A Measure of Texture Directionality

Manil Maskey and Timothy S. Newman

University of Alabama in Huntsville, Huntsville, AL, U.S.A.

Keywords:

Texture, Directionality, Orientedness, User Study.

Abstract:

Determining the directionality (i.e., orientedness) of textures is considered here. The work has three major

components. The ﬁrst component is a new method that indicates if a texture is directional or not. The new

method considers both local and global aspects of a texture’s directionality. Local pixel intensity differences

provide most of the local aspect. A frequency domain analysis provides most of the global aspect. The second

component is a comparison study (based on the complete set of Brodatz textures) of the method versus the

known, competing methods for determining texture directionality. The third component is a user study of the

method’s utility.

1 INTRODUCTION

Image texture, while hard to well-deﬁne, involves

some local order repeating over a larger area

(Hawkins, 1970). In addition to having inherent fea-

tures such as the size and degree of regularity in rep-

etition, some textures also have orientation or other

inherent features. Texture features have been used ex-

tensively in a variety of computer vision and pattern

recognition applications. For example, Shiranita et

al. have used texture features to determine the quality

of meat (Shiranita et al., 1998). Gorkani and Picard

have used texture orientation to detect images of ur-

ban areas (Gorkani and Picard, 1994). Mudigonda

et al. have used texture features for detecting tissue

masses in mammograms (Mudigonda et al., 2001).

Texture features have also been extensively used to

retrieve matching images from large image databases

(Smith and Chang, 1996)(Saha et al., 2004)(Kekre

et al., 2010).

Research has shown that certain characteristics

of textures are readily perceived by human and ani-

mal vision. For example, studies (Hubel and Wiesel,

1968)(Blake and Holopigan, 1985) have found that

the visual cortex of monkeys includes numerous de-

tectors sensitive to orientation of structures in the

visual ﬁeld. Textures also help in visually dif-

ferentiating surfaces (Beck, 1982)(Nothdurft, 1985).

In addition, orientations within textures offer tex-

ture segregation cues to the visual system (Noth-

durft, 1990)(Nothdurft, 1991). Additionally, Ware

and Knight (Ware and Knight, 1992) have performed

a user study that suggested that humans perceive there

to be a number of visual characteristics of textures,

such as regularity, size, and orientation.

In this paper, our focus is on determining if a tex-

ture is directional and on the use of directional tex-

tures. Directionality may be a useful feature for vision

and pattern recognition since it would allow for differ-

entiating between (i.e., classifying) textures. It may

also be useful in multimedia, visualization and graph-

ics applications. To support using texture directional-

ity as a texture discriminator, a new measure that can

determine the directionality status for a texture is in-

troduced and validated here. We also present the ﬁrst

comparison study of texture directionality measures–

that study includes comparison of the new measure

against the existing measures, using user sentiment as

a baseline.

The rest of the paper is organized as follows.

Section 2 brieﬂy discusses related work. Section 3

presents the new texture directionality measure. Sec-

tion 4 presents the comparison of the directionality

measures. Section 5 describes the user study. Sec-

tion 6 analyzes the results, and Section 7 provides the

conclusion and future work.

2 BACKGROUND

A number of frameworks for computing various types

of texture measures have been reported (e.g., (Haral-

ick, 1979)). In addition, some applications have used

such measures. For example, Chetverikov has mea-

432

Maskey M. and Newman T..

A Measure of Texture Directionality.

DOI: 10.5220/0005312904320438

In Proceedings of the 10th International Conference on Computer Vision Theory and Applications (VISAPP-2015), pages 432-438

ISBN: 978-989-758-090-1

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

sured texture regularity using a gray-level difference

histogram feature (Chetverikov., 1984) and later used

the measure in applications such as structural defect

detection (Chetverikov and Hanbury, 2002). Cao et

al. have derived a texture sharpness measure that is

used in quantifying sharpness of digital images (Cao

et al., 2009).

Our focus here is directional textures, so next we

discuss previous work on texture directionality.

2.1 Textures and Directionality

Tamura et al. (Tamura et al., 1978) conducted an

early study on the role of textures in human percep-

tion. They also introduced texture measures based on

spatial intensity variation, one of which aimed at esti-

mating overall directionality in an image. Their direc-

tionality measure was based on the sharpness of peaks

in a histogram of high magnitude gradient pixels. The

gradient values were estimated using mask-based hor-

izontal and vertical directional difference estimates at

each pixel. If a pixel’s gradient magnitude was above

a threshold, it was considered to be high magnitude.

