not possible to confirm nor reject the hypothesis. As can be seen in Table (1), the only correlation that surpasses the critical p value is Assertiveness-Fittest. Since the magnitude of this correlation is smaller than 0.1, it can be considered a weak or non-existent correlation, thus it does not support any strong claims. Although the current number of participants is too low to allow for significant results, the overlapping area of the Starting and Final Contrast Scores suggest that generally a higher Final Contrast Score is reached than the starting Contrast score was. Another remarkable finding is the distribution of both Agreeableness, and Openness Intellect. Although we do not have a reference population to compare to, the high scores for Openness Intellect and Agreeableness among our participants are in line with findings on volunteer bias which is common among studies which rely on volunteers Dollinger & Leong (1993).the distribution of scores for of our participants can be found in the appendix in section A.

5.1 Founder effect

The Founder effect is defined as the loss of genetic variation that occurs in a small population that is isolated from a bigger population. The population encounters a so called ‘Bottleneck’. Because of a small population, genetic drift4 _{will take place, and in time the new population will}

differ significantly from the parent population (Provine, 2004)(Barton & Charlesworth, 1984). A famous example of the Founder effect are the Galapagos Finches (Grant et al., 1976).

Since in our pixel-image ‘population’ only one ‘individual’ is chosen to give all the genes for the next generation. This is actually an extreme example of the Founder effect. This has quite an effect on the results of the Pixel-Game, because in the first generation of the Pixel-Game there is quite a lot of variation, and after choosing the first image, all other generations will be based on this one image, therefore a lot of variation is lost. In the ‘relative fittest’ column however, Founder effect has been corrected for, see Table (1). Because here the contrast change is measured relative of the first generation. However, when the founder generation starts with a very high contrast, even when selection pressure is on higher contrast, relative fitness will not be very high, since in this case contrast tends to decrease (Figure 5).

5.2 Mutation-selection balance

When selection and random mutation counteract, as in the Pixel-Game, the question arises whether it is possible to preserve certain aspects of an image if it then mutates randomly. This is important to discuss since it allows us to measure if participants significantly tried to select certain properties of an image if the chance of random mutations giving the same images is negligible. We will look at three properties that participants may wish to preserve in their images. The first is the specific colours of pixels, the second is the Contrast score, and the third is the entropy of their images.

5.2.1 Colour preservation

To give an indication of the probability of keeping pixel colours fixed, the following calculation is done. In this calculation we define a mutation of a pixel as a colour change of at least 16 on the gray-scale range for the colour change to become noticeable. Then, the chance that a single pixel retains its colour can be approximated by

4_{Genetic drift is a process where allele frequencies in a population are determined by chance, for example a}

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pc= Rµ+10 µ−10 exp h_(x−µ)2 2σ2 i dx R255 0 exp h_(x−µ)2 2σ2 i dx , (6)

where x is the end result of a mutation among the gray-scale range, σ is the standard deviation of the mutation (30 in our case), and µ is the start value of the pixel5_{. When we evaluate this}

numerically we find that pc = 0.406. If we then look at the chance for the whole image to stay

unaltered we find P = (0.406)64= 9.102 × 10−26 ≈ 0. We therefore conclude that for an image consisting of 64 pixels the chance that it stays unaltered after a random mutation is practically zero.

When you lower the amount of pixels you want to preserve and increase the number of images however, the probability of an unaltered image is

pn= 1 − 1 − (pc)x

9

, (7)

where x is the number of pixels you want to preserve, and the 9 corresponds to the number of images that get produced in the Pixel-Game after a mutation. This is the probability that none of the newly created images maintains the original value for each of the n pixels. We see that this probability is higher and for a low number of pixels this probability is not negligibly small. In figure (4) we plot pxgiven by (7) as a function of the number of pixels x you want to preserve.

Figure 4: Chance of preservation of pixel colours plotted against the number of conserved pixels. In ‘Selecting most similar option’ participants actively select images with the most possible preserved pixel colours. In ‘Random choice’ there is no selection pressure.

5.2.2 Contrast score preservation

Instead of the colours of individual pixels, participants may also try to minimize or maximize the Contrast Score CS. In figure (5) the chance of trying to maximize the Contrast Score is displayed. This is calculated by summing over the sum of probability density on the right side of each contrast

5_{Since this is a numerical approach, µ was chosen at a value of 127, since the grey-scale of the pixels ranges}

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value C and dividing it by the total amount. Since the mutation is given in the change in pixels, the probability of landing on lower or higher contrast values can be calculated in the same manner as holding on to one or more pixels, where an increase at random is calculated by equation (7). Concretely, this gives us equation (8) for lowering contrast by random choice and equation (9) for maintaining or increasing contrast by choice. The graph of chance for decreasing contrast, is given by a vertical mirror image across the mean CS and is displayed below in figure (5).

