FIBER ORIENTATION DISTRIBUTION OF PAPER SURFACECALCULATED BY IMAGE ANALYSIS
Toshiharu Enomae

Yoon-Hee Han

Akira Isogai

Assistant Professor

Ph.D. Candidate

Professor

enomae@psl.fp.a.u-tokyo.ac.jp
Paper Science Laboratory, Department of Biomaterial Sciences
Graduate School of Agricultural and Life Sciences
The University of Tokyo
JAPAN

ABSTRACT
Anisotropy of paper is an important parameter oforientation distribution as a function of angle θ when themachine direction of a web or sheet is set to θ = 0. Fiberpaper structure. Image analysis technique was improved

orientation occurs due to a flow of pulp suspension

for accurate fiber orientation in paper surfaces. Image

including the turbulence level and orienting shear, so theanalysis using Fast Fourier Transform was demonstrated

flow condition may alter it through web or sheet thickness

to be an effective means to determine fiber orientation

and across the wire plane. Fiber orientation is importantangle and its intensity. Binarization process of micrographbecause it affects greatly physical properties like

images of paper surface and precise calculation foranisotropy in strength, drying shrinkage and wet straining,

average Fourier coefficients as an angular distribution by

and further two-sidedness in the case its variation ofinterpolation developed were found to improve thein-plane orientation through sheet thickness present [1].

accuracy. This analysis method was applied to digital

To determine fiber orientation, there are several

optical micrographs and scanning electron micrographs ofmethods developed [2]. Anisotropy in mechanicalpaper. A laboratory handsheet showed a large deviation inproperties like tensile strength and elastic modulus, elastic

the average value of fiber orientation angle, but somemodulus calculated from velocity at which ultrasoundkinds of machine-made paper showed about 90 degrees intravels in paper and apparent density of paper are easily

the orientation angle with very small deviations asmeasured and indicates anisotropy well, Structural

expected. Korea and Japanese paper made in theproperties like diffraction [3,4] or reflection [5] of light

traditional ways showed its own characteristic depending

particularly with a laser beam, dielectric permittivity ofon its hand making processes.

microwave [6], X-ray diffraction also can be an
appropriate parameter for anisotropy.

KEY WORDS

Some researchers applied image analysis for purposes

Fourier transform, Japanese paper, Korean paper, fiber

like this. Scharcanski and Dodson [7,8] used a local image

orientation distribution, fiber orientation intensity

gradient of all pixels for images by β-radiography andlight transmission. They estimated orientation angle as a

INTRODUCTION
Pulp fibers take a variety of spatial configuration in
paper and its alignment is an important aspect of paper
structure. Statistically, fiber alignment is defined as a fiber

direction to maximize the total of length of gradientvectors projected to its direction.
Also in textile and nonwoven fields, there areresearchers who tried to determine fiber orientation. Kim

et. al [9] recorded video images of thermally bonded

nonwoven.

nonwovens from polypropylene fibers during tensile
deformation and calculated changes of fiber orientation

FIBER ORIENTATION DETERMINED BY IMAGE

distribution function by image analysis. They revealed that

ANALYSIS

fiber reorientation progress during elongation more

Fourier transform
Fourier Transform (FT) is useful for detecting

remarkably in the cross direction than in the machine
direction and it depends on the anisotropy of the structure

periodicity in signals and images. To paper, it is applied

and the bond pattern. Thorr et. al [10] designed a sensor

for investigating wire mark, flocculation size, etc.

capable of measuring locally the mass per unit area of

Supposed an image f(x, y) , where f means a gray level at

nonwoven geotextiles with illumination of an integrating

position (x, y), Equation (1) expresses F(kx, ky), namely,

sphere. They exhibited that the orientation distribution

FT of f(x, y). Equation (2) expresses Inverse Fourier

curve corresponded well to the vertical orientation inTransform (IFT).