They also reported user studies that considered the

correlation between human perception and their mea-

sures. The studies used 16 (of the 111) Brodatz image

archive textures of various types. All possible com-

binations of pairs of these 16 images were shown to

the participants, who then identiﬁed one texture from

each pair that best exhibited the directionality charac-

teristic. (Five other texture properties were also stud-

ied similarly.) Their study suggested that their direc-

tionality measure was highly correlated with the hu-

man responses.

Another texture directionality measure was de-

ﬁned by Picard and Gorkani (Picard and Gorkani,

1992). Their measure was based on a steerable pyra-

mid deﬁned with steerable ﬁlters like the ones de-

scribed by Freeman and Adelson (Freeman and Adel-

son, 1991). Picard and Gorkani’s pyramid had four

levels, where the lowest level was the actual tex-

ture. At each level, the steerable ﬁlters were used to

compute each pixel’s dominant orientation and orien-

tation “strength.” Then, orientation histograms were

constructed for each level based on the orientation

strength values. After smoothing, the histogram peaks

were found. Next, the orientation histograms for each

level were combined. Finally, the measure of texture

directionality was computed from this combination.

Picard and Gorkani applied their measure to all 111

Brodatz textures and subsequently validated the mea-

sure via user study on the same textures.

Abbadeni (Abbadeni, 2000) and colleagues (Ab-

badeni et al., 2000) have proposed a measure of tex-

ture directionality based on a variance statistic, the

auto-covariance function g. g expresses the covari-

ance between the original image and a shifted version

of that image, as shown in Eqn. 1:

g(δ

, δ

) =

i j

−δ

−1

∑

i=0

−δ

−1

∑

j=0

I (i, j) I (i + δ

, j + δ

(1)

where n

and n

are the number of columns and rows

in the image I, respectively, the δ terms represent

shifts, 0 ≤ δ

≤ n

− 1 and 0 ≤ δ

≤ n

− 1, and

i j

= (n

− δ

)(n

− δ

). The approach found the gra-

dient of the auto-covariance at each pixel. The pixels

whose gradient exceeded a threshold t were consid-

ered to be oriented. In addition, if a sufﬁcient number

of pixels were considered to be oriented, then the im-

age was considered to be a texture with a dominant

orientation, denoted by Θ

, and a directionality value

, deﬁned as shown in Eqn. 2:

∑

−1

i=0

∑

−1

j=0

(i, j)

∗ n

) − N

, (2)

where N

is the number of non-oriented pixels. Ab-

badeni also performed a user study to validate the

measure.

Hagh-Shenas and Interrante (Hagh-Shenas and In-

terrante, 2005) have also described a texture direc-

tionality measure. It is based on the Discrete Fourier

Transform (DFT). It reduced DFT aliasing artifacts

by applying a Hanning window to the original texture

and then applying DFT on the Hanning-modiﬁed tex-

ture. Next, the DFT output was Gaussian-smoothed

and converted into polar coordinates. The 180

◦

-range

of frequency values in the polar coordinates were di-

vided into 18 equal intervals (through the DC point).

Each interval was also radially divided by 64 cir-

cles, generating, in all, 18x64 locations. The val-

ues at these locations were stored in an 18x64 matrix

called the Discrete Fourier Polar Coordinates Matrix

(DFPM). Using the DFPM, a directionality measure,

, was computed, as shown in Eqn. 3:

∑

i=1

(M(i) − f (i))

n ∗ M(i)

, (3)

where f(i) is the sum of the i

column in the DFPM,

M(i) is the maximum value in that column, and n=64

columns.

Sikora et al. (Sikora, 2001) and Wu et al. (Wu

et al., 1999) have used Gabor ﬁlter banks with scale

and orientation sensitive ﬁlters to design texture fea-

tures. These features were used to measure a concept

related to directionality, the structuredness, of an im-

age. Manjunath et al. (Manjunath et al., 2001) have

AMeasureofTextureDirectionality

433

also described texture descriptors that incorporate di-

rectional features for sub-regions of a texture. The

set of features over all the sub-images were then used

to formulate a feature vector for image indexing and

retrieval. Directionality of the texture itself was not

computed; hence, the texture is not classiﬁed as di-

rectional or non-directional.