PCSmax CSi=CS pdf(CSi) PCSmax CSmin=CS pdf(CSi) (8) 1 − 1 − PCSmax CSi=CS pdf(CSi) PCSmax CSmin=CS pdf(CSi) 9 (9)

Figure 5: Chance of preservation of a Contrast Score plotted against Contrast Score. In ‘lower CS choice’ participants actively select images with the lowest possible CS value. In ‘random choice’ there is no selection pressure. ‘convergence lower CS’ is the value of the average lowest CS it is possible to achieve after 50 generations by selecting the lowest CS each generation. ‘mean CS’ is the mean CS value of all possible images based on the pdf. ‘very high CS’ is a relatively very high value of CS.

5.2.3 Entropy preservation

We can also ask the question whether it is possible to achieve a specific entropy value if a player of the Pixel-Game has as goal to achieve for example the least contrast. In this case the player is trying to minimize the entropy of the image. The chance that after a mutation the entropy of the image decreases is defined as the ratio of the number of possible pictures that have lower contrast to the number of possible pictures that have higher contrast

pΩ=

Ω(CS−)

Ω(CS+)

, (10)

where Ω is the multiplicity of specific CS values, CS−are all the values of CS that are lower than

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CS0. In figure (6) below the chance of a lower entropy after a random mutation as a function of

the specific entropy value is displayed.

Figure 6: The chance of getting a lower entropy value after a random mutation as a function of the entropy value S which is calculated in equation (5). In ‘lower S score’ the participant actively tries to keep their entropy low. In ‘random choice’ the participant randomly chooses one of the 9 pixel images. ‘convergence lower S’ is the point which corresponds with the largest multiplicity. ‘very low S’ is a relatively very low value of S.

5.3 Concluding remarks regarding the discussion

What these three things, conservation of pixels, conservation of contrast, and conservation of low entropy concretely mean regarding the results, is that whenever a Big Five aspect correlates with a gain in entropy during the selection process it might both be the result of entropy convergence because it is statistically necessary as well as the preference of the participant. This is exemplified in Table (1). Therefore, future research with larger data sets are still needed, as the p values of the starting values of the entropy exceed the critical value of α. Those Big Five aspects which have the most variance in start entropy are also those aspects which have the most outspoken correlation with regard to relative fitness of the chosen. This, however, is counter intuitive, as these are the same participants which initially would have chosen a lower entropy image. Another option for further research, is focusing on choices between two pixel images, such that every participant makes choices between options from the same total set. This way the variance in starting values is averted and the preference for higher or lower entropy values can be established with as much participants as our current study has.

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6 Conclusion

In this research, correlation between content-less image preference and Big Five Aspects is inves-tigated. For each Big Five Aspect a correlation was found but statistical significance has not been reached. Therefore the hypothesis can not be rejected before further research with a larger sample size has been done.

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A

Other notable Histograms

Figure 7: Histogram showing the distribution of Agreeableness aspect scores of the participants

Figure 8: Histogram showing the distribution of Openness aspect scores of the participants

B

Participant recruitment flyer

In order to gather participants for the Pixel-Game we distributed flyers across Science Park during the data gathering phase of our research. The flyer we used is displayed below in figure (9).

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C

Big Five Aspect Scale

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Here are a number of characteristics that may or may not describe you. For example, do you

agree that you seldom feel blue, compared to most other people? Please fill in the number that

best indicates the extent to which you agree or disagree with each statement listed below. Be as

honest as possible, but rely on your initial feeling and do not think too much about each item.

Use the following scale:

1 - - - 2 - - - 3 - - - 4 - - - 5

Strongly Neither Agree Strongly

Disagree Nor Disagree Agree

1. ___ Seldom feel blue.

2. ___ Am not interested in other people's problems.

3. ___ Carry out my plans.

4. ___ Make friends easily.

5. ___ Am quick to understand things.

6. ___ Get angry easily.

7. ___ Respect authority.

8. ___ Leave my belongings around.

9. ___ Take charge.

10. ___ Enjoy the beauty of nature.

11. ___ Am filled with doubts about things.

12. ___ Feel others' emotions.

13. ___ Waste my time.

14. ___ Am hard to get to know.

15. ___ Have difficulty understanding abstract ideas.

16. ___ Rarely get irritated.

17. ___ Believe that I am better than others.

18. ___ Like order.

19. ___ Have a strong personality.

20. ___ Believe in the importance of art.

21. ___ Feel comfortable with myself.

22. ___ Inquire about others' well-being.

23. ___ Find it difficult to get down to work.

24. ___ Keep others at a distance.

25. ___ Can handle a lot of information.

26. ___ Get upset easily.

27. ___ Hate to seem pushy.

28. ___ Keep things tidy.

29. ___ Lack the talent for influencing people.

30. ___ Love to reflect on things.

31. ___ Feel threatened easily.

32. ___ Can't be bothered with other's needs.

33. ___ Mess things up.

34. ___ Reveal little about myself.

35. ___ Like to solve complex problems.

