vision

Article The Influence of on Algorithms that Predict the Speed and Comfort of Reading

Arnold Wilkins 1,* , Katie Smith 1 and Olivier Penacchio 2 1 Department of Psychology, University of Essex, Wivenhoe Park, Essex, Colchester CO4 3SQ, UK; [email protected] 2 School of Psychology and Neuroscience, University of St. Andrews, St Mary’s Quad, South Street St Andrews, Fife KY16 9JP, UK; [email protected] * Correspondence: [email protected]

 Received: 21 January 2020; Accepted: 9 March 2020; Published: 12 March 2020 

Abstract: 1. The speed with which text can be read is determined in part by the spatial regularity and similarity of vertical letter strokes as assessed by the height of the first peak in the horizontal autocorrelation of the text. The height of this peak was determined for two passages in 20 fonts. The peak was unaffected by the size of the text or its content but was influenced by the font design. Sans fonts usually had a lower peak than serif fonts because the presence of serifs usually (but not invariably) resulted in a more even spacing of letter strokes. There were small effects of justification and font-dependent effects of font expansion and compression. 2. The visual comfort of images can be estimated from the extent to which the Fourier amplitude spectrum conforms to 1/f. Students were asked to adjust iBooks to obtain their preferred settings of font and layout. The preference was predicted by the extent to which the Fourier amplitude spectrum approximated 1/f, which in turn was jointly affected by the design of the font, its weight and the ratio of x-height to line separation. Two algorithms based on the autocorrelation and Fourier transformation of text can be usefully applied to any orthography to estimate likely speed and comfort of reading.

Keywords: font; spatial periodicity; discomfort; reading speed; autocorrelation; Fourier amplitude spectrum

1. Introduction There have been many studies of the effects of typographic variables on reading [1,2] including the effects of letter size (x-height)[3], line spacing (leading)[4] and (e.g., serif vs. sans serif [5]. Text is a complex stimulus in which the effects of typographic variables interact together and with other variables such as familiarity [6] to determine the speed and comfort of reading. In this paper, it is shown that despite this complexity, simple algorithms that measure the shape of text are able to predict both reading speed and choice of font. They do so by registering the extent to which the spatial periodicity of text interferes with vision, and may have relevance for both normal and low-vision reading. One algorithm measures the periodicity from letter strokes, whereas the other measures aspects of the periodicity from lines of text.

2. Horizontal Spatial Periodicity Weaver [7] reported the case of a lady who experienced seizures when reading. She found that the seizures occurred only when she was reading material printed in Times or , and not when reading the same material printed in or . Her observations were confirmed electrophysiologically. Times and Palatino are fonts with serifs, whereas Arial and Verdana are sans serif fonts. Serifs have little effect on reading [5]. However, the fonts differ not only with respect

Vision 2020, 4, 18; doi:10.3390/vision4010018 www.mdpi.com/journal/vision Vision 2020, 4, 18 2 of 16 Vision 2020, 4, x FOR PEER REVIEW 2 of 16 toserifs serifs but but in inthe the periodicity periodicity of ofthe the letter letter strokes, strokes, as asillustrated illustrated in Figure in Figure 1. 1In. InArial Arial and and Verdana, Verdana, the thespace space between between the the strokes strokes within within a aletter letter is is greate greaterr than than that that between between letters, letters, whereas inin TimesTimes andand Palatino,Palatino, thethe letterletter strokesstrokes areare evenlyevenly spaced,spaced, givinggiving thethe typefacetypeface aa spatialspatial regularityregularity referredreferred toto byby typographerstypographers as asrhythm rhythm. .