Lastly, it should be noted that Healey and Enns

(Healey and Enns, 1999) have presented an overview

of the development of understandings and applica-

tions of texture in computer vision, graphics and vi-

sualization.

3 NEW TEXTURE

DIRECTIONALITY MEASURE

A focus of our work is determining if a texture sam-

ple is directional. In this section, we describe the pro-

cessing steps for our texture directional determination

scheme. Our scheme considers both local and global

aspects of directionality, which is one difference from

most prior work.

The scheme acts as a measure that indicates if a

texture is directional or non-directional. It examines

directional intensity variations in texture as an initial

step, then does a frequency domain analysis of the

texture. This examination of intensity variation along

predeﬁned directions is aimed at identifying the more

certain highly directional and highly non-directional

textures ﬁrst. Frequency domain analysis of the re-

maining textures provides more information on the

texture directionality.

Computing the measure consists of applying the

following steps to the texture sample.

Step 1. Compute pixel intensity differences along

the 0, 45, 90 and 135 degree directions (from the hori-

zontal) using a 3x3 neighborhood mask on each pixel

of the texture.

Step 2. Compute the mean pixel intensity differ-

ences along each direction.

Step 3. Compute the max and min pixel intensity

differences.

Step 4. Classify the texture as highly directional,

highly non-directional, or possibly directional, using

the following rules. If the difference, d, between the

max and min pixel intensity differences is greater than

a threshold t

, classify the texture as highly direc-

tional. If d is greater than another threshold t

, then

classify the texture as highly non-directional (we use

> t

). Classify all textures with t

≤ d ≤ t

as pos-

sibly directional. They need to be investigated further.

(Note: The local intensity variation approach taken

here is similar to the local binary pattern (LBP) con-

cept (Ojala et al., 2002). However, instead of using

the variation as a texture discrimination measure like

LBP does, we compute a global orientation measure

for the texture.)

Step 5. Stop if the texture was classiﬁed as highly

directional or highly non-directional. Otherwise, pro-

ceed to Steps 5a, 5b, and 5c:

Step 5a. Apply a Fourier transform. (Our ap-

proach uses the Fourier tranform to assess geometric

characteristics within a texture.)

Step 5b. Apply a Hough line transform to the out-

put of Step 5a to identify existence of lines. The

Hough transform is used to ﬁnd structures in the

Fourier transformed texture. Presence of linear-like

structure in the Fourier transformed texture may in-

dicate that the texture is oriented. The Hough line

transform uses the line formulation shown in Eqn. 4:

xcosθ + ysinθ = ρ. (4)

Eqn. 4 speciﬁes a line passing through (x, y) that is

perpendicular to the line from the origin to (ρ, θ) in

polar space. For each point (x,y) on that line, ρ and θ

are constant. The set of possible lines passing through

(x, y) is obtained by solving for ρ and θ. An accu-

mulator counts the number of times each (ρ, θ) com-

bination describes a credible line passing through a

pixel. Points that are collinear yield higher counts for

the (ρ, θ) parameters describing their common line.

Any time the accumulator count is high (we use 90

for our textures, which are size 128x128), we hypoth-

esize such a line is present.

Step 5c. If one or many lines exist in the output

of Step 5b, then classify the texture as a highly direc-

tional texture.

We use Hough processing after the Fourier step

to allow some textures with disconnected directional

components to be identiﬁed as directional (e.g., tex-

ture D102 from the Brodatz image archive); the lo-

cal pixel difference method does not deal well with

disconnected directional components. Furthermore,

our approach also allows textures with multiple dom-

inant directions to be detected as directional. Figure 1

shows such a texture, D102, with multiple dominant

directions. Figure 2 shows the Fourier transformation

of texture D102. The presence of straight lines in Fig-

ure 2 indicates that texture D102 is directional.

Since most prior texture directionality measures

have been based on a local texture model, they may

ignore some global aspects of texture directionality

that could be utilized in human visual perception. Our

measure, however, considers both local and global

texture directionality (via its use of local pixel differ-

ence and Fourier and Hough steps). One limitation is

that our measure only reports if the texture is oriented

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434

Figure 1: D102.

Figure 2: Fourier transform of D102.

or not; it does not report direction (i.e., the angle of

texture’s orientation). We hope to address this limita-

tion in future work.