36. ___ Keep my emotions under control.

37. ___ Take advantage of others.

38. ___ Follow a schedule.

39. ___ Know how to captivate people.

40. ___ Get deeply immersed in music.

41. ___ Rarely feel depressed.

42. ___ Sympathize with others' feelings.

43. ___ Finish what I start.

44. ___ Warm up quickly to others.

45. ___ Avoid philosophical discussions.

46. ___ Change my mood a lot.

47. ___ Avoid imposing my will on others.

48. ___ Am not bothered by messy people.

49. ___ Wait for others to lead the way.

50. ___ Do not like poetry.

51. ___ Worry about things.

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53. ___ Don't put my mind on the task at hand.

54. ___ Rarely get caught up in the excitement.

55. ___ Avoid difficult reading material.

56. ___ Rarely lose my composure.

57. ___ Rarely put people under pressure.

58. ___ Want everything to be “just right.”

59. ___ See myself as a good leader.

60. ___ Seldom notice the emotional aspects of

paintings and pictures.

61. ___ Am easily discouraged.

62. ___ Take no time for others.

63. ___ Get things done quickly.

64. ___ Am not a very enthusiastic person.

65. ___ Have a rich vocabulary.

66. ___ Am a person whose moods go up and down easily.

67. ___ Insult people.

68. ___ Am not bothered by disorder.

69. ___ Can talk others into doing things.

70. ___ Need a creative outlet.

71. ___ Am not embarrassed easily.

72. ___ Take an interest in other people's lives.

73. ___ Always know what I am doing.

74. ___ Show my feelings when I'm happy.

75. ___ Think quickly.

76. ___ Am not easily annoyed.

77. ___ Seek conflict.

78. ___ Dislike routine.

79. ___ Hold back my opinions.

80. ___ Seldom get lost in thought.

81. ___ Become overwhelmed by events.

82. ___ Don't have a soft side.

83. ___ Postpone decisions.

84. ___ Have a lot of fun.

85. ___ Learn things slowly.

86. ___ Get easily agitated.

87. ___ Love a good fight.

88. ___ See that rules are observed.

89. ___ Am the first to act.

90. ___ Seldom daydream.

91. ___ Am afraid of many things.

92. ___ Like to do things for others.

93. ___ Am easily distracted.

94. ___ Laugh a lot.

95. ___ Formulate ideas clearly.

96. ___ Can be stirred up easily.

97. ___ Am out for my own personal gain.

98. ___ Want every detail taken care of.

99. ___ Do not have an assertive personality.

100. ___ See beauty in things that others

might not notice.

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Use the following scale:

1 - - - 2 - - - 3 - - - 4 - - - 5

Strongly Neither Agree Strongly

Disagree Nor Disagree Agree

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BFAS Scoring Key:

Neuroticism

Withdrawal: 1R, 11, 21R, 31, 41R, 51, 61, 71R, 81, 91

Volatility: 6, 16R, 26, 36R, 46, 56R, 66, 76R, 86, 96

Agreeableness

Compassion: 2R,12, 22, 32R, 42, 52R, 62R, 72, 82R, 92

Politeness: 7, 17R, 27, 37R, 47, 57, 67R, 77R, 87R, 97R

Conscientiousness

Industriousness: 3, 13R, 23R, 33R, 43, 53R, 63, 73, 83R, 93R

Orderliness: 8R, 18, 28, 38, 48R, 58, 68R, 78R, 88, 98

Extraversion

Enthusiasm: 4, 14R, 24R, 34R, 44, 54R, 64R, 74, 84, 94

Assertiveness: 9, 19, 29R, 39, 49R, 59, 69, 79R, 89, 99R

Openness/Intellect

Intellect: 5, 15R, 25, 35, 45R, 55R, 65, 75, 85R, 95

Openness: 10, 20, 30, 40, 50R, 60R, 70, 80R, 90R, 100

Reverse response scores for items followed by “R” (i.e. 1=5, 2=4, 4=2, 5=1). To compute scale

scores, average completed items within each scale. To compute Big Five scores, average scores

for the two aspects within each domain.

Reference:

DeYoung, C. G., Quilty, L. C., & Peterson, J. B. (2007). Between facets and domains: 10

Aspects of the Big Five. Journal of Personality and Social Psychology, 93, 880-896.

Contact Colin DeYoung (cdeyoung@umn.edu) for additional information.

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D

Pixel image with maximum CS

The pixel image which has the highest Contrast Score CSmax is displayed in figure (10)

Figure 10: A chessboard pattern pixel image with the maximum value of CS.

Acknowledgment

This research was carried out as the thesis for the bachelor B`eta Gamma. We thank our supervisors Jelle Zandveld and Martijn Egas for their feedback during our research. Also we would like to thank the participants of the Pixel-Gama who took time to play our game and fill in the questionnaire.

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Entropy as a measure of attractiveness in visual preference of images without content