progress of fibers during a tensile test of a needle-punchedy = N −1 x = N −1

F (k x , k y ) = ∑
y =0

⎧

2π

⎫

∑ f ( x, y) exp⎨⎩− i N (k x + k y)⎬⎭
x

x =0

…(1)

y

(k x = 0,1,L, N − 1 k y = 0,1,L, N − 1)
k = N −1f ( x, y ) =k x = N −1
1 y
⎧ 2π
⎫
F (k x , k y ) exp⎨− i(k x x + k y y )⎬∑2 ∑N k y =0 k x =0
N
⎩
⎭

…(2)

( x = 0,1,L, N − 1 y = 0,1,L, N − 1)
Fiber orientation distribution by Fourier Transformpixels (Fig. 1a, for example) to minimize improper

Image analysis is a powerful tool for determining

shading in the peripheral. Secondly, the images werefiber orientation. Major direction of fibers was determinedbinarized using a dynamic threshold method of simple

following the next steps.

moving average (Fig. 1b). In this method, white (level

Firstly, micrographs captured by several methods

255) or black (level 0) of every pixel was judged bymentioned in the experimental section as a 256 gray levelcomparing to its surrounding pixels in the 41 by 41pixels

image or one converted from 24 bit color images were

block. Moving average method used can correct shading

trimmed to a size of 1024 by 1024 pixels or 512 by 512

of images taken under inhomogeneous illumination.

(a)

(b)

(c)

Fig. 1 Micrograph with digital optical microscope (a), binary image (b) and power spectrum (c)Additionally, this way of binarization can extract edges ofangle from the XY coordinate origin, the radius passes justfibers out of focus under top fibers in focus or even inthrough some positions but mostly only near the positions.

whole out-of-focus images. Binarization was performed

Then, interpolation was applied in the following manner.

using a shareware application, PopImaging V.3.1, Digital

Suppose amplitude of a Fourier coefficient A(X, Y) at

being kids, Co. Ltd., Japan. Thirdly, for Fast Fourier

a position (X, Y) in the XY frequency space (See Fig.2).

Transform (FFT) was computed with these binary images

We designed the calculation method that amplitude A(X,using an application of Visual Basic 6.0, Microsoft Corp.

Y) at that point with center angle θ and radius r is given by

developed by the authors. Figure 1c is an example of a

Equation (3). Then, mean amplitude A(θ ) in every

power spectrum. The FFT routine was programmed

direction of center angle θ was calculated according tofollowing a general textbook.

Equation (4) and was defined as the fiber orientation

In the process of determining fiber orientation from

distribution in this work.

the Fourier transformed image, amplitude of FourierA(xn, yn+1)

coefficient was added in the radius direction from theorigin, that is, the center of the image toward theA(X,Y)

peripheral and its mean was determined from 0 to 180rdegrees of center angle θ. But, a problem occurs in thisdyprocess. This addition was found to be not as easy as we
expected because each position meaning frequency of theA(xn+1, yn+1)θA(0, 0)dx
A(xn, yn)A(xn+1, yn)

Fourier coefficient in the XY coordinates cannot be easily
converted to the corresponding point in the polar
coordinates exactly. If one draws a radius of a given center

Fig. 2 Schematic diagram of calculation ofmean amplitude every radius direction

A( X , Y ) = A( r cos θ , r cos θ )= (1 − d x )(1 − d y ) A( x n , y n ) + d x (1 − d y ) A( xn +1 , y n ) + (1 − d x )d y A( xn , y n +1 ) + d x d y A( xn +1 , y n +1 )

…(3)

n

⎛n ⎞ 2A(θ ) = ⎜ − 1⎟∑ A( r cos θ , r sin θ )⎝ 2 ⎠ r =2
Adding starts with r = 2 in this equation and not with…(4)

those at 0 or 90 degrees, respectively). A(0, 0) is usuallyr = 1 or r = 0. the reason is as follow: at r = 0, A(0, 0)

by far larger than other amplitudes and affects the mean

meaning an average of gray level of all the pixels in theamplitude too much. To eliminate this adverse effect, theoriginal micrographs, is the amplitude under consideration

calculation was programmed to start with r = 2.

