Analysis of Texture Characteristics Associated

with Visual Complexity Perception

Xiaoying GUO, Chie Muraki ASANO, Akira ASANO, Takio KURITA, and Liang LI

O P T I C A L R E V I E W Vol. 19, No. 5 (2012)

Analysis of Texture Characteristics Associatedwith Visual Complexity PerceptionXiaoying GUO

1�, Chie Muraki ASANO2, Akira ASANO

3, Takio KURITA1, and Liang LI

4

1Graduate School of Engineering, Hiroshima University, Higashihiroshima, Hiroshima 739-8521, Japan2Department of Lifestyle Design, Yasuda Women’s University, Hiroshima 731-0153, Japan3Faculty of Informatics, Kansai University, Takatsuki, Osaka 564-8680, Japan4Ritsumeikan Global Innovation Research Organization, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan

(Received January 24, 2012; Accepted June 18, 2012)

In our previous work we determined that five important characteristics affect the perception of visual complexity of atexture: regularity, roughness, directionality, density, and understandability. In this paper, a set of objective methods formeasuring these characteristics is proposed: regularity is estimated by an autocorrelation function; roughness iscomputed based on local changes; directionality is measured by the maximum line-likeness of edges in differentdirections; and density is calculated from the edge density. Our analysis shows a significant correlation between theobjective measures and subjective evaluations. In addition, for the estimation of understandability, a new approach isproposed. We asked the respondents to name each texture, and then we sorted all these names into different types,including names that were similar. We discovered that understandability is affected by two factors of a texture: themaximum number of similar names assigned to a specific type and the total number of types.# 2012 The Japan Society of Applied Physics

Keywords: Kansei, visual perception, visual complexity, texture, texture perception, understandability

1. Introduction

Understanding of visual perception of textures has a widerange of applications from computer science (imageprocessing and image segmentation) to arts (the design ofproduct surfaces, packages, carpets, and wallpapers).1) Forinstance, understanding the visual perception of textures ishelpful in the process of image retrieval and helps artistschoose a texture for artwork or a product that evokes aparticular emotion.

With the explosive growth of digital technologies, anincreasing number of visual images (including textures) arebeing created. Some designers and artists want to obtaintextures that evoke certain Kansei feelings such as complex-ity, comfort, and warmth. Hence, an efficient approach forfinding these images is necessary. Kansei is a Japanese wordthat refers to higher-order functions of the brain, includingsensibility, emotion, impression, feeling, inspiration. Kanseiengineering is a method of connecting human sensibilitywith engineering applications. It can ‘‘measure’’ feelings andshows their relationships to certain objective properties.Textures are visually described by Kansei words such as‘‘simple’’ and ‘‘complex’’. However, the criteria for judging atexture as simple or complex are unclear. Hence, in order toaddress the problem of finding textures that evoke complexfeelings, three steps are required: (1) Identifying the texturecharacteristics that affect human visual complexity percep-tion, (2) Developing methods to measure these character-istics, and (3) Mapping the perception of visual complexitywith these texture characteristics.

In our previous work,2) we identified five low-levelcharacteristics that are used by humans to perceive the

visual complexity of textures; namely, regularity, roughness,directionality, density, and understandability. Visual com-plexity is a function of not only each individual character-istic but also of interactions between them. In this study, weaim to develop a set of methods to objectively determinethese characteristics. Then we correlate the objectivemeasures of these characteristics with subjective evaluationof them, which is necessary for associating visual complex-ity with texture characteristics.

In this study, we developed a set of objective methods tomeasure the first four texture characteristics (regularity,roughness, directionality, and density). Regularity is theproperty of variations across a whole texture. We estimatedregularity using an autocorrelation function that extracts theperiodicity of texture variations. Roughness is defined byvariations within a small area. Hence, we estimated rough-ness using the changes in a small region. Directionality isdefined by the orientation of edges, because image edgeshave a significant influence on visual perception. Therefore,directionality was measured using the main orientationof edges in different directions. Similarly, density wasmeasured using the edge density. The results of thecorrelation analyses show significant correlations betweenthe objective measures and subjective evaluations of thesetexture characteristics.

We propose a new method for estimating the fifth texturecharacteristic (understandability). Our previous work2)

showed that the understandability of a texture is related toa human’s prior knowledge and experience. As alreadyknown, naming is a straightforward approach that reflectsone’s knowledge and experience. Therefore, we analyzedunderstandability using an experiment that involved namingtextures. For each texture, we asked the respondents to givea name, and then we sorted the names into different types,�E-mail address: guoxiaoying@hiroshima-u.ac.jp

OPTICAL REVIEW Vol. 19, No. 5 (2012) 306–314

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including names that were similar, although not identical.These experimental results demonstrate that it is possible toevaluate the understandability of a texture using its names.In addition, these results show that the understandability of atexture can be estimated from two factors: (1) the maximumnumber of similar names belonging to a specific type and(2) the total number of types for a texture. The larger thenumber of similar names for a texture, the more under-standable it is. The larger the number of types for a texture,the less understandable it is.