Figure 1. The horizontal periodicity in the letter strokes for the word minimum printed in Times, Figure 1. The horizontal periodicity in the letter strokes for the word minimum printed in Times, Palatino, Arial and Verdana. The font size has been chosen to equate the x-height. The pattern beneath Palatino, Arial and Verdana. The font size has been chosen to equate the x-height. The pattern beneath each word is that formed by the central part of the letter strokes. each word is that formed by the central part of the letter strokes.. The rhythm of a typeface can be assessed using horizontal autocorrelation, the correlation of anThe image rhythm with of aa secondtypeface versioncan be assessed of itself, using displaced horizontal horizontally autocorrelation, by a small the correlation amount (lag).of an Theimage mathematical with a second technique version can of be itself, understood displaced by imagininghorizontally text byprinted a small on amount the transparency (lag). The ofmathematical an overhead projector.technique When can be two understood identical transparencies by imagining are text superimposed printed on andthe intransparency register, the of light an transmittedoverhead projector. through When them istwo at itsidentical maximum transparen (the correlationcies are superimposed is 1.0). When and the topin register, transparency the light is movedtransmitted horizontally through across them theis at lower its maximum one, the lag(the increases correlation and is the 1.0). transmitted When the lighttop transparency decreases (the is correlationmoved horizontally decreases). across It reaches the lower a minimum one, the when lag aincreases majority and of letter the transmitted strokes on the light top decreases transparency (the arecorrelation in the spaces decreases). between It reaches letters on a minimum the lower transparency.when a majority As of the letter top strokes transparency on the istop moved transparency further, andare in the the lag spaces increases between further, letters the on transmitted the lower lighttransp increasesarency. As (and the the top correlation transparency increases), is moved reaching further, aand maximum the lag increases when the further, majority the of transmitted letter strokes light on increases one transparency (and the correlati lie on theon neighbouring increases), reaching letter strokesa maximum on the when other. the majority of letter strokes on one transparency lie on the neighbouring letter strokesThe on height the other. of the first peak in the horizontal autocorrelation is therefore a measure of the spatial periodicityThe height of the of typeface, the first dependentpeak in the onhorizontal both the autocorrelation shape and spacing is therefore of neighbouring a measure letter of the strokes. spatial Wilkinsperiodicity et al. of [ 8the] showed typeface, that dependent the height on of both the firstthe shape peak in and the spacing horizontal of neighbouring autocorrelation letter of astrokes. word determinedWilkins et al. how [8] stripedshowed in that appearance the height the of wordthe firs wast peak judged in the to horizontal be. More importantly, autocorrelation they of showed a word thatdetermined the height how of thestriped peak in predicted appearance the speedthe word with was which judged the word to be. could More be importantly, read aloud. they Words showed with highthat peakthe height were readof the about peak 10%predicted more slowlythe speed than with those which with the low. word The could peak alsobe read predicted aloud. the Words speed with of silenthigh peak visual were search read through about a10% paragraph more slowly of text. than Reducing those with the autocorrelationlow. The peak also by compressingpredicted the words speed nearof silent the middle visual andsearch expanding through them a paragraph at the edges of text. (leaving Reducing their length the autocorrelation unchanged) increased by compressing reading speed,words even near thoughthe middle readers and preferred expanding to them read anat undistortedthe edges (leaving version their of the length text [ 8unchanged)]. One of the increased reasons forreading the eff speed,ects of spatialeven though periodicity readers on readingpreferred speed to read concerns an undistorted the ways inversion which of the the eyes text move [8]. One across of textthe whenreasons reading. for the effects of spatial periodicity on reading speed concerns the ways in which the eyes moveDuring across a text rapid when eye movementreading. (saccade), one eye generally leads and the other follows, resulting in a misalignmentDuring a rapid of theeye eyesmovement that requires (saccade), correction one eye when generally the eyes leads come and to the rest other [9]. Jainta,follows, Jaschinski, resulting andin a Wilkinsmisalignment [10] measured of the eyes saccades that requires and vergence correction movements when the eyes when come their to participants rest [9]. Jainta, read Jaschinski, German sentences.and Wilkins When [10] themeasured words hadsaccades a high and first vergence peak in themovements horizontal when autocorrelation, their participants the eyes read rested German on eachsentences. word forWhen longer the duringwords had the vergencea high first eye peak movements in the horizontal that corrected autocorrelation, the misalignment the eyes (vergence rested on error).each word The realignmentfor longer during took the longer vergence with a eye spatially movements periodic that word corrected because the themisalignment alignment was(vergence then moreerror). precise. The realignment took longer with a spatially periodic word because the alignment was then moreLittle precise. is known about the effect of typographic variables on the size of the horizontal autocorrelation, even inLittle the twois known studies about in which the the effect spatial of periodicitytypographic has variables been shown on tothe aff ectsize reading. of the Thehorizontal first of theautocorrelation, present studies even therefore in the measuredtwo studies the in eff whichect of typographicthe spatial periodicity variables on has the been autocorrelation. shown to affect reading. The first of the present studies therefore measured the effect of typographic variables on the autocorrelation.

Vision 2020, 4, 18 3 of 16

3. Study 1 Study 1 explored the way in which the first peak in the horizontal autocorrelation of text varies with font and layout. Twenty common fonts were selected, shown in the first column of Table1.

Table 1. A total of 20 fonts showing the mean of the first peak in the horizontal autocorrelation (AC peak) and the residuals after fitting a 1/f cone to the Fourier amplitude spectrum.

Font AC Peak Residuals 1012 × Andale mono 0.196 3.92 Arial 0.395 5.10 Ayuthaya 0.283 4.62 Booster Next Medium 0.310 3.96 Calibri 0.410 3.38 sans serif regular 0.403 4.74 0.403 3.74 0.408 3.76 Open Sans 0.359 4.36 Raleway medium 0.366 4.06 Verdana 0.387 4.20 Athelas regular 0.423 3.40 0.434 4.40 Bookman Old Style 0.427 4.91 Cambria 0.432 5.28 serif Century 0.413 5.30 Charter Roman 0.426 3.70 Garamond 0.398 5.16 bright 0.433 4.05 Times 0.445 5.03

3.1. Comparison of 20 Fonts

3.1.1. Procedure A passage from “Small House at Allington” by Anthony Trollop and a passage from “Middlemarch” by George Eliot were generated using Microsoft Word for Mac 2011 version 14.6.8. They were printed to the 15 inch Retina screen of an Apple Macbook Pro running OSX 10.11.6. The passage was prepared in each of the 20 fonts listed in Table1, nominal 10 point in size, with default letter spacing, and with a ragged right margin and an interlinear spacing of 1.15 points. The page was 20.5 cm in width and 28.5 cm in height and was saved with a resolution of 5.67 pixels per mm. The horizontal autocorrelation of a central section of the page 512 512 pixels in size was obtained using Matlab with iteration of × the corr2d function.

3.1.2. Results Figure2 shows a plot of the first peak in the horizontal autocorrelation for the 20 fonts. As can be seen, the peak is very similar for the two passages of text but differs for each font. The absolute value of the difference in the autocorrelation for the two text samples averaged only 0.0092 (SD 0.0064), demonstrating that the method shows reliable differences attributable to the font design, and not the content of the text. The mean value for each font is shown in the second column of Table1. Vision 2020, 4, 18 4 of 16 Vision 2020, 4, x FOR PEER REVIEW 4 of 16

0.5 Sans serif 0.4 Serif first Open sans

0.3 Booster Ayuthaya

peak 0.2 Andale autocorrealtion

0.1 Eliot 10pt: Eliot 0 0 0.1 0.2 0.3 0.4 0.5 Trollope 10 point: autocorrelation first peak

FigureFigure 2. 2.The The first first peak peak in in the the horizontal horizontal autocorrelation autocorrelation of of two two pages pages of of text, text, one one containing containing text text from from EliotEliot and and the the other other from from Trollope. Trollope. Both Both samples samples were were printed printed in in one one of 20of 20 fonts. fonts. The The fonts fonts with with low low firstfirst peak peak in thein the autocorrelation autocorrelation have have been been identified. identified.