4 COMPARISON OF TEXTURE

DIRECTIONALITY MEASURES

We next report on our comparison study. It evalu-

ates our directionality measure versus the four prior

measures. In our comparison, we applied all the mea-

sures to the complete archive of 111 Brodatz textures.

Previously, only Picard and Gorkani have reported a

complete test, for their measure alone, on the entire

Brodatz archive. Thus, the report here represents the

ﬁrst comprehensive comparison of the existing and

new texture directionality measures.

Table 1: List of consistently-classiﬁed textures.

Directional Non-directional

D1,D6,D11,D15,D18,D20, D2,D23,D28,D30,

D24,D25,D26,D34,D36,D37, D32,D33,D40,D41,

D47,D49,D50,D51,D52,D53, D54,D60,D62,D63,

D55,D56,D65,D68,D70,D72, D66,D67,D75,D88,

D76,D77,D78,D79,D83,D94, D89,D91,D100,

D95,D96,D105,D106 D109,D111

For the Abbadeni measure, we had to make two

assumptions due to incomplete information in their

paper: (1) the threshold for whether a pixel is ori-

(a) D1 (b) D6

Figure 3: Sample textures that are consistently- classiﬁed

(D1 and D6 directional; D2 and D23 non- directional).

ented, and (2) the criterion to determine a dominant

orientation. We determined these thresholds for our

work here as follows. (1) We have used the aver-

age orientation of all the pixels in the texture as the

threshold to determine which pixels are oriented. (2)

If more than half the texture’s pixels are oriented then

we consider that texture to have a dominant orienta-

tion. We label textures with a dominant orientation as

directional textures.

Table 1 lists textures from the Brodatz archive

that were classiﬁed consistently by the directional-

ity measures (i.e., the table shows the texture images

for which the ﬁve measures were in agreement). Ta-

ble 2 lists the Brodatz texture images for which the

ﬁve measures disagreed, with N and D used to de-

note classiﬁcation as non-directional and directional,

respectively. We have computed the Pearson correla-

tion coefﬁcient (Jackson, 2009) for only these incon-

sistencies to measure the correlation among all mea-

sures. The Pearson correlation coefﬁcient here tests

the null hypothesis that there is no signiﬁcant corre-

lation in data. Table 3 shows the correlation matrix,

using a 95% level of conﬁdence value. We discovered

that our measure and Hagh-Shenas’s measure had the

best correlation. The second best correlation was our

measure with Picard and Gorkani’s measure.

5 USER STUDY

A subset of the Brodatz textures was used in our

user study, which we describe next. We consider the

study’s results as a ground truth to compare the tex-

ture directionality measures.

The study’s protocol, which was approved by the

AMeasureofTextureDirectionality

435

Table 2: Classiﬁcation of remaining Brodatz textures by

measure (T= Tamura et al., H=Hagh-Shenas and Interrante,

P=Picard and Gorkani, A=Abbadeni et al., and M=My mea-

sure), with N indicating a non-directional classiﬁcation and

a D indicating a directional one.

ID T H P A M

D3 D D D N D

D4 N D N N N

D5 N N N D N

D7 D D D D N

D8 N N D D N

D9 N D N N N

D10 N D D N N

D12 D D D D N

D13 D N D D N

D14 D N D D N

D16 N D D D N

D17 N D D D N

D19 N N N D N

D21 N D D D D

D22 N D D D D

D27 N N N D N

D29 N N N D N

D31 D N N N N

D35 D D D N D

D38 N N D D N

D39 N N N D N

D42 N N D D N

D43 N N D D N

D44 N D D D N

D45 N N D N N

D46 D N D D D

D48 N N D D N

D57 N D N N N

D58 N N N D N

ID T H P A M

D59 N N D D N

D61 N N N D N

D64 D D D N D

D69 D N D D N

D71 N D N N N

D73 N N N D N

D74 D N N N N

D80 N N D N N

D81 N D D N N

D82 N D D N N

D84 N N D D N

D85 N D D D D

D86 N D N D N

D87 N N D N N

D90 N N N D N

D92 N D N D N

D93 D N D N N

D97 N N D D D

D98 N N D N N

D99 N N N N D

D101 N D D N D

D102 N D D D D

D103 D D D N N

D104 D D D N N

D107 N N D N N

D108 N N D D N

D110 N N N D N

D112 N N N D N

institution’s Human Subjects Committee, involved

ﬁrst providing a 2-3 minute overview about textures

to each participant. All participants considered the

same set of questions, with the study administered in

a computerized form. Participants were isolated from

each other.