and it is common to every radius direction. Brightness,A(θ ) is an irregular function with some peaks atthat is, mean gray level of a micrograph is not reallyangle θ perpendicular to fibers alignment direction. This

related to fiber orientation, therefore A(0, 0) should not be

curve was approximated to an ellipse. FFT and thenincluded. Even at r = 1, A(0, 0) is partially included in the

inverse FFT after low-pass filtering in frequency domain

calculation without θ =0 or 90 degrees (Fourier(frequency n>3 cut off) were performed with the curve,

coefficients at 180 and 270 degrees are all the same withinitially. This process is equivalent to an approximation toa sine curve. The maximum value a and minimum value b

FFT routine can be used also for this purpose, but far fromand center angle α, that is, θ at A(θ ) = b were adopted asexact elliptic approximation in the case of higher

lengths of major and minor axes and the orientation angle

orientation intensity. Another elliptic approximation with afor elliptic parameters. Figure 3 demonstrates an ellipse

nonlinear least square method of realizing more suitable

determined in this way. This result corresponds to thefitting is now under programming.

sample data of Fig.1. This procedure is simple and the3000000-3000000300000Mean amplitude

300000Mean Amplitude
FFT approximation
Elliptic approximation

0-300000

Mean amplitude distr
Elliptic approximation

0

45

90

135

180

Center angle, degree

Fig. 3 Fiber orientation distribution and elliptic approximation (left) and its representation as afunction of center angle θ.
in the traditional Korean way in a craft center of Zangji,

EXPERIMENTAL

Korea. Sample Yoshi-j is Japanese paper made with rice

Paper samples
The samples used were fine copier paper of 67.4 g/m2

powder in Yoshino, Nara, Japan.

Method of acquiring surface image

in basis weight, circular laboratory handsheets frombeaten bleached kraft pulp of 69.7 g/m2, handmade

Digital Microscope DG-2, Scholar Co. Ltd., Japan
2

Japanese paper (Washi) from kozo fibers of 48.9 g/m andwas used to acquire reflected light images of paper

wood-containing paper including recycled pulp at 50 % of

surfaces at 100 times magnification. Specimens on a2

51.5 g/m .
Additionally, restoration paper for ancient arts andscanning stage were illuminated at a low-angle with lightwhich is composed in such a way that light beams coming

documents was used. they were Korean paper (Hanji)from six point sources arranged equilateral-hexagonallymade in the traditional way that an extra slurry flow out inare concentrated in a cone-shaped plastic to emphasize

all directions over the edges of a bamboo wire frame

mountains and valleys on surfaces. Five images were

(Iryong-k) and made following the traditional Japanese

captured from each of evenly spaced 9 locations of top,

way that an extra slurry is thrown away over the edge of

middle and bottom by left, center and right of a sheet.

the opposite side of the craftsman (Iryong-j) both in a craft

Individual images were 1792 by 1184 pixels in size, but

center in Iryong, Korea. Sample Zangji-k was also madetheir central 1024 by 1024 pixel regions corresponding to1.66 by 1.66 mm2 were subjected to FFT followed byintensity.

image analysis. Micrographs taken with a scanningelectron microscope, S-4000, Hitachi, Japan were also

RESULTS AND DISCUSSION

used as an image object for the image analysis. Specimens

Figure 4 shows images of paper surfaces photographed2

were cut to an area of 8 by 4 mm from distant 2 locations

with the digital microscope for four kinds of paper

within a sheet. Micrographs were taken at 40 times

samples in the left column and their binary images, FFT

magnification using an image capture device to a size of

power spectra and fiber orientation distributions with

2392 by 1942 pixels and trimmed afterwards to 2 images

elliptic approximation. Each sample image in this figureeof 1024 by 1024 pixels corresponding to 1.27 by 1.27

was selected from 30 or 40 (for a handsheet) images ofmm2 for image analysis.