AsAs can can be seenbe seen from from Table Table1, the 1, font the with font lowest with lowest autocorrelation autocorrelation was a “typewriter” was a “typewriter” font in which font in eachwhich letter each had letter the samehad the width. same Of width. the proportional Of the proporti fonts,onal the fonts, two the with two lowest with autocorrelationslowest autocorrelations were Openwere Sans Open and Sans Raleway and medium.Raleway medium. Arial and Arial Verdana and had Verdana autocorrelations had autocorrelations less than 0.4. less Although than 0.4. theseAlthough are all these sans serifare all fonts, sans theserif remaining fonts, the clusterremain ofing fonts cluster with of autocorrelationsfonts with autocorrelations greater than greater 0.4 includedthan 0.4 many included fonts many with serifs,fonts with but also serifs, Gill but sans. also The Gill di sans..fference The in difference the first peak in the in thefirst horizontal peak in the autocorrelationhorizontal autocorrelation was significantly was significantly greater for thegreater fonts for with the serifsfonts with than serifs those than without those t(18) without= 3.45, t(18) p == 0.003.3.45, p = 0.003.

3.1.3.3.1.3. Discussion Discussion ThereThere were were di ffdifferenceserences in in the the horizontal horizontal autocorrelation autocorrelation of of a pagea page of of text text that that were were due due almost almost entirelyentirely to to the the font font (typeface) (typeface) and and not not the the content content of of the the text. text. Evidently, Evidently, a singlea single page page of of text text provides provides forfor averaging averaging su sufficientfficient to to remove remove most most of of the the variability variability from from content. content. 3.2. Serifs Versus Rhythm 3.2. Serifs Versus Rhythm The difference in the first peak of the horizontal autocorrelation between the serif and sans serif The difference in the first peak of the horizontal autocorrelation between the serif and sans serif fonts was not due to the serifs themselves, but the effect of the serifs on the rhythm of the typeface, fonts was not due to the serifs themselves, but the effect of the serifs on the rhythm of the typeface, evident in Figure1. This was demonstrated by a subsequent comparison of Lucida bright and Lucida evident in Figure 1. This was demonstrated by a subsequent comparison of Lucida bright and Lucida sans. The letter shapes and spacings are similar in the Lucida although Lucida bright contains sans. The letter shapes and spacings are similar in the Lucida typefaces although Lucida bright serifs. Two identical passages from Trollope were prepared, one in Lucida bright and one in Lucida sans, contains serifs. Two identical passages from Trollope were prepared, one in Lucida bright and one in each 12 point. The tracking (letter spacing) was identical. The autocorrelations of the two typefaces are Lucida sans, each 12 point. The tracking (letter spacing) was identical. The autocorrelations of the shown in Figure3 and are very similar. The first peaks in the autocorrelations were 0.323 and 0.284 two typefaces are shown in Figure 3 and are very similar. The first peaks in the autocorrelations were respectively. Evidently, the serifs per se did not contribute much to the first peak in the horizontal 0.323 and 0.284 respectively. Evidently, the serifs per se did not contribute much to the first peak in autocorrelation. Perea [11] compared serif and sans serif versions of Lucida and found no effect of the horizontal autocorrelation. Perea [11] compared serif and sans serif versions of Lucida and found serifs on mean fixation duration and only minor effects on the number of progressive saccades. no effect of serifs on mean fixation duration and only minor effects on the number of progressive saccades.

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Figure 3. The horizontal autocorrelation of two identicalidentical passages of text from Trollope, oneone inin LuciaLucia sanssans andand thethe otherother LucindaLucinda bright.bright. 3.3. Equating Empty Space 3.3. Equating Empty Space Although all the fonts had the same nominal point size, they differed in width and in the height Although all the fonts had the same nominal point size, they differed in width and in the height of the central body of the letters (x-height). The x-height of Times nominal 14 pt was similar to that of of the central body of the letters (x-height). The x-height of Times nominal 14 pt was similar to that Google Open Sans nominal 12 pt, for example. Although the line spacing was nominally 1.15 pt, it of Google Open Sans nominal 12 pt, for example. Although the line spacing was nominally 1.15 pt, it differed from one font to the next, partly to maintain a similar ratio of x-height to line space. Other things differed from one font to the next, partly to maintain a similar ratio of x-height to line space. Other being equal, the larger the area of empty white page, the greater the autocorrelation. The variation things being equal, the larger the area of empty white page, the greater the autocorrelation. The between fonts therefore depended in part on this variation and not on the spatial periodicity between variation between fonts therefore depended in part on this variation and not on the spatial periodicity letters. Further, the smaller the size of the letters, the fewer the pixels used to create the letter form, between letters. Further, the smaller the size of the letters, the fewer the pixels used to create the letter and the greater the degradation in shape. form, and the greater the degradation in shape. 3.3.1. Procedure 3.3.1. Procedure In order to compare the autocorrelation of different fonts independently of these factors, the text fromIn Trollope order to was compare created the in autocorrelation 28 point, and the of sizedifferen normalisedt fonts independently to give an x-height of these of 27factors, pixels the for text all fonts,from Trollope using the was imresize created function in 28 point, in Matlab and (bicubicthe size interpolation),normalised to croppinggive an x-height the width of of27 thepixels fragment for all atfonts, 1168 using pixels. the imresize function in Matlab (bicubic interpolation), cropping the width of the fragment at 1168 pixels. 3.3.2. Results 3.3.2. Results Figure4 shows the relationship between the autocorrelation obtained using this method and that originallyFigure obtained 4 shows for the the relationship 10 pt font. Thebetween correlation the autocorrelation is 0.91. obtained using this method and that originally obtained for the 10 pt font. The correlation is 0.91.