5.1 Subjects

Twenty two individuals participated in the study.

Twelve were atmospheric science graduate students

and ten were environmental scientists.

5.2 User Study Task

In the study, participants were asked to perform a

task, which we describe next. Each participant com-

pleted classiﬁcation of 15 Brodatz textures (shown

Table 3: Pearson Correlation Coefﬁcient for inconsistent

classiﬁcation.

T H P A M

T 1

H 0.17379 1

P 0.24871 0.25472 1

A -0.21738 -0.27275 -0.05432 1

M 0.20521 0.34405 0.28949 -0.03257 1

Table 4: User classiﬁcation of the textures.

D9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

D14 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1

D21 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 1 2 2 2 2 2

D25 2 2 2 2 1 1 0 2 2 2 2 2 2 2 2 2 2 2 1 1 2 0

D31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

D34 2 2 2 2 1 1 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2

D49 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

D53 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2

D58 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0

D60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

D65 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

D75 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0

D78 0 1 1 1 2 0 0 1 1 0 1 1 1 1 1 0 1 1 2 1 1 0

D86 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

D97 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1

in Figure 4) into one of three classes: highly direc-

tional, highly non-directional, and somewhat direc-

tional. Like Tamura, we selected these 15 at random,

5 per classiﬁcation (from our measure). We used a

small subset rather than the complete set of Brodatz

textures to avoid user fatigue.

The overall results from the task are shown in

Table 4, where highly non-directional, highly direc-

tional, and somewhat directional textures are denoted

by 0, 2, and 1, respectively. The rows of the table

list individual textures. The columns of the table list

participant classiﬁcations.

Comparisons of classiﬁcations produced by the

user task against those from the existing direction-

ality measures are reported in Table 5. In the ta-

ble, the highly directional and somewhat directional

classes from the user task are grouped together. N and

ND represent directional and non-directional, respec-

tively. Our method concurs with the user study results

93% of the time. We believe that this is due to global

directionality being addressed by our method as well

as in human vision.

6 ANALYSIS

Next, we present a comparison of the directionality

measures performance. We do so using a comparison

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436

Table 5: Task 1 classiﬁcations vs. the classiﬁcations from the ﬁve measures.

D9 D14 D21 D25 D31 D34 D49 D53 D58 D60 D65 D75 D78 D86 D97

User Study ND ND D D ND D D D ND ND D ND D ND ND

Our Metric ND ND D D ND D D D ND ND D ND D ND D

Abbadeni ND D D D ND D D D D ND D ND D D D

Picard and Gorkani ND D D D ND D D D ND ND D ND D ND D

Hagh-Shenas D ND D D ND D D D ND ND D ND D D ND

Tamura ND D ND D D D D D ND ND D ND D ND ND

(a) D9 (b) D14 (c) D21

(d) D25 (e) D31 (f) D34

(g) D49 (h) D53 (i) D58

(j) D60 (k) D65 (l) D75

(m) D78 (n) D86 (o) D97

Figure 4: The Brodatz textures used in Task 1.

of classiﬁers mode, where the user study result is used

as the ground truth set and each measure is used as a

classiﬁer. Classiﬁer performance is considered here

using precision versus recall. Precision is the ratio of

the number of correct classiﬁcations to the total num-

ber of classiﬁcations. Recall is the ratio of the number

of correct classiﬁcations to the total number of correct

classiﬁcations.

Figure 5 shows the plot of precision versus re-

Figure 5: Precision versus recall comparison of texture ori-

entation measures.

call for all texture orientation measures using the user

study results as ground truth. The ﬁgure suggests that

our measure has high precision at all recall levels, in

particular that our new method’s precision exceeds

that of the existing measures.

7 CONCLUSIONS

In this paper we have presented a new texture direc-

tionality measure and validated the measure with user

studies. The measure allows determination of suitable

directional textures. We have also compared, for the

ﬁrst time, the existing texture orientation measures us-

ing an identical set of images. In the future, we hope

to study other aspects of texture orientedness, such

as allowing for determination of which direction is a

dominant one in a directed texture.

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