each paper sample so that it came closest to its mean value

Restoration paper samples were photographed withof orientation angle and intensity. Table 1 shows thethe digital microscope at two locations about 100mm apartstatistic results on fiber orientation angle. The laboratory

within a sheet. Five micrographs were taken at eachhandsheet was evaluated to have some orientation angle

location and subjected to image analysis. In the images,

statistically because every calculated angle falls between 0

the bottom side is the craftsman’s side.

and 180 degrees, but the confidence level was large

Gloss and ultrasound velocity anisotropy
As a method other than image analysis fordetermining fiber orientation, anisotropy in gloss andultrasound velocity were chosen. Velocity of ultrasoundtraveling in a sheet is known to be proportional to a squareroot of elastic modulus as shown by Equation (5).

E = ρC 2…(5),where E, ρ and C are dynamic elastic modulus in GPa,
apparent density of sheet in g/cm3 and ultrasound velocity
in km/s. Measurement was made every 30 degrees inin-plane angle from the long side direction. Simply, theratio of the highest velocity to the lowest velocity wascalculated as orientation intensity.
Gloss anisotropy is assumed to be associated withsurface roughness anisotropy primarily due to surface
geometry generated by fiber orientation although its
formulation is difficult. Specular gloss was measured at 85
degrees of incident and reflected lights with a glossmeter,
GM-268, Konica Minolta, Japan. In-plane angle was
likewise every 30 degrees. The ratio of the highest gloss to
the lowest gloss was calculated as gloss orientation

enough to judge it is almost random. Perfectly randomorientation would give the confidence level of about 16
and 29, depending on the sample numbers, for the digital
microscope and SEM images, respectively. The orientation
angle of other samples shows about 90 degrees with theconfidence level of as low as 1 for digital microscope
images. On the other hand, the SEM images show
different orientation angles, presumably because small
areas were photographed. The value of the confidence
level of the copier paper for SEM was rather high(meaning large deviation) because of one exceptional
image present with a different orientation angle caused bya large fiber. If this is ignored, the result is consistent withthat for digital microscope. Table 2 shows the statistic
results on fiber orientation intensity determined by image
analysis, specular gloss and ultrasound velocity. For every
method, the intensity had very low values of theconfidence level (meaning stable data). Image analysis
provided larger intensity values than the other two
methods for the laboratory handsheet. But, overall, if theintensity is less than 1.10, the orientation is almost
random; and if more than 1.20, it is clear and intense.
Anisotropy of gloss in specular gloss was similar to that
determined by image analysis. That of ultrasound velocity

Fig. 4 Digital microscope images, binary images, FFT spectra and fiber orientation distributions
with elliptic approximation of each representative specimen for four kinds of paper.

TABLE 1 ORIENTATION ANGLE DETERMINED BY FOURIER IMAGE ANALYSIS
Laboratory
handsheet

Copier paper

Japanese paper

Wood-containing
paper

Image analysis- Digital microscope
Average, degree

109

91

88

93

95% confidence level, degree

7

1

1

1

Average, degree

115

84

95

Not measured

95% confidence level, degree

20

14

4

Not measured- Scanning Electron Microscopy (SEM)TABLE 2 ORIENTATION INTENSITY DETERMINED BY VARIOUS METHODS
Laboratory
handsheet

Copier paper

Japanese paper

Wood-containing
paper

Average

1.09

1.09

1.21

1.15

95% confidence level

0.01

0.00

0.01

0.01

Image analysis- Digital microscope- Scanning Electron Microscopy (SEM)
Average

1.07

1.07

1.15

Not measured

95% confidence level

0.02

0.01

0.01

Not measured

Average

1.00

1.10

1.17

1.25

95% confidence level

0.07

0.02

0.04

0.02

Average

1.00

1.63

1.85

2.15

95% confidence level

0.02

0.01

0.00

0.04

Specular gloss of 85º

Ultrasound velocity

resulted in higher values than the other method.