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0.5

0.4

first peak, first 0.3

0.2

0.1 10 lines, x-height equated x-height lines, 10 Autocorrelation 0 0 0.1 0.2 0.3 0.4 0.5 Autocorrelation first peak, 10pt, 512x512 fragment

Figure 4. Correlation between text from Trollope 10 pt with 1.15 pt interline spacing. and the same passage normalised for x-height, for the 20 fonts listed in Table1. The points for Open Sans and Times areFigure surrounded 4. Correlation by a circle between anda text square from respectively. Trollope 10 pt with 1.15 pt interline spacing and the same passage normalised for x-height, for the 20 fonts listed in Table 1. The points for Open Sans and Times 3.3.3.are Discussion surrounded by a circle and a square respectively. Evidently, the first peak in the horizontal autocorrelation is largely independent of any image 3.3.3. Discussion changes associated with scale and spacing, at least over the range of scale examined. Google Open Sans isEvidently, surrounded the first by a peak circle in and the Timeshorizontal by a squareautocorrelation in Figure is4 .largely Note thatindependent Google Open of any Sans image is consistentlychanges associated a font with with low scale autocorrelation, and spacing, andat least Times over one the with range high of autocorrelation.scale examined. Google Open Sans is surrounded by a circle and Times by a square in Figure 4. Note that Google Open Sans is 3.4.consistently Horizontal a Spacingfont with low autocorrelation, and Times one with high autocorrelation.

3.4.1. Font Compression and Expansion 3.4. Horizontal Spacing The spacing of letters may be expected to affect the lag at which the autocorrelation reaches its peak,3.4.1. butFont the Compression effect of expansion and Expansion on the height of the first peak in the autocorrelation depends on the intraThe andspacing interletter of letters space may and be isexpected not easily to affect predicted. the lag Wilkins at which et the al. [autocorrelation8] showed that reaches for Times its thepeak, autocorrelation but the effect of is atexpansion its peak on when the height the letter of the spacing first peak is default: in the autocorrelation the peak decreases depends with on both the expansionintra and interletter and compression. space and By iscontrast, not easily Verdana predicted. showed Wilkins comparatively et al. [8] showed little changethat for with Times letter the spacing.autocorrelation The eff ectsis at of its interword peak when and interletterthe letter spacingspacing onis readingdefault: arethe known peak decreases to interact with with fontboth characteristicsexpansion and [12 compression.]. By contrast, Verdana showed comparatively little change with letter spacing. The effects of interword and interletter spacing on reading are known to interact with font 3.4.2. Justification characteristics [12]. The word processor used in the previous studies achieved right justification by varying the space between3.4.2. Justification but not within words, and the average spacing between words was increased when the text was justified. The passage by Trollop was printed using Microsoft Word in one of four fonts (Times, The word processor used in the previous studies achieved right justification by varying the space Century, Verdana and Open Sans). Each was printed in one of three nominal sizes (10 pt, 12 pt, 14 pt) between but not within words, and the average spacing between words was increased when the text with both right justification and ragged right margins—a total of 24 samples. was justified. The passage by Trollop was printed using Microsoft Word in one of four fonts (Times, The autocorrelation of the 24 samples was obtained using an algorithm that analysed 10 lines Century, Verdana and Open Sans). Each was printed in one of three nominal sizes (10 pt, 12 pt, 14 pt) without interline spacing. The effect of font size was inconsistent, but there was a small but consistent with both right justification and ragged right margins—a total of 24 samples. effect of justification: it increased the first peak in the autocorrelation for all four fonts, although only The autocorrelation of the 24 samples was obtained using an algorithm that analysed 10 lines by an average of 3.3%. The average spacing between words increased when the text was justified and without interline spacing. The effect of font size was inconsistent, but there was a small but consistent the extra blank white page increased the autocorrelation. effect of justification: it increased the first peak in the autocorrelation for all four fonts, although only by an average of 3.3%. The average spacing between words increased when the text was justified and the extra blank white page increased the autocorrelation.

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4. Discussion of Study 1 The first peak in the horizontal autocorrelation of words has been shown to influence the speed with which they can be read both in a list [8] and as connected meaningful sentences [10]. The peak is high when vertical strokes of letters resemble each other and are evenly spaced, and words are then read more slowly [8,10]. Serif fonts generally have a higher peak, not because of the serifs themselves but because of their effect on the rhythm of the typeface. Other aspects of text spacing and layout have a comparatively small effect. Although the peak has been shown to influence reading speed, familiarity with font design is, however, also likely to influence speed of reading [6], and this may have a larger effect.

5. Vertical Spatial Periodicity Certain periodic patterns, particularly stripes, can be uncomfortable to look at. They can induce perceptual illusions of movement, shape and colour [13]. The patterns responsible for discomfort and illusions have characteristics similar to those of patterns that induce electroencephalographic abnormalities, or seizures, in patients with photosensitive epilepsy, suggesting a neurological rather than optical basis for the visual effects [14]. There are large individual differences in susceptibility to the illusions and associated discomfort and these differences are related to a person’s history of headaches. There are several convergent lines of evidence that the visual cortex is hyperexcitable in migraine headache. It is therefore parsimonious to explain the individual differences in susceptibility to the visual effects of stripes in terms of individual differences in cortical excitability [15]. The successive lines of text resemble a pattern with spatial frequency, luminance contrast, and duty cycle (the proportion of background luminance in the pattern) sufficient to induce discomfort and even seizures [16,17]. This can best be understood using Fourier analysis. Fourier analysis is a mathematical technique that decomposes images into components. The components are typically (but not necessarily) sine-wave patterns with a variety of spatial frequencies, orientations and phases. Consider the small sample of the image in Figure5. An enlarged version of the sample is shown in the left insert and the profile of the luminance over space is shown in the top graph. This waveform can be created by adding together the waveforms numbered 1-4 immediately below. The peak–trough amplitude of these waves is directly proportional to their wavelength. The spatial frequency, f, of the waves is the reciprocal of their wavelength, and so the amplitude is proportional to 1/f. This means that when the logarithm of the amplitude is plotted against the logarithm of the spatial frequency, a straight line with a slope of 1 results. It turns out that − most images from nature have a Fourier amplitude spectrum with a slope close to 1 [18]. − The visual system has adapted to process natural images. Field [19] argued that the bandwidths of channels tuned to spatial frequency are optimized for a 1/f amplitude spectrum. Their bandwidth remains constant when expressed on an octave scale, so that a similar amount of information is carried by each channel. Atick and Redlich [20] have argued that the shape of the contrast sensitivity function enables images with a 1/f spectrum to be coded efficiently. The contrast sensitivity is low (the channel has low gain) for low spatial frequencies that have a high amplitude, and this conserves metabolic energy. In computational models of the visual system, striped patterns, which are rare in nature and do not conform to a 1/f structure, result in an excess of ‘neural activity’ and a non-sparse distribution of ‘neural’ firing [21]. Wilkins [22] reviewed neuroimaging studies and concluded that images that are uncomfortable to observe are generally associated with an elevated haemodynamic response, consistent with the computation models and suggesting that the discomfort is a homeostatic mechanism that avoids excessive cerebral metabolism. Vision 2020, 4, x FOR PEER REVIEW 8 of 16

of 1/f to the two-dimensional Fourier amplitude spectrum of the grey-level image, and the residuals were weighted by a contrast sensitivity function gleaned from the literature; the size of the residuals predicted discomfort, see Figure 6. Note that patterns of stripes have a Fourier amplitude spectrum that is not well fit by a cone, consisting of a few component spatial frequencies. They are therefore patterns that produce some of the largest residual scores, and they are uncomfortable to look at. Vision 2020The, 4, 18algorithm had not hitherto been applied to text, and so in the next study, we assessed 8its of 16 effectiveness in this context.

Figure 5. Illustration of the component waves in Fourier analysis. The variation in luminance over Figure 5. Illustration of the component waves in Fourier analysis. The variation in luminance over space (luminance profile) of the sample shown at the top and enlarged in the first row of the left hand space (luminance profile) of the sample shown at the top and enlarged in the first row of the left inset can be thought as composed of the addition of the waves shown below and numbered 1–4. The hand inset can be thought as composed of the addition of the waves shown below and numbered 1–4. amplitude decreases with their spatial frequency as shown in the right-hand inset. The amplitude decreases with their spatial frequency as shown in the right-hand inset.

It is therefore possible to argue that images are processed inefficiently by the brain if they are unnatural and do not have a 1/f amplitude spectrum. According to this hypothesis, images are uncomfortable to look at when they are processed inefficiently and require excessive metabolism. Observers have been asked to rate the discomfort from images of modern art and of filtered visual noise or shapes [23,24]. For all categories of image, the discomfort was minimal for those images with a 1/f Fourier amplitude spectrum. An algorithm with no free parameters can account for more than 25% of the variance in observers’ ratings of discomfort [25]. The algorithm fitted a cone with a slope of 1/f to the two-dimensional Fourier amplitude spectrum of the grey-level image, and the residuals were weighted by a contrast sensitivity function gleaned from the literature; the size of the residuals predicted discomfort, see Figure6.

Vision 2020, 4, 18 9 of 16 Vision 2020, 4, x FOR PEER REVIEW 9 of 16

Figure 6. Schematics of the method used in [25]. (a) Amplitude spectrum of a natural image in log–log coordinates.Figure 6. Schematics Each vertex of on the the method surface used has threein [25]. coordinates: (a) Amplitude two correspondingspectrum of a natural to the logarithm image in oflog– thelog spatial coordinates. frequency Each in thevertex two-dimensional on the surface Fourier has three domain coordinates: (frequencies two corresponding with a DC component to the logarithm have beenof the discarded spatial forfrequency display in purposes). the two-dimensional The third (vertical) Fourier coordinatedomain (frequencies corresponds with to a the DC amplitude component ofhave the spectrum been discarded of the image for display at these purposes). frequencies. The (b )third Family (vertical) of circular coordinate regular conescorresponds of slope to 1 /fthe withamplitude a (continuously) of the spectrum varying of gain. the (imagec) Amplitude at these spectrumfrequencies. pictured (b) Family in (a) of with circular its best regular fit amongst cones of theslope (continuous) 1/f with familya (continuously) of two-dimensional varying gain. cones (c pictured) Amplitude in (b ).spectrum (d) Residuals pictured after in the (a cone) with of its best best fit fit is removed.amongst the After (continuous) [25]. family of two-dimensional cones pictured in (b). (d) Residuals after the cone of best fit is removed. After [25]. Note that patterns of stripes have a Fourier amplitude spectrum that is not well fit by a cone, consisting6. Study of2 a few component spatial frequencies. They are therefore patterns that produce some of the largest residual scores, and they are uncomfortable to look at. Study 2 applied the algorithm to text and showed that it predicted the choice people make when The algorithm had not hitherto been applied to text, and so in the next study, we assessed its reading text in electronic books. These books, presented on an electronic screen, permit readers to effectiveness in this context. choose the font and the size and to choose from a limited range of colours. 6. Study 2 6.1. Predicting Readers’ Choice of Text Characteristics Study 2 applied the algorithm to text and showed that it predicted the choice people make when reading6.1.1. Participants text in electronic books. These books, presented on an electronic screen, permit readers to choose the font and the size and to choose from a limited range of colours. Seven female and eight male students and staff at the University of Essex, aged 18–63, took part. 6.1. Predicting Readers’ Choice of Text Characteristics 6.1.2. Procedure 6.1.1. Participants Each participant was shown publications from iBooks. The books were presented in double- pageSeven format female on an and Apple eight MacBook male students Pro with and staa 15ff inatch the Retina University screen. of The Essex, participants aged 18–63, were took asked part. to “make the text as easy to read as possible” using the iBook tools. With the tools, one of eight fonts 6.1.2.could Procedure be selected (Original, Athelaf, Charter, , Iowan, Palatino, Servarek and )Each participantin a variety was of sizes. shown The publications text could be from black iBooks. on a white The books background were presented or on a sepia in double-page background, formator the on text an could Apple be MacBook white on Pro a withblack a background. 15 inch Retina When screen. the Theparticipants participants had were finished asked their to “make settings thethe text image as easy of the to readscreen as was possible” saved. using Each participan the iBook tools.t adjusted With two the texts, tools, one one from of eight “The fonts Other could Woman” be selectedby Laura (Original, Wilson Athelaf, and one Charter, from Georgia,“The Angel” Iowan, by Palatino, Katerina Servarek Diamond. and The Times texts New were Roman) originally in a varietypresented of sizes. in their The default text could settings: be black Original on a white and Times background New Roman or on a with sepia an background, x-height of or 2.3 the and text 2.2 mm, respectively, and line spacing of 6.8 and 4.9 mm. The work was carried out with permission of

Vision 2020, 4, 18 10 of 16 could be white on a black background. When the participants had finished their settings the image of the screen was saved. Each participant adjusted two texts, one from “The Other Woman” by Laura Wilson and one from “The Angel” by Katerina Diamond. The texts were originally presented in their default settings: Original and Times New Roman with an x-height of 2.3 and 2.2 mm, respectively, and line spacing of 6.8 and 4.9 mm. The work was carried out with permission of the University of Essex Ethics committee and in accordance with the Code of Ethics of the World Medical Association (Declaration of Helsinki). Informed consent was obtained.

6.1.3. Results The final settings of texts had x-heights that ranged from 1.9 to 2.9 mm, with line spacing that ranged from 4.4 to 8.4 mm. There was no consistent change in the x-height or line spacing relative to the original text: respectively, 52% and 63% of settings showed an increase. The ratio of x-height to line spacing ranged from 31% to 46% and also did not change consistently, decreasing in 56% of cases. Although there was no consistent change in typographic parameters, the adjusted text nevertheless showed a consistent change in the residuals calculated by the algorithm: 29/30 settings (14/15 participants) showed a decrease as compared to the original, indicating that the parameters of the text were altered in combination so as to be closer to those of natural images. Seven of the 15 participants changed the background colour from white to sepia and one used a black background for one of the two texts. The residuals were lower for the sepia background because of the reduction in luminance contrast. Nevertheless, for all the eight participants who chose a white background, the residuals were lower for the adjusted text than for the original in every case, averaged for the two samples.

6.1.4. Discussion In all cases but one, participants adjusted the iBook text in a direction predicted by the final version of the algorithm from [25]. Although the x-height and line separation did not change consistently, the text was adjusted in a manner to which the algorithm was sensitive. The adjustments were such as to make the text more like images from nature, a change consistent with a reduction in discomfort. Given that the algorithm was successful in predicting choice of typographic variables, it was important to ascertain more systematically which typographic variables affected the output of the algorithm.

6.2. Fonts and the Algorithm Output

6.2.1. Procedure The passages from Trollope and Eliot were set in the 20 different fonts given in Table1, 10 pt in size, with a line spacing of 1.15 pt. They were analysed using the final algorithm of [25].

6.2.2. Results The residuals obtained for the two text samples are expressed as a scatterplot in Figure7. The correlation explains 87% of the variance and indicates that the residuals are affected primarily by the font, with little contribution from the textual content. The absolute value of the difference between the text samples averaged 5.0% (SD 2.7%). Table1 shows the average of the residuals for the two samples. Among the conventional fonts, Open Sans had one of the lowest residuals. Vision 2020, 4, 18 11 of 16 Vision 2020, 4, x FOR PEER REVIEW 11 of 16

6

5.5

5 , text sample 2 sample text ,

12 4.5

4

3.5 Residualsx10 3 3456 Residuals x 1012, text sample 1

Figure 7. Residuals for the two samples of texts from Eliot and Trollope for each of the 20 fonts listed in FigureTable1. 7. The Residuals lower the for residuals, the two samples the more of similar texts from the textEliot to and images Trollope from for nature. each Theof the points 20 fonts for Openlisted inSans Table and 1. Times The lower are surrounded the residuals, by a the circle more and similar a square the respectively. text to images from nature. The points for Open Sans and Times are surrounded by a circle and a square respectively. 6.2.3. Discussion 6.2.3.The Discussion font had a clear effect on the size of the residuals of the images of a page of text. The nominal size ofThe the font font had was a held clear constant, effect on although the size of there the wasresiduals variation of the in images x-height, of which a page may of text. have The contributed nominal sizeto the of di thefferences font was in residuals. held constant, although there was variation in x-height, which may have contributed to the differences in residuals. 6.3. Font Weight 6.3. FontThere Weight were large differences between fonts in the residuals obtained when a 1/f cone was fitted to the two-dimensionalThere were large Fourierdifferences amplitude between spectrum fonts in th ofe the residuals page using obtained the algorithmwhen a 1/f [ 25cone]. If was the fitted page toresembles the two-dimensional a pattern of horizontal Fourier amplitude lines, giving spectrum large residual of the page scores using as a result,the algorithm then the [25]. contrast If the of page that “grating”resembles will a pattern be influenced of horizontal by the weightlines, givingof the font.large Weight residual is typicallyscores as useda result, to refer then to the the contrast differences of thatbetween “grating” “light”, will “medium” be influenced and “bold”by the versionsweight of of the fonts font. but Weight there isis continuumtypically used of weight to refer that to canthe differencesbe assessed between from the “light”, average “medium” thickness and of the“bold” letter ve strokes.rsions of Infonts order but to there estimate is continuum the weight of weight of the that20 fonts, can be the assessed sentence from “The the quick average brown thickness fox jumped of th overe letter the lazy strokes. dog” In was order printed to estimate in each ofthe the weight fonts. ofThe the central 20 fonts, section the ofsentence the line “The from quick the baseline brown tofox the jumped top of over those the letters lazy without dog” was ascenders printed comprisedin each of thea rectangular fonts. The sectioncentral ofsection the page. of the The line weight from the was ba estimatedseline to the as thetop numberof those ofletters black without pixels divided ascenders by comprisedthe total pixels a rectangular in the rectangle. section The of the weight page. for The sentences weight printedwas estimated in 11, 12 as and the 14 number point were of black calculated pixels dividedand the correlationsby the total pixels between in the the rectangle. estimates The obtained weight was for high sentences (>0.967). printed The estimatesin 11, 12 and for 1114 point werevaried calculated 15%–24% and as shown the correlations in Figure8 between. the estimates obtained was high (>0.967). The estimates for 11 point varied 15%–24% as shown in Figure 8. There was a moderate but significant correlation (r = 0.624, p = 0.003) between the algorithm output and the weight of the font as defined above, shown in Figure 9. The effect of font weight on the algorithm can therefore be understood in terms of the contrast of the striped lines or “grating” formed by the lines of text. The next study investigated the effects of the parameters of text layout.

Vision 2020, 4, 18 12 of 16 Vision 2020, 4, x FOR PEER REVIEW 12 of 16

Vision 2020, 4, x FOR PEER REVIEW 12 of 16

Figure 8. Weights of 20 fonts as estimated from the percentage of black pixels in a line of text. Figure 8. Weights of 20 fonts as estimated from the percentage of black pixels in a line of text. There was a moderate but significant correlation (r = 0.624, p = 0.003) between the algorithm output and the weight of5.5 the font as defined above, shown in Figure9. The e ffect of font weight on the algorithm can therefore be understood in terms of the contrast of the striped lines or “grating” formed byFigure the lines8. Weights of text. of5.0 20 fonts as estimated from the percentage of black pixels in a line of text.

12 4.5 5.5 4.0 5.0 3.5

12 4.5 3.0

Residualsx10 4.0 2.5 3.5 2.0 3.0

Residualsx10 10 15 20 25 2.5 Percent black pixels in x-height section 2.0 Figure 9. The correlation between10 font weight 15 and the output 20 of the algorithm 25 (residuals) [25]. Percent black pixels in x-height section 6.3.1. Procedure

Seventy-twoFigure 9. The samples correlation from between Trollope font were weight set andin Century, the output Times, of the Open algorithm Sans (residuals) and Verdana, [25]. 10, 12, Figure 9. The correlation between font weight and the output of the algorithm (residuals) [25]. and 14 point in size, with 1, 1.15 and 1.5 point interline spacing, with and without justification. They The next study investigated the effects of the parameters of text layout. were6.3.1. analysed Procedure using the algorithm from [25]. The samples of text with expanded letter spacing were 6.3.1.also analysed. Procedure Seventy-two samples from Trollope were set in Century, Times, Open Sans and Verdana, 10, 12, 6.3.2.and Seventy-two14 Results point in size, samples with 1, from 1.15 Trollope and 1.5 point were setinte inrline Century, spacing, Times, with Open and without Sans and justification. Verdana, 10, They 12, andwere 14 analysed point in size,using with the algorithm 1, 1.15 and from 1.5 point [25]. interlineThe samples spacing, of text with with and expanded without letter justification. spacing Theywere There was no relationship between the residuals obtained and the number of words per page (r werealso analysed. analysed using the algorithm from [25]. The samples of text with expanded letter spacing were = 0.03). The residuals were unaffected by the right margin, ragged or justified. The x-height also had also analysed. little6.3.2. effect. Results There was a weak tendency for texts with large interline spacing to have lower residuals, but by far the strongest relationship between the output of the algorithm and the typographic variablesThere concerned was no relationship the ratio of betweenx-height theto line residuals spacing. obtained This relationship and the number accounted of words for 79%per pageof the (r = 0.03). The residuals were unaffected by the right margin, ragged or justified. The x-height also had little effect. There was a weak tendency for texts with large interline spacing to have lower residuals, but by far the strongest relationship between the output of the algorithm and the typographic variables concerned the ratio of x-height to line spacing. This relationship accounted for 79% of the

Vision 2020, 4, 18 13 of 16

Vision 2020, 4, x FOR PEER REVIEW 13 of 16 6.3.2. Results variance;There see was Figure no relationship 10. Pages in between which the the text residuals was wi obtaineddely spaced and relative the number to the ofheight words of the per letters page (rwere= 0.03 evidently). The residuals more similar were unato imagesffected from by the the right natural margin, world, ragged and or potentially justified. Themore x-height comfortable. also had little eTheffect. ratio There of x-height was a weak to line tendency spacing for can texts be withlikened large to the interline duty spacingcycle of the to have “grating” lower formed residuals, by buthorizontal by far the lines strongest of text. relationship The lower the between ratio, thethe outputgreater of the the departure algorithm from and thea 50% typographic duty cycle variables and the concernedlower the theFourier ratio power of x-height of the to “grating” line spacing. formed This by relationship the lines of accounted text. In current for 79% typographic of the variance; practice, see Figurethe ratio 10 .of Pages x-height in which to line the spacing text was is typically widely spaced 35%–45%. relative The to present the height findings of the suggest letters werethat this evidently might moreusefully similar be decreased to images by from increasing the natural line world, spacing. and potentially more comfortable.

8.0

7.0

6.0

5.0 12 4.0

3.0

2.0 Residualx10 1.0

0.0 20 30 40 50 60 Ratio of x-height to line spacing (%)

Figure 10. Relationship between the output of the algorithm (residuals) [25] and the ratio of x-height toFigure line spacing 10. Relationship for 72 texts, between withvarious the output fonts, of the font algori size andthm spacing,(residuals) with [25] and and without the ratio justification. of x-height Theto line font spacing with one for of 72 the texts, lowest with residuals, various fonts, Open font Sans, size had and a ratiospacing, of x-height with and to without line spacing justification. of 43%, whichThe font was with large, one relative of the tolowest other re fonts.siduals, Note Open that iBooksSans, had currently a ratio permitof x-height the selection to line spacing of font butof 43%,not thewhich ratio was of x-height large, relative to line spacing,to other fonts. except Note in so that far as iBooks line spacing currently co-varies permit with the selection font. The of di fffonterences but not in thethe iBook ratio of selections x-height were to line not spacing, therefore except attributable in so far to as line line spacing spacing but co-varies to other with aspects font. of The the differences typefaces thatin the the iBook algorithm selections was also were successful not therefore at capturing. attributable to line spacing but to other aspects of the typefaces that the algorithm was also successful at capturing. The ratio of x-height to line spacing can be likened to the duty cycle of the “grating” formed by7. General horizontal Discussion lines of text. The lower the ratio, the greater the departure from a 50% duty cycle and the lowerTwo themathematical Fourier power properties of the of “grating” text have formedbeen studied: by the (1) lines the ofspatial text. periodicity In current of typographic the vertical practice,strokes of the letters, ratio of which x-height affects to line reading spacing speed, is typically and (2) 35%–45%. the degree The of present departure findings from suggest the Fourier that thisamplitude might usefully spectrum be typical decreased of natural by increasing images, linewhic spacing.h determines visual comfort of images, including text. Overall, the correlation between these two measures for the 20 fonts in Table 1 is only 0.082, 7. General Discussion suggesting that the measures are independently useful. Open Sans is one of the few fonts that performTwo well mathematical on both measures. properties of text have been studied: (1) the spatial periodicity of the vertical strokesModels of letters, of the which way in a ffwhichects reading words are speed, read andtypically (2) the represent degree (1) of the departure detection from and the integration Fourier amplitudeof visual features spectrum to typical build letters, of natural and images, (2) the whichintegration determines of letter-level visual comfort information of images, to reach including word text.identification, Overall, the as described correlation by between the original these intera twoctive measures activation for the model 20 fonts [26] and in Table its descendants1 is only 0.082, [27– suggesting29]. The approach that the measuresadopted in are this independently paper differs useful. fundamentally. Open Sans It is onetreats of text the fewas a fonts shape that and perform shows wellthat onthere both are measures. aspects of reading that depend upon the similarity of shapes at various spatial scales, irrespectiveModels of thetheir way identity in which as parts words of letters are read ortypically words. represent (1) the detection and integration of visualMany features studies to have build investigated letters, and eye (2) movements the integration across of text letter-level but usually information without attention to reach wordto the identification,detail of font asand described text design, by the and original often interactivewith monocular activation recording, model [ 26e.g.,] and [30]. its The descendants present findings [27–29]. Thesuggest approach that detailed adopted binocular in this paper recordings differs fundamentally. that measure vergence It treats textwill as show a shape effects and of shows font and that layout there on binocular eye movements across text. The autocorrelation encompasses in a single measure aspects of crowding and spatial uncertainty of letter position, which are key features of recent models of word reading, e.g., [31]. The

Vision 2020, 4, 18 14 of 16 are aspects of reading that depend upon the similarity of shapes at various spatial scales, irrespective of their identity as parts of letters or words. Many studies have investigated eye movements across text but usually without attention to the detail of font and text design, and often with monocular recording, e.g., [30]. The present findings suggest that detailed binocular recordings that measure vergence will show effects of font and layout on binocular eye movements across text. The autocorrelation encompasses in a single measure aspects of crowding and spatial uncertainty of letter position, which are key features of recent models of word reading, e.g., [31]. The autocorrelation has a face validity in terms of the cues to vergence that are used following each saccade, and the large effect on reading speed is understandable in these terms, and may even explain why crowding and eccentricity jointly determine reading rate [32]. Nevertheless, it seems likely that crowding and spatial uncertainty are insufficiently captured simply by autocorrelation. The effects of crowding increase with eccentricity, and no account of the decrease in acuity with eccentricity has been taken in the autocorrelation measure used here. This might be significant if the results are to be applied to low vision reading, particularly reading that uses peripheral retina. There is convergent evidence that in migraine, and perhaps in headache more generally, the visual cortex is hyperexcitable [33], and that as a result, individuals can be particularly susceptible to discomfort from patterns of stripes [14], including stripes in text [16]. In this paper, we have shown how the vertical stripes in text are affected by the selection of font and the horizontal stripes by text layout. It is stripes of this kind and the visual stress [13] they evoke that can have an on reading similar to that from low vision. With the advent of electronic text, it is possible without additional cost to choose fonts with little rhythm and to increase the spacing between lines of text [34]. It is possible in principle, but not in practice. Currently, the selection of fonts and spacing in electronic books is insufficient to accommodate individual preference or indeed to optimize text according to the principles exposed here; and there are no algorithms available with electronic books to guide users’ choice of font and spacing. The height of the first peak in the horizontal autocorrelation varies considerably for different fonts, but is high for Sassoon Primary, a font used in schools. Sassoon Primary is read more slowly than Verdana by school children [35], as predicted by the higher autocorrelation of Sassoon Primary, notwithstanding the children’s greater familiarity with this latter font. The question arises as to whether Open Sans might provide a better font for children than those currently in use. There are three aspects of the font that would then need to be changed, however. The q would need a tail to distinguish it from p. Similarly, the b and d would need to be distinguished, perhaps by removing the base of the stem of the b or adding a small tail to the stem of the d. Finally the upper case i and lower case L would need to be distinguished, for example by adding a small tail at the base of the lower case L. (Interestingly, these are changes that were systematically applied in a study that created a new font, Eido, to improve low-vision reading [36].) The changes could be very slight and would in any event have little or no effect on the autocorrelation or residuals. The alterations would be simple to make and would be admissible within the terms of the open license.

8. Conclusions The general principles and methods described in this paper can be applied to all languages and all orthographies and can be used to guide the design of any typeface and any written material. For example, spatial periodicity has been shown to affect the reading of Chinese logograms [37]. The present findings suggest, surprisingly, that font design has the potential to affect reading fluency and comfort appreciably. Similar algorithms may be applicable to music manuscripts [38].

Author Contributions: Conceptualization, A.W.; methodology, A.W.; software, A.W. and O.P.; validation, K.S., A.W. and O.P. investigation, K.S.; resources, A.W. and K.S.; writing—Original draft preparation, A.W.; writing—Review and editing, A.W. and O.P. All authors have read and agreed to the published version of the manuscript. Vision 2020, 4, 18 15 of 16

Funding: This research received no external funding. Acknowledgments: We thank the participants. We thank Kalvis Jansons for advice. Conflicts of Interest: The authors declare no conflict of interest.

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