The rest of this paper is organized as follows. In x2, relatedworks are introduced. In x3, the experiments are described.Section 4 presents the measures for regularity, roughness,directionality, density, and understandability. Section 5presents the discussion, and x6 concludes the paper.

2. Related Work

2.1 Visual complexityIn recent decades, visual complexity has become an

important and appealing issue. In the fields of bothpsychology and computer science, a number of researchershave defined the concept of visual complexity in theirstudies. Scha and Bod3) described complexity as beinglargely a function of the number of elements that an imageconsists of and their order of placement in the image.Heylighen4) suggested that the perception of complexity iscorrelated with the amount of variety in the visual stimulus.Heaps and Handel5) defined complexity as ‘‘the degree ofdifficulty in providing a verbal description of an image’’.Similarly, Li6) suggested that complexity is related tocertain measures of difficulty concerning the object or thesystem. Although some researchers have created their owndefinitions of visual complexity, its definition remains vagueand ill-defined.

Many studies have investigated visual complexity. In thefield of psychology, Olive et al.7) investigated the perceptualdimensions of the visual complexity of scenes. In this study,34 participants used the method of hierarchical groupingto classify indoor scenes. The results showed that visualcomplexity was represented by several dimensions suchas the number of objects, clutter, openness, symmetry,organization, and the variety of colors. Pieters et al.8)

investigated the visual complexity of advertising. Theydistinguished two types of visual complexity (featurecomplexity and design complexity) in advertising andproposed a objective measure for each. Saleem et al.9)

studied the visual complexity of three dimensional (3D)shapes and introduced an approach based on view similarityto determine the perceived shape complexity.

In the field of computer science, a number of researchershave focused on evaluating visual complexity usingmathematical methods. Andrienko et al.10) developed acomplexity measure based on mean information gain andapplied it to two-dimensional (2D) structures. Patel andHolt11) compared a pattern measure proposed by Linger andSalingaros with respondents’ perceptions of the complexityof background image scenes; the results showed that ahigh and positive correlation existed between mathematical

measures and the subjects’ perceptions. Furthermore, Rigauet al.12) proposed a new framework for investigating thecomplexity of an image by using information theory.In addition, Cardaci et al.13) presented a fuzzy model ofvisual complexity that fitted well with subjective measuresof complexity. Finally, Michailidou14) studied the visualcomplexity of web pages and defined ViCRAM, a frame-work that describes the visual complexity of web pages.These studies have made progress to some extent inmeasuring visual complexity by using information theoryand pattern methods.

2.2 Visual perception of texturesMany studies regarding the visual perception of textures

have been conducted. Tamura et al.15) developed six textureproperties (coarseness, contrast, directionality, line-likeness,regularity, and roughness) that correspond to human visualperception. In addition, they developed computationalmeasures and compared them with the psychologicalmeasurements given by respondents. The comparisonindicated strong correlations between certain properties.Amandasun and King16) investigated five properties oftexture corresponding to human visual perception: coarse-ness, contrast, busyness, complexity, and texture strength.Fujii et al.17) presented a set of measures for textureparameters that correspond to the perception of visualtexture. Liang Li et al.18) proposed a method of evaluatingthe visual impression of gray-scale textures using morpho-logical manipulation. They used this method to investigatethe influences of global features and local features on thevisual perception of similarity.

Perceptual dimensions of textures have also beenproposed. Rao and Lohse19,20) proposed that three dimen-sions were important to texture perception: (1) repetitivevs non-repetitive; (2) high contrast and non-directional vslow-contrast and directional; and (3) granular, coarse andlow-complexity vs granular, coarse and high-complexity.Cho et al.21) extended the number of perceptual dimensionsof texture to four: coarseness, regularity, contrast, andlightness. However, few studies have been conducted on thevisual perception of complexity in textures.

3. Experiments

Two experiments were conducted in this study. In ourprevious work,2) we identified five low-level characteristicsthat are used by humans to perceive the visual complexity oftextures: regularity, roughness, directionality, density, andunderstandability. To analyze the relationship between thesecharacteristics and visual complexity, the first experimentinvolved a series of paired comparisons.

It is difficult to estimate the understandability of texturesusing mathematical methods. Therefore, the second experi-ment involved estimating the understandability by namingtextures. In this experiment, we asked the respondents toname each texture. Then we sorted the names into differenttypes, including names that ware similar, although notidentical. We attempted to estimate the understandability oftextures by the types and number of names.

OPTICAL REVIEW Vol. 19, No. 5 (2012) 307X. GUO et al.

3.1 Experimental setup3.1.1 Respondents

For each experiment, 30 respondents from HiroshimaUniversity with a background in information engineering,education, management, or social economics participatedin the experiment. Although some of the respondents wereengaged in image science, they were unaware of the purposeof this study. Their ages ranged from 20 to 35 years old.All respondents had normal or corrected-to-normal vision.

3.1.2 Apparatus and stimuliTwenty texture images were selected for the experiments

(Fig. 1). The sample images were obtained from a standardsource, Brodatz’s album,22) which has been widely used inthe fields of texture analysis and visual perception.