an orientation angle of 173 degrees. This means that fibers

Ultrasound does not travel along the sheet surface, butwere oriented in the horizontal direction from the view ofalong the inside and the reverse side. Therefore, if fiber

the craftsman. Iryong-j and Zangji-k showed highorientation of a sheet is varied from one side to the reverse

orientation intensity in the direction of back and forth.

side, it follows that the velocity distribution does not

Yoshi-j is characteristic of Japanese paper and wascorrespond to the fiber orientation in the surface of one

considered to show high orientation intensity in the backside.

and forth direction, but the intensity was rather low,presumably rice powder particles present in the fiber

Table 3 shows the image analysis result of therestoration paper. The orientation angle of three samples

network disturbed fiber orientation practically and reduced

resulted in high values (large deviation) of the confidence

the contrast of the original micrograph pictorially.

level, but the rest showed very low values, that is, very
stable. Iryong-k at location 1 showed strong intensity withTABLE 3 FIBER ORIENTATION ANGLE AND INTENSITY OF HANDMADE SHEETS OF KOREA AND JAPANKind of paper

Iryong-k

Location

1

Iryong-j
2

1

Zangji-k
2

1

Yoshi-j2

12

Orientation angle
Average, degree

173

87

94

109

105

99

95

85

95% confidence level, degree

4

53

4

29

19

5

4

5

Average

1.26

1.10

1.23

1.16

1.19

1.19

1.13

1.12

95% confidence level

0.04

0.04

0.04

0.04

0.02

0.06

0.03

0.02

Orientation intensity

Mark R. E., "Determination of paper sheet fiber

CONCLUSION
Image analysis using Fast Fourier Transform wasorientation distributions by a laser optical diffraction

demonstrated to be an effective means to determine fiber

method", J. Applied Polymer Science, Vol. 34, No. 3,

orientation angle and its intensity. Binarization process of

pp 1145-1157, 1987

micrograph images of paper surface and precise

4.

Fiadeiro, P.T., Pereira, M.J.T., Jesus, M.E.P. and Silvy,

calculation for average Fourier coefficients as an angular

J.J., "The surface measurement of fibre orientation

distribution by interpolation developed in this researchanisotropy and misalignment angle by laser

were found to improve the accuracy. This method was

diffraction", J. Pulp and Paper Sci., Vol. 28, No.10,

applied to digital optical micrographs and scanning

pp.341-346, 2002

electron micrographs of paper. A laboratory handsheet

5.

Abe Y., Todoroki, H., Takeuti, N. and Sakamoto, A.,showed a large deviation in the average value of fiber"Measurement method of fiber orientation on paperorientation angle, but some kinds of machine-made paper

surface", Japan Tappi J., Vol. 49, No. 5, pp 849-860,

showed about 90 degrees in the orientation angle with

1995 (in Japanese)very small deviations as expected. Korea and Japanese

6.

Osaki, S., "Microwaves quickly determine the fiber

paper made in the traditional ways showed its own

orientation of paper", Tappi, Vol. 70, No.2, pp.105-,characteristic depending on its hand making processes.

1987
7.

analysis for paper anisotropy and its variability",

ACKNOWRIGEMENT

Appita, Vol. 49, No.2, pp100-104, 1996

This research was partially supported by Fukutake
Foundation for Promotion of Culture (2003).

Scharcanski, J. and Dodson, C. T. J., "Texture image

8.

Scharcanski, J. and Dodson, C. T. J., "Local spatial
anisotropy and its variability", J. Pulp Paper Sci., Vol.
25, No. 11, pp393-397, 1999

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