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Approximate surface development of the left side half-trunk by a free-formed model.

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AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 76165-173 (1988)
Approximate Surface Development of the Left Side
Half-Trunk by a Free-Formed Model
KUMI ASHIZAWA, TANEMI KUKI, AYANO KUSUMOTO,
EMIKO TSUTSUMI, AND SUMIYO KATO
Institute of Human Living Sciences, Otsuma Women’s Uniuersity, Sanbancho, Chiyoda-ku, Tokyo 10.2,Japan
KEY WORDS
Moire topography, Female trunk, Static and
stretched postures
ABSTRACT
The approximate surface development, skin length, and surface area of the left side of the trunk of 51 female students were compared with
regard to static and stretched postures. The data for each subject were obtained
from geometrical models generated by moire topography with a computer.
When the chest was stretched, the anterior surface, the shoulder line, and the
arm-base line were transformed from concave to convex, and a gap oriented
toward the nipple widened out. The skin elongated vertically and transversely,
except at the side of the waistline, where the skin contracted. The area at the
top of the trunk decreased about 25%, while the other parts of the trunk
increased 8-15%. The total anterior area was 1.20 m2 for the static posture
and 1.29 m2 for the stretched posture. When the posterior surface was stretched,
the shoulder line changed from convex to concave, the side line from quasistraight to concave, and gaps oriented toward the chest line disappeared. The
skin elongated most at the infrascapular region (20-35%),while the neck base
line contracted (- 11%).The center of the back and the lower arm base areas
enlarged the most (25%)and the lumbar area enlarged the least (12%).The
total posterior area was 1.26 m2 in the static posture and 1.37 m2 in the backstretched posture. In conclusion, the back skin elongated and enlarged more
when stretched than the frontal skin.
Moire topography, a n optical three-dimensional measurement method, makes it possible to analyze body form as it is transformed
by different postures, although only selected
parts of the body can be analyzed at one time
by this method. This kind of analysis is impossible with anthropometry because physiological conditions (e.g., kinesthetic adjustment, breathing) make a posture very unstable during measurement. Therefore, with
anthropometry, only the static standing posture can be studied, and no comparisons have
been made of the same subject in different
postures, except occasionally in applied anthropology. In moire topography, arbitrary
measurement points are photographed in
rapid succession to eliminate the effect of
body movements. Reproduction of measurement at the specific moment is ensured because the data are recorded in the pho-
0 1988 ALAN R. LISS, INC.
tographs. Any optical distortion can be corrected at the time of analysis.
The history of moire topography is described concisely by Theocaris (1969). The
idea was proposed by Foucauld in 1859, the
principle became established, and metrological applications, such as rigid body translations and angular displacement or linear and
angular displacement in deformed bodies,
were carried out in the 1950s and 1960s.
Application of this method to human body
measurement was reported by Takasaki
(1970,1973).It has been extended since then
to various fields of morphology, such a s anthropology, anatomy, and paleontology (Kanazawa, 1980; Kanazawa et al., 1983, 1985;
Received March 9, 1987; accepted October 16,1987.
166
K. ASHIZAWA ET AL.
Ozaki and Kanazawa, 1984; Endo and Baba,
1985), and to surgery for clinical diagnoses
and postoperative estimation (Moreland et
al., 1981; Drerup et al., 1983). Since teeth
and bones are rigid and immobile, this application was not very difficult in practice. But
the application to living subjects demanded
solutions to problems stemming from the fact
that man cannot sustain his posture for long
because of physiological conditions. To solve
these problems, two methods were proposed.
The first was the development of a position
holder (Otsuka et al., 1979). This holder helps
the subject to keep his posture, and is useful
in measurements of limited parts of the body
surface. However, this kind of ensured posture does not allow for natural positioning.
The second solution, for use in whole trunk
surface measurement, was the use of multiple moire cameras around a subject to take
pictures from different angles in a time interval so short that no body movements due to
neurological effects and breathing are involved (Ashizawa, 1978; Ashizawa and Tarumi, 1979; Ashizawa et al., 1983).
Before working with living subjects, Ashizawa and colleagues (Ashizawa and Tsutsumi, 1979a,b; Ashizawa and Tsurumaki,
1979; Ashizawa et al., 1979) used plaster torsos, molded from living subjects, and photographed them using a moire camera from a
fixed position and turning the plastic torso.
This can be considered the same as photographing a living subject simultaneously
from various directions; i t is the only method
that avoids the physiological effects. However, the data were obtained by hand with
much effort, and this limited the number of
subjects. All of the reports in this period covered only the tridimensional measurements,
without any somatological applications.
The next step was the use of the computer
to facilitate the quantitative analysis of the
data, because moire fringes on a picture give
enormous amounts of information. Hattori
and Nishio (1982) studied the diurnal change
in the back relief of five students by photographing moire fringes before, during (disturbing their sleep every hour), and after
sleep from 10 P.M. to 6 A.M. Ashizawa et a].
(1985a,b) compared the form of normal
schoolchildren’s backs with those of children
with scoliosis.
Using the moire method and a computer,
Nagashima et al. (1983) generated a surface
moael of a human plaste; trunk. The theory
introduced in their research originated from
Bezier’s method (1970) and Hosaka and Kimura’s method (1978). Bezier’s curved segments and patches are defined geometrically
by polygons and nets, and are highly controllable. This method is known for its use in the
automobile design system UNISURF of Regie
Renault (Bezier, 1970). However, with this
method there is a problem of linkage. Theoretically it is possible to link curved segments and surfaces smoothly, but it is too
complicated to apply to complex surfaces such
as the human body. But Hosaka and Kimura
improved this method with a n invention that
smoothly links numerous curved surfaces.
Once all of the coordinates on a n object are
stored, a geometrical model can be generated
with a computer. Nagashima showed that
the model of a human plaster trunk presents
not only a simple set of geometrical information, but can also be used for various applications, e.g., sectional views, contour lines,
shaded moire contours, and approximate surface development. In this report, we introduce this modeling method for use in livingsubject trunk moire topography, and compare surface developments in static standing
posture and stretched postures in each
subject.
MATERIALS AND METHODS
The subjects were 51 Japanese female students aged 19.3 to 27.0 years (average, 21.5
years). At the time of moire-photography, anthropometry was applied to determine the
physique of the subjects compared with the
average for the Japanese population as a
whole. Means and standard deviations of 20
measurements were presented in a short report (Ashizawa et al., 1986). In brief, compared with the standard group, aged 20-24,
the average subject’s physique is slightly
taller and larger, but not heavier: they presented a smaller Rohrer index.
Photographing displacement
For this method, three projection-type
moire cameras (Fujinon Moire Camera FM40, with Asahi Pentax MX and Motor Drive)
are arranged at 45” and 90” to the subject
(Fig. 1).The focal length is fixed on this moire
camera at 1,800 mm, and the radial distance
r between the focal point (i.e., the focal plane)
and the center point is taken as 125 mm.
This r is determined according to the subject’s physique, and in this s&dy we used
SURFACE DEVELOPMENT OF THE TRUNK
\
/
CAMERA 2
CAMERA 1
Fig. 1. Photographing displacement.
125 mm, which had been determined to be
the most suitable figure for an average young
Japanese female physique (Ashizawa et al.,
1983).
From the ceiling of the photographing
room, a thread is suspended crossing the optical axis of each camera at right angles 300
mm from the center point to the camera. On
the thread, two marks (Ml, M2, Fig. 3) are
placed 200 mm apart; the upper mark is at
the height of the optical axis of the photographing system (1,290 mm) and corresponds
to the mean acromial height. The scale ratio
and moire fringe degree on the body surface
can be calculated with regard to the distance
between these upper and lower marks.
The subject is placed on the center point,
facing camera 1;one picture of the front and
two pictures of left half of the trunk are taken
from the 45" and 90" angles, by camers 1,
and 2 and 3, respectively, at F5.6 and %-
167
second successive shutter speed. The picture
taken by camera 1 is used only for postural
confirmation, not for analysis.
Subjects
Crosses are affixed on the left surface of
the upper half of the trunk (Fig. 2). Their
intersecting points are anatomical control
points for the surface shape to be used in
subsequent model generation (Fig. 6).
The subjects stand on the center point with
their eyes open and feet apart at hip width.
They are photographed standing in three
postures: 1) standing naturally with arms
relaxed at her sides, 2) chest stretched forward, hands behind the Iower back, and
shoulders pulled backward with much force,
and 3) upper back flexed forward, hands
clasped in front, pulling the shoulders forward with much force.
Fringe depth calculation
Concerning the principles of moire phenomena, refer to optical textbooks or to the
very brief presentation in previously published in this journal (Ashizawa et al., 1985a).
A detailed optical and mechanical description of the projection-type moire camera used
in this study can be found in Suzuki et al.
(1981). Briefly, the camera consists of projection and photographic systems; when the
standard grating mounted on the projection
system is projected on the subject, a transformed grating is formed on the body; overlapping this transformed grating with the
standard grating mounted on the photographic system produces moire fringes on the
subject.
The depth of each moire fringe from the
focal plane h N is given by the equation
hN
=
bfb-f)NP/fl-(b-f)NP
where N is the degree of moire fringe, b is
the lens-to-subjectdistance (the distance from
the principal point of the lens to the focal
plane); 1is the distance between the two principal points of the system lenses; f i s the focal
length; and P is the grating pitch. The depth
between two neighboring moire fringes can
be obtained by subtracting hN-1 from hN- In
this study, b is 1,800 mm, 1 is 400 mm, f is
150 mm, and P is 0.1 mm, so that the depth
between two neighboring fringes-the - 10th
to the -9th, for example-is 4.70 mm and it
is 5.22 mm from the +9th to the +loth
fringes.
K. ASHIZAWA ET AL.
168
Fig. 2. Subject’s postures: 1) natural standing, 2) chest
stretched, and 3) upper back stretched.
Determination of the fringe degree on the
photograph and correction of the central
projection
These parameters are determined geometrically using a thread suspended from the
ceiling on which two marks are placed 200
mm apart. The depth from focal plane to the
shadows on the body surface (D) is calculated
as follows:
D
=
(2tan 01 (b-T‘-s)/(tan a +tan 0)
So the distance from the principal point to
the shadow mark on the body surface (bob)
is obtained as follows:
bob
=
b
-
D
Referring to Table 1, we can determine the
fringe degree on the photograph. The geo-
TABLE 1. Depth of each moirf?fringe from the focal
plane [hN)and depth between two neighboring fringes
Depth between
two neighboring
fringes (mm)
Fringe degrees- h N (mm)
- 10th
-9
-8
-7
-6
-5
-4
- 3rd
-2nd
- 1st
0 (focus)
+ 1st
+2nd
+3rd
+4th
+5
+6
+7
+8
+9
+ -10
1,751.82
1,766.00
1,770.78
1,775.59
1,780.42
1,785.27
1,790.15
1,795.06 I
1,800.00
i
i’
1.814.97 ,
1;s20.02 1
1,825.10
1,830.20
1,835.33 I
1,840.49 I
1,845.68
1.850.90
1
’
4.70
4.73
4.75
4.78
4.80
4.83
4.86
4.88
4.91
4.94
4.96
4.99
5.02
5.05
5.07
5.10
5.13
5.16
5.19
5.22
LIGHT
t
I
I
I
200m
bT
b
2 bT
I
i
CT
Focal
plane
Ce
______/
(D) from focal plane to the mark shadows on the body
surface. (M1,
upper mark; M2,lower mark on the thread.)
Fig. 3. Geometrical relation to determine the depth
bob
Thread
!MI'
I
Mark
shadows
on t h e
body
surface
er
2bT-b
___i
I
K. ASHIZAWA ET AL.
170
metrical relation which leads to this formula
is presented in Figure 3.
The arbitrary coordinate (Xmeasured, Ymeasued, and Zcomputed) on the photograph contains an error derived from the central projection of camera. It is corrected according to
the following formulae:
RESULTS AND DISCUSSION
Approximate surface development
There are 278 of these small rectangles,
125 on the anterior side, 135 on the back, and
18 on the subaxial part. An example is presented in Figure 4. Data on the surface opposite the extension side cannot be obtained
with moire topography, because the fringes
Xreal = ((d+b)/b)Xmeasured
are not formed in the sulci formed by postural change. Therefore, only the stretched
Yreal = ((d+ bYb) Ymeasured
side is the object of analysis in this study.
The small rectangles were arranged in orwhere b is the lens-to-subjectdistance, and d der as follows: First, those at the level
is the distance between the arbitrary coordi- marked with an x (Fig. 4) were arranged
horizontally. This horizontal line on the annate and the focal plane.
terior surface corresponds to the chest cirGeneration of surface model
cumference at the nipple. Then the other
The coordinates of the control points small rectangles were arranged vertically so
(crosses on the trunk) and those on each as to connect their upper and lower sides
moire fringe were entered with an X-Y digi- with the corresponding sides of their neightizer. On one photograph 30 fringes, with 15 bors. The anterior body surfaces, static and
points maximum for each fringe, can be en- stretched, are on the left in Figure 4. The
tered. Two photographs taken by cameras 2 two posterior views are on the right. The
and 3 (45" oblique front and back photo- localities where distinctive features appear
graphs), give all the fringe information are indicated by arrows. The observations in
needed. The body surface can be approxi- this figure are representative of all subjects.
mated by dividing each of the distorted large In the anterior view, the chest stretching
rectangles, demarcated by the crosses stuck caused the shoulder line (a) and the arm-base
on the torso, into nine small rectangles line (b) to change from concave to convex,
(patches). The computer system and pro- and a gap at the nipple level (c) to widen out.
grams are given in Tsutsumi's thesis (1985). In the posterior view, the shoulder line (d)
_-
st r e t ch eci
Static
Static
Fig. 4. An example of body surface development.
Stretched
SURFACE DEVELOPMENT OF THE TRUNK
changed from convex to concave; the side line
(el changed from quasi-straight to concave,
and the gaps oriented toward the chest line
0 disappeared. Thus, the small rectangles
indicate skin movement as affected by postural alteration.
Change of sectional length on the trunk
surface
The distance between markers stuck on the
subject's trunk was measured in the static
and stretched postures. Then the mean percentage of alteration caused by the posture
change, either increase or decrease, was calculated (Fig. 5).
When the chest was expanded, the skin
elongated both vertically and transversely,
except at the side of the waist line where the
skin contracted. However, the degree of elongation was not large. Vertically, the lower
part of the anterior arm-base line increased
0.3-1.5%;the median line, 5.7-7.5%;the line
from the median line to the nipple, 3.8-8.8%;
the line beneath the nipple, 6.7%; and the
side line, 8.0%.Transversely, the upper chest
line increased 6.5%;the middle chest line,
5.4-16.3%;the chest line, 5.4-7.4%; the line
between the waist and the chest line, 3.03.8%;and the medial waistline, 0.9%. The
largest elongation was on the lateral part of
middle chest line (16.3%).Here the skin is
-
Anterior S l d e
Posterior Side
> 30.08
SEe >
20.05;
+
'lO.o'
4
< 9.9%
1
contraction
Elongation
=SEE
-
>10.0%
...... Not e x a m i n e d
9.9%
Fig. 5. Mean percentage of linear elongation and contraction of the trunk skin.
171
pulled by the border of the M. pectoralis major. The lateral side waistline contraction is
negligible, -0.01%.
When the back is stretched, the transverse
elongation exceeds the vertical. The latter is
less than 9.9%(0.6-9.6%)for all section lines,
while the former is more than 10%.The elongation of the skin is greatest at the infrascapular region: medial part, 20.6%;and lateral
part, 35.5%.Only two section lines contract:
the neck-base line -10.8%, and the upper
part of the lateral scapular line - 1.6%.
To summarize, the trunk skin stretches
more on the back than on the front. On the
back the transverse extension is greater than
the vertical extension. The extension is
larger on the skin near the arm-base than on
the median part, on both back and frontal
trunk surfaces.
Change of surface area
Usually the body surface area is estimated
mathematically using anthropometric data,
or by applying a special thin paper sheet or
silicon to the skin on a living subject, or by
molding a living subject in plaster of Paris,
or directly from cadavers (Boyd, 1975; Martin et al., 1984). With the second and third
methods, the subject is forced to make a sacrifice in time and in work. This makes it
impossible to obtain the surface area from a
sufficient number of subjects to treat statistically. In contrast, once a geometric model
of the trunk is generated, we can obtain the
data any time from a large number of subjects. In this study, we calculate the area of
each large rectangle marked by four crosses
stuck on the trunk by adding the nine small
rectangle areas.
Figure 6 shows the mean percentage of surface area change caused by stretching for
each large rectangle. At the top of the trunk
(i.e., the neck-base and shoulder ridge),
stretching reduced the surface 25-26% on
the anterior and 30-50% on posterior sides.
On the other parts of the trunk, stretching
enlarged the skin area. On the anterior side,
the pit of the stomach and the arm-base were
enlarged the most (15%)and the lower body
side was enlarged the least (8%).The total
anterior area is 1.20 m2 for the static posture, and 1.29 m2 for the stretched posture.
On the posterior side, the center of the back
and the lower arm-base enlarged the most
(24-26%) and the lumbar area enlarged the
least (11-13%). The total posterior area is
1.26 m2 for the static posture and 1.37 m2 for
172
K. ASHIZAWA ET AL.
2). (Japanese text with English summary.) J. Home
Econ. Jpn. 30260-265.
Ashizawa, K, and Tsutsumi, E (197910) Moire photogrammetry of human trunk basic lines for garment planning. (Japanese text with English summary.) J. Home
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Ashizawa, K, Tsutsumi, E, Kurihara, S, Yoshizawa, T,
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Otsuma Womens Univ. 19:49-61.
Ahsizawa, K, Kuki, T, and Kusumoto, A (1985a) Fringe
patterns and measurement on dorsal moire topography in Japanese children, aged 13 and 14. Am. J. Phys.
Anterior S i d e
P o s t e r i o r Side
Anthropol. 68:359-365.
Ashizawa, K, Kusumoto, A, Kuki, T, Otsuka, Y, Yatagai,
Fig, 6. Mean percentage of surface area change of the
T, and Idesawa, M (1985b) Protuberant line and melarge rectangles on the trunk caused by stretching
dian line 3-D courses studied on the back of Japanese
(shaded area represents decreased surface).
children, aged 13 and 14, using moire topography. J.
Hum. Ergol. 14.4-52.
Ashizawa, K, Kato, S, Kuki, T, Kusumoto, A, and Tsutsumi, E (1986) Anthropometrical data of Japanese female students obtained in parallel with moire
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the stretched posture. Thus stretching en- Bezier,
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larges the back skin more than it does the
Numerique. Paris: Masson et Cie.
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Boyd, E (1975) The Growth of the Surface Area of the
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We have described moire topography, a
technique for three-dimensional measure- Drerup, B, Frobin, W, and Hierholzer, E (eds) (1983)
Moire Fringe Topography and Spinal Deformity. Stuttment of body parts in changing position. This
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technique should have a wide range of appli- Endo, B, and Baba, H (1985)Examination of nonmetrical
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industry, analysis of deformities in orthopedNippon 93:461-486.
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ACKNOWLEDGMENTS
curves and surfaces in interactive CAD. Proc. Cod.
Interactive Technique in CAD. Los Angeles: IEEE
The authors wish to thank Dr. Lowell AdComputer Society, 78CH-l289-8C,pp. 151-156.
ams for his kind revision of the manuscript. Kanazawa,
E (1980) Principal component analysis of
This study was supported by a Grant in Aid
three-dimensional coordinates of landmarks on the
for General Scientific Research, the Ministry
Nippon 88209-228.
Japanese skull. J. Anthropol. SOC.
of Education, Science, and Culture (No. Kanazawa, E, Sekikawa, M, and Ozaki, T (1983) Threedimensional measurements of the occulusal surface of
60540536),Japan.
upper first molars in a modern Japanese population.
Acta Anat. (Basel) 116:90-96.
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summary.) Thesis for the