In the first experiment, sample images were placed on asingle screen and shown to respondents one by one in arandom order. In the second experiment, sample imageswere placed on a webpage and shown to respondents one byone in a random order. One of the experimental objectives ofthe second experiment was to acquire the reaction timebetween the respondent viewing the texture and giving thename. Thus, there was a timer programmed by javaScript onthe webpage. A wireless mouse was used to start and stopthe timer. In both experiments, the screen was part of a 46-inch plasma display. The experiments were conducted in alaboratory with normal illumination. The respondents wererequired to sit 2m from the screen.

3.2 Semantic differential methodThe semantic differential (SD) method is the most popular

way to acquire Kansei information from respondents’ verbalreaction.23) Respondents describe their feelings about thescenes or products on a rating scale (usually a 5-point ora 7-point Likert scale). The scales are often designed froma pair of adjectives, for instance, simple and complex. Inthis paper, a 7-point Likert scale was used in the firstexperiment and a 5-point Likert scale was used in the secondexperiment.

3.3 Experiment I: A paired comparison evaluationThe method used in this experiment was paired compar-

ison evaluation, which is widely used in the field ofpsychology.24) The method of paired comparison is perhapsthe most straightforward way of presenting items forcomparative judgment.

Five pairs of adjectives were used for the pairedcomparison evaluation: namely irregular versus regular,low density versus high density, nondirectional versusdirectional, smooth versus rough, and understandable versusabstract. The five pairs of comparisons were defined asfollows. (1) Regularity: irregular versus regular. Regularitywas defined as variation in the placement rule of textureprimitives (or texture elements), in agreement with thedefinition of regularity in Tamura’s research. (2) Density:low density versus high density. Density was used for testingwhether the perceived primitives and edges were dense orsparse. (3) Directionality: nondirectional versus directional.The directionality of texture was related to primitive shapeand the global placement rule, in agreement with Tamuraet al. (4) Roughness: smooth versus rough. This property isfundamentally related to touch; however, when we observeeach texture, we can decide if the texture feels roughor smooth. (5) Understandability: understandable versusabstract. This was related to respondents’ prior knowledgeand experience.

After an introduction to the experiment and a briefexplanation, the respondents were instructed to view all theimages one by one. For each paired comparison, therespondents scored the corresponding perception on a 7-point Likert scale. The scale and its anchor-point phrases areshown in Fig. 2. The order of the presentation of the sampleswas randomized to avoid any order effect. Table 1 shows theaverage scores for the complexity and paired comparisonsevaluated by the respondents. The scores of complexity wereobtained from the experiment of assessing visual complexityof textures proposed in our previous paper,2) in which weasked the respondents to give the score of visual complexityon textures according to their own impression on a 7-pointLikert scale from 1 (very simple) to 7 (very complex).

3.4 Experiment II: Naming the texturesThis experiment used the naming of textures to measure

the respondents’ understandability. In addition, the reactiontime between the respondent viewing the texture and givingits name was also recorded.

d112d111d109d107d88

d74d72d67d64d62

d47d43d42d40d27

d26d20d15d13d10

Fig. 1. Texture images used in the experiments.

1 2 3 4 5 6 7

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Irregular Regular

Low density High density

Directional

Rough

Abstract

Nondirectional

Smooth

Understandable

Fig. 2. (Color online) The 7-point rating scale used in the firstexperiment.

OPTICAL REVIEW Vol. 19, No. 5 (2012)308 X. GUO et al.

The respondents were given a brief introduction, whichincluded how to operate the webpage and the criteria fornaming a texture. On the webpage, a button controlled thedisplay of texture and enabled starting and stopping of thetimer: once the button was pressed, after 500ms, the textureappeared and simultaneously the timer began. Once therespondent thought of a name for the texture, the button waspressed quickly; the texture disappeared and respondentimmediately gave the name. The names given by therespondents were not constrained to any predetermined list,but were given according to respondents’ visual perceptionsand understanding. However, the names were required to benouns rather than descriptive adjectives. For instance, thename of a flower-like texture should be ‘‘flower’’ or a wordgroup including flower, not a description of somethingbeautiful or nice. If the respondent could not give a possiblename, he or she could answer, ‘‘I do not know’’. Before theexperiment began, the respondent was required to use thetest webpage to become familiar with its operation.

After the introduction of the experiment, the respondentwas asked to concentrate on the webpage. The respondentclicked the button to view the texture and clicked the buttonagain when he or she thought of a name for the texture. Inaddition, after naming each texture sample, two questionswere asked and the respondent recorded his or her answeron a 5-point Likert scale. The two questions were ‘‘Howdifficult was it to name this image?’’ with a score from 1(very easy) to 5 (very difficult), and ‘‘How familiar were youwith this image?’’ with a score from 1 (very familiar) to 5(very unfamiliar). All texture samples were tested one byone using the above procedure. Finally, the respondentwas required to fill out a questionnaire. The questions inthe questionnaire are shown in the Appendix.

3.4.1 ResultsIn this experiment, we obtained data on names of each

texture, reaction time (RT), difficulty score of naming(DSN), familiarity score of the textures (FST), and thequestionnaire answers. We categorized the names intodifferent types, including names that were similar, althoughnot identical. We also ranked the number of similar namesbelonging to a specific type, and chose the maximumnumber of different types (MNDT) as a salient property foreach texture. The number of types (NT), MNDT, RT, DSN,and FST are shown in Table 2.

In the experiment, the respondents were required to fill outa questionnaire (shown in the Appendix). The questionnairewas used to analyze the reasons that influenced respondents’understanding of the textures. We plotted the frequenciesof their choices in Fig. 3. For question (1), the frequenciesof choices A and C are equal (93.3%). However, forquestion (2), the frequency of choice C is much higher thanthat of choice A, which indicates that imagination has moreinfluence on the respondents’ understanding of the texturesthan having seen similar content before.

4. Objective Methods and Results

In this section, we develop a set of measures for thetexture characteristics of regularity, roughness, directional-ity, density, and understandability. These computationscan facilitate the realization of image retrieval based onsubjective feeling.

4.1 RegularityRegularity is the property of variations in a placement

rule across a whole texture.15) For a regular texture, theextraction of texture periodicity is very important inanalyzing the regularity.25) In this study, we employed anautocorrelation function (ACF) to extract the periodicity of

Table 1. Average scores for the complexity and pairedcomparisons.

Com. Reg. Den. Dir. Rou. Und.

d10 4.27 4.07 4.47 4.67 4.47 3.70d13 5.80 1.70 5.00 3.27 6.07 5.03d15 4.77 2.47 5.70 4.23 4.93 4.43d20 4.07 6.10 6.17 6.30 4.10 3.67d26 1.43 6.53 2.53 6.63 2.87 1.07d27 5.80 2.43 5.27 1.87 5.20 5.20d40 3.53 3.43 3.40 3.40 3.40 2.17d42 2.93 4.17 2.50 3.60 3.10 1.50d43 3.07 2.53 1.83 4.37 2.33 3.90d47 2.47 6.53 2.80 6.60 2.13 2.00d62 4.37 2.43 3.73 2.23 4.70 4.80d64 3.03 6.13 5.07 6.30 3.93 1.73d67 3.30 3.53 5.33 3.03 3.40 3.50d72 5.27 2.73 4.73 4.87 5.30 3.23d74 4.10 4.27 5.37 3.23 3.53 2.93d88 3.07 4.60 3.17 3.47 2.83 2.57d107 5.50 1.57 4.80 1.38 5.20 6.07d109 5.47 2.33 5.07 1.43 5.00 6.10d111 5.50 2.77 6.47 2.07 4.40 4.93d112 5.63 2.83 5.97 2.03 4.60 5.40

Com., Complexity; Reg., Regularity; Den., Density;Dir., Directionality; Rou., Roughness; Und., Understandability

Table 2. Data from the experiment on naming the textures.

NT MNDT RT(s) DSN FST

d10 7 17 5.91 2.93 2.93d13 9 11 4.96 2.53 2.47d15 7 17 5.90 2.90 2.90d20 4 18 6.05 3.43 3.13d26 1 30 2.33 1.13 1.07d27 10 12 8.27 3.40 3.43d40 3 21 5.61 2.50 2.37d42 1 30 3.16 1.37 1.40d43 8 15 5.89 2.73 2.67d47 5 16 5.69 3.07 2.77d62 6 10 5.93 3.07 3.03d64 3 21 4.62 2.20 2.17d67 6 17 7.23 3.00 3.07d72 5 25 3.78 2.00 1.90d74 6 13 6.26 2.53 2.67d88 6 10 4.23 2.37 2.20d107 9 10 6.67 3.97 3.70d109 8 4 10.32 4.17 4.20d111 13 9 6.08 3.13 3.13d112 6 10 5.79 3.17 2.93

OPTICAL REVIEW Vol. 19, No. 5 (2012) 309X. GUO et al.

the texture and measure the regularity that corresponds tohuman visual perception.

4.1.1 Autocorrelation functionThe ACF is a a 2D function defined as

�ð�x;�yÞ ¼XM�1

x¼0

XN�1

y¼0

pðx; yÞpðxþ�x; yþ�yÞMN

; ð1Þ

where pðx; yÞ is the input signal and pðxþ�x; yþ�yÞ is theshift vector of the input. M and N refer to the signal size inthe horizontal and vertical directions, respectively. For animage, pðx; yÞ denotes the gray value at the position of ðx; yÞ,and pðxþ�x; yþ�yÞ denotes the neighborhood gray valueat a position shift from ðx; yÞ by a distance of �x inthe horizontal direction and �y in the vertical direction.Usually, the ACF is normalized as

�ð�x;�yÞ ¼ �ð�x;�yÞ� XM�1

x¼0

XN�1

y¼0

pðx; yÞ2�

MN; ð2Þ

where the denominator in eq. (2) is the maximum value ofthe ACF and represents the power of the image. Afternormalization, the ACF takes a maximum value of 1.0 at theorigin.17)

4.1.2 Regularity extracted from the ACFThe ACF of an image can be used to detect repetitive

patterns of texture elements. For regular textures, theautocorrelation function will have peaks and valleys. Peaksin the autocorrelation function of a regular-texture imagecharacterize the texture periodicity.25)

From the calculated ACF, regularity can be extracted bymeasuring the amplitude of the maximum peak in the x andy directions17) (see Fig. 4). In Fig. 4, �1 related to theperiodicity of the texture, and it reflects the regularity ofthe texture. Therefore, regularity is represented by �1. Bycomparing the heights of the maximum peaks in bothdirections, we found the maximum peak in the x direction.

By applying the ACF to the sample images, we calculatedregularity by measuring the amplitude of the maximumpeak.

4.1.3 ResultsWe compared the calculated values of regularity with the

subjective values of regularity to verify the hypothesis thatregularity calculated by the ACF relates to the perceivedregularity. Figure 5 shows a high correlation (r ¼ 0:840,p < 0:01) exists between the calculated regularity and thatevaluated subjective.

93.33

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Fig. 3. (Color online) Frequencies of choices A, B, and C in thequestionnaire.

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Fig. 4. (Color online) One-dimensional ACF along the x and ydirectional of texture d47 in Fig. 1.

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y by

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r = 0.840p < 0.01

Fig. 5. (Color online) Relationship between the regularitycalculated by the ACF and that evaluated subjectively.

OPTICAL REVIEW Vol. 19, No. 5 (2012)310 X. GUO et al.

4.2 RoughnessRoughness was originally meant for tactile textures, not

for visual ones.15) However, when we observe textures suchas those shown in Fig. 6, we can identify the rougher texture.Visual roughness is affected by the texture’s features. Fora rough texture, the grey values change quickly in a localregion. Conversely, for a smoother texture, the gray valueschange slowly in a local region.

4.2.1 Roughness calculationAccording to the results of our experiments on visual

roughness, we emphasized the effect of local changes in thetexture. Homogeneity refers to the closeness of distributionof elements in the gray level concurrence matrix (GLCM).It is used to measure local changes in the texture. The largerthe homogeneity, the more smooth and flat the texture is.Hence, we use homogeneity to estimate the smoothness of atexture, shown as

H ¼Xg1

Xg2

pðg1; g2Þk þ jg1 � g2j ; ð3Þ

where H indicates the smoothness of a texture, pðg1; g2Þ isthe GLCM, and the effect of k is to avoid the denominatorbeing equal to zero.

For the measure of roughness, we introduce eq. (4). Wesuppose the smoothness of a white image is 1. For eachtexture, compared with the white image, it is visually rough.So the relative roughness can be estimated by

R ¼ 1� kH; ð4Þwhere R is the roughness of a texture. 1 is supposed as thevalue of smoothness of a white image.

The values of H and R are affected by the value of k. Inour experiment, k ¼ 1, 0.1, 0.01, and 0.001 yielded differentvalues of correlation coefficients (r) between subjectiveroughness and calculated roughness, respectively 0.681,0.718, 0.721, and 0.722. Note that the absolute value of rslowly increases as the k decreases. Finally, we fixed k equalto 0.001 as follows:

�r ¼ rk � rk0 < 0:001; ðk ¼ k0=10Þ; ð5Þwhere r is the correlation coefficient, When �r satisfied theabove condition, we fixed the k value.

4.2.2 ResultsWe plotted the correlation between the calculated and

evaluated values of roughness (Fig. 7). Note that thecalculated roughness is related to the visual roughnessestimation by the subjects.

4.3 DirectionalityFor an image, the edges have a large influence on human

visual perception and the orientation of the edges reflectsthe orientation of the textures. Subjects’ visual judgmentson directionality are vulnerable to the effects of linearedges.

4.3.1 Directionality calculation based on texture edgesThe line-likeness and orientation of edges help us

characterize the directionality of a texture. In this study,we applied line-likeness measurement on the edges of atexture to calculate the line-likeness of a texture, from whichthe directionality of the texture could be extracted. Thedetailed procedures follow:

a) Detect the edges of the texture image using the Cannyalgorithm.

b) Calculate the line-likeness using eq. (6).15)

Fdir ¼Xni

Xnj

PDdði; jÞ

� cos jði� jÞ � 2�=nj� Xn

i

Xnj

PDdði; jÞ; ð6Þ

where PDd is the n� n local directional co-occurrencematrix of points at distance d. This matrix is defined asthe relative frequency with which two neighboring cellsseparated by a distance d along the edge direction occur onthe image. Variables i and j are the direction codes in matrixPDd. In this experiment, eight directions were includedin matrix PDd, and d ¼ 6 yielded the best correlationcoefficient r.

c) After the line-likeness was calculated for each direc-tion, the maximum value of the line-likeness was regardedas the directionality of the texture. That is because themaximum line-likeness reflects the existence of many linesin that orientation, which creates impression of the visualdirectionality.

Fig. 6. A smooth texture and a rough texture.

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Cal

cula

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roug

hnes

s

r = 0.722p < 0.01

linear regression

Fig. 7. (Color online) Correlation between the calculated andevaluated (subjective) values of roughness.

OPTICAL REVIEW Vol. 19, No. 5 (2012) 311X. GUO et al.

4.3.2 ResultsWe compared and plotted the relationship between the

calculated and evaluated (subjective) values of directionality(Fig. 8). The correlation (r ¼ 0:746, p < 0:01) indicatesthat the line-likeness of edges well characterizes thedirectionality of a texture. It also indicates that theorientations of the edges have a large impression on theperceived visual directionality.

4.4 DensityThe visual density of a texture refers to the density of

visual information in the texture. Normally, the visualinformation of a texture is contained in the edges ofprimitives or regions of color change. Vaidyanathan andLynch26) hold the view that texture can be modeled as anarrangement of visible edges that in turn amalgamate intopatterns. Hence, it is intuitive to relate the pixel number ofedges in an image to the number and spatial arrangementof primitives. The pixel number of edges in a fixed-sizeregion tells us how busy the region is.

4.4.1 Density calculationRespondents visually perceive a texture with many edges

as dense. Therefore, we used the method of measuring theedge density to represent the visual texture density. Theedge density can be determined by the ratio between thepixel number of the extracted edges and the pixel number ofthe whole texture as follows:

�den ¼ Nedges=Nimg; ð7Þwhere �den is the edge density of a texture. Nedges is the pixelnumber of the extracted edges and Nimg is the pixel numberof the whole texture.

In this study, we compared several edge detectionalgorithms (i.e., Roberts, Prewitt, Sobel, and Canny), andwe finally adopted the Canny algorithm, because it gave thebest results for edge detection.

4.4.2 ResultsTo verify whether the edge density can be used to represent

the visual density of a texture, we compared and plotted thecorrelation between the edge density and the visual density(Fig. 9). The high correlation (r ¼ 0:790, p < 0:01) betweenthe edge density and human’s visual density suggests that theedges in a texture significantly influence visual perception.More edges indicate more objects and primitives, and morevisual information in the texture.

4.5 UnderstandabilityIn our previous study, we demonstrated that the under-

standability of a texture was related to a human’s priorknowledge and experience. Naming a texture is a goodway to reflect one’s prior knowledge and experiences. Wehypothesized that the understandability of a texture could beestimated by the names given to it by respondents. For aneasy understood texture, most respondents have a commonunderstanding of it, and they will give the same or similarnames for it. In contrast, for an abstract texture, respondentshave a unique understanding of it, and they will give a widevariety of names for it. Therefore, we conducted the secondexperiment to verify this hypothesis.

In the second experiment, we obtained data involving NT,MNDT, RT, DSN, FST, and so on. Correlation analyseswere used to analyze the relationships between MNDT andunderstandability, NT and understandability, and RT andunderstandability. The correlation coefficients between themwere respectively �0:797, 0.796, and 0.710, respectively.The analyses results showed both MNDT and NT weresignificantly related to understandability. The larger thenumber of similar names for a texture, the more under-standable it is. The more types the texture evokes, the lessunderstandable it is.

The analysis results indicate that it is possible to evaluatethe understandability of a texture by the names given to it. Inaddition, they show that understandability can be estimatedfrom two factors: the maximum number of similar namesbelonging to a specific type, and the total number of typesfor a texture. The understanding of a texture is also relatedto the reaction time: it takes longer for us to think of namesfor less understandable textures.

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0.7

Evaluated directionality

Cal

cula

ted

dire

ctio

nalit

y

linear regression

r = 0.746p < 0.01

Fig. 8. (Color online) Relationship between the calculated andevaluated (subjective) values of directionality.

1 2 3 4 5 6 70.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Evaluated density

Cal

cula

ted

dens

ity

linear regression

r = 0.790p < 0.01

Fig. 9. (Color online) Relationship between the calculated edgedensity and the evaluated visual density.

OPTICAL REVIEW Vol. 19, No. 5 (2012)312 X. GUO et al.

5. Discussion

Our previous paper identified five characteristics thataffect the perception of visual complexity in a texture:regularity, roughness, directionality, density, and under-standability. Among these characteristics, regularity,density, directionality, and roughness reflect the primarycharacteristics of a texture image, whereas understandabilityreflects respondents’ prior knowledge and experience.Hence, we can conclude that visual complexity perceptionis related to the objective characteristics of a texture as wellas respondents’ subjective knowledge.

In this study, correlation analysis is used to investigatecorrelations between the characteristics of textures andvisual complexity. The results of the analysis are shown inTable 3. Note that complexity is strongly correlated withunderstandability (r ¼ 0:877, p < 0:01), which indicatesthat prior knowledge and experience considerably affecthuman perception of complexity; this is in agreement withthe definition of complexity in Webster’s dictionary; i.e., acomplex object is one that is difficult to understand or dealwith. Interestingly, roughness shows a high correlation(r ¼ 0:879, p < 0:01) with the perception of complexity.This might be partly because respondents perceive rough-ness to be associated with the imagination of texture images(which relates to understandability); this is demonstratedby the correlation between roughness and understandability(r ¼ 0:712, p < 0:01). In addition, complexity is highlyrelated to regularity (r ¼ �0:794, p < 0:01) and direction-ality (r ¼ �0:711, p < 0:01).

Visual complexity is a function of not only each individualcharacteristic but also of interactions between them, which isdemonstrated by the correlation coefficients of perceptualcharacteristics in Table 3. The correlation between regularityand understandability is high (r ¼ �0:838, p < 0:01). Ingeneral, textures characterized by regular placement areeasy to understand, leading to a perception of less visualcomplexity. Similarly, the correlation between directionalityand understandability is also very high (r ¼ �0:763,p < 0:01). Interactions exist between roughness and under-standability, regularity and roughness, and directionalityand roughness. Therefore, it is suggested that respondentsused a different combination of these characteristics whileevaluating the visual complexity of a texture.

A set of objective methods was employed to measurethe characteristics of a texture. For regular textures, theautocorrelation function will have peaks and valleys. As has

been previously established, peaks in the autocorrelationfunction of a regular-texture image characterize the textureperiodicity.17) For the regularity of a texture, we adoptedthe ACF to extract the periodicity of the texture and measurethe regularity corresponding to human visual perception.The validity of ACF analysis for determining the regularityof a texture was examined by comparing the calculatedregularity with subjective scores of regularity. The highcorrelation (r ¼ 0:840, p < 0:01) between them showed thevalidity of ACF analysis.

Edges have a significant influence on human visualperception.26) Respondents perceive a texture with manyedges as dense. Therefore, we used the method of measuringthe edge density to represent the visual texture density.Similarly, the perception of directionality is easily affectedby the orientations of the edges. Hence, we regarded themaximum line-likeness of edges in different directions asthe main direction of the texture. The results showed thatthe calculation of the maximum line-likeness of edgesrepresented the visual direction of the texture. Similarly,the correlation between objective methods and subjectiveevaluations was validated.

We measured visual roughness mathematically based onthe gray changes in a small region. The more changes in thelocal region, the more rough the texture is. We compared thecalculated roughness and subjective roughness. The resultshowed that the calculated roughness was related to thesubjective roughness. However, human visual roughness isalso influenced by the imagined tactile feeling of a texture,not just by its objective features. In other words, viewersuse knowledge stored in memory to attribute meaning to animage of a texture.27) When they look at a texture, they canimagine whether it will feel rough or smooth. If one regardsthe texture as the surface of a product, then he or sheimagines how the surface would feel.

We introduced a new approach to estimate the under-standability of a texture by naming it. In the experiment ofnaming the textures, all respondents were Chinese, whichensured that they all had the same cultural background.In addition, both DSN and FST were obtained from therespondents. As has been shown, an easy to name textureis familiar and easy to understand. In our experiment, thecorrelations between DSN and understandability (r ¼ 0:811,p < 0:01) and FST and understandability (r ¼ 0:826, p <0:01) also verified this result. In addition, MNDT and CTwere significantly related to understandability. Therefore,the understandability of a texture can be estimated from twoaspects: the maximum number of similar names belonging toa specific type and the total number of types for a texture.The larger the number of similar names for a texture, themore understandable it is. The more types the textureevokes, the less understandable it is.

6. Conclusion

Five important texture characteristics involved in theperception of visual complexity of texture images wereidentified in our previous paper:2) regularity, roughness,directionality, density, and understandability. Visual com-

Table 3. Correlation matrix of perceptual characteristics of atexture and visual complexity.

Reg. Den. Dir. Rou. Und.

Com. �0:794aÞ 0.590aÞ �0:711aÞ 0.879aÞ 0.877aÞ

Und. �0:838aÞ 0.484 �0:763aÞ 0.712aÞ

Rou. �0:753aÞ 0.480 �0:491Dir. 0.716aÞ �0:386Den. �0:177

a) p < 0:01

OPTICAL REVIEW Vol. 19, No. 5 (2012) 313X. GUO et al.

plexity is a function of not only each individual character-istic but also of interactions between them.

In this study, computational measures of the first fourcharacteristics were developed and correlated with humanvisual perceptions of them. For regularity, we adopted theautocorrelation function to extract the periodicity of atexture and measure the regularity. The result showed thatthe computational regularity was significantly correlatedwith the subjective regularity. For roughness, we measuredthe gray changes within a small region to mathematicallycalculate visual roughness. The comparison showed that thecalculated roughness was related to the subjective rough-ness. The subjective perception of directionality was easilyaffected by edges. Hence, we regarded the maximum line-likeness of edges in different directions as the main directionof a texture. The results showed that the calculation of themaximum line-likeness of edges represented the subjectivedirection of a texture. For density, we employed the methodof calculating the edge density. A comparison between thecalculated density and subjective density indicated that thesubjective density was vulnerable to the influence of edges.

A method of measuring the understandability of a texturewas developed. The experimental results showed that it waspossible to evaluate the understandability of a texture bynaming it. In addition, the results showed that under-standability could be estimated from two factors of a texture:its maximum number of similar names belonging to a specifictype and its total number of types. The larger the number ofsimilar names for a texture, the more understandable it is. Themore types the texture evokes, the less understandable it is.

This study has helped determine relationships betweenobjective (calculated) and subjective (perceived) texturecharacteristics. This will facilitate the mapping betweenobjective texture characteristics and humans’ perceptions ofvisual complexity. It will also facilitate image retrieval basedon subjective feelings. In particular, we introduced a newmethod to measure humans’ understandability of a texture.

In this study, however, the number of textures used inthe experiments was limited because it was difficult forrespondents to evaluate many textures in one experiment.In addition, the objective methods should be improved tobetter match the subjective evaluations. In a future study,we will aim to improve the algorithms for the five texturecharacteristics discussed above, and we will model thevisual complexity of the textures associated with thesecharacteristics.

Acknowledgment

The authors thank the respondents who participated in theexperiments.

Appendix

In the experiment of naming the textures, we asked therespondents to fill out a questionnaire, which was helpful foranalyzing the reasons that influenced their understanding oftextures. The questions in the questionnaire were as follows:

1. Which reasons helped you easily understand eachimage?

A. You have seen the image content or similar contentbefore.

B. The image is simple and regularly composed.C. You can easily imagine the image.D. (if you have any

other reasons)2. Which one of the above reasons (A, B, C, or D)

influenced you most?

References

1) W. Groissboeck, E. Lughofer, and S. Thumfart: Inf. Sci. 180(2010) 2065.

2) X. Y. Guo, C. M. Asano, A. Asano, and T. Kurita: 2011ICBAKE, 2011, p. 260.

3) R. Scha and R. Bod: Inf. Informatiebeleid 11 (1993) 54 [inDutch].

4) F. Heylighen: The Evolution of Complexity (Kluwer AcademicPress, Dordrecht, 1997) p. 17.

5) C. Heaps and S. Handel: J. Exp. Psychol. Hum. Percept.Perform. 25 (1999) 299.

6) W. Li: Complex Syst. 5 (1991) 381.7) A. Olive, M. L. Mack, M. Shrestha, and A. Peeper: Proc. 26th

Annu. Meet. Congnitive Society, 2004, p. 1041.8) R. Pieters, M. Wedel, and R. Batra: J. Mark. 74 (2010) 48.9) W. Saleem, A. Belyaev, D. Wang, and H. P. Seidel: Comput.

Graph. 35 (2011) 580.10) Y. A. Andrienko, N. V. Brilliantov, and J. Kurths: Eur. Phys. J.

B 15 (2000) 539.11) L. N. Patel and P. Holt: 2000 ACIV, 2000, p. 119.12) J. Rigau, M. Feixas, and M. Sbert: Eurographics Workshop

Computational Aesthetics in Graphics, Visualization andImaging, 2005, p. 177.

13) M. Cardaci, V. D. Gesu, M. Petrou, and M. E. Tabacchi: FuzzySets Syst. 160 (2009) 1474.

14) E. Michailidou: Accessibility Comput. 86 (2006) 24.15) H. Tamura, S. Mori, and T. Yamawaki: IEEE Trans. Syst. Man

Cybern. 8 (1978) 460.16) M. Amadasun and R. King: IEEE Trans. Syst. Man Cybern. 19

(1989) 1264.17) K. Fujii, S. Sugi, and Y. Ando: Psychol. Res. 67 (2003) 197.18) L. Li, A. Asano, and C. Muraki Asano: Opt. Rev. 17 (2010) 90.19) A. R. Rao and G. L. Lohse: GVGIP: Graphical Models Image

Process. 55 (1993) 218.20) A. Ravishankar Rao and G. L. Lohse: Vision Res. 36 (1996)

1649.21) Y. R. Cho, V. Yang, and P. E. Hallett: Percept. Psychophys. 62

(2000) 735.22) P. Brodatz: Textures: A Photographic Album for Artists and

Designers (Dover, New York, 1966).23) M. Kokubun, M. Konishi, M. Kuwasumi, and H. Iguchi: Proc.

26th Annu. Conf. IEEE Industrial Electronics Society (IECON2000) 3 (2000) 1592.

24) C. H. Coombs, R. M. Dawes, and A. Tversky: MathematicalPsychology: An Elementary Introduction (Prentice-Hall,Englewood Cliffs, NJ, 1970) p. 235.

25) H. C. Lin, L. L. Wang, and S. N. Yang: Pattern Recognit. Lett.18 (1997) 433.

26) G. Vaidyanathan and P. M. Lynch: Proc. IEEE Energy andInformation Technologies in the Southeast (Southeastcon’89)2 (1989) 733.

27) R. V. Egmond, P. Lemmens, T. N. Pappas, and H. D. Ridder:Proc. SPIE Proc. 7240 (2009) 72400B.

OPTICAL REVIEW Vol. 19, No. 5 (2012)314 X. GUO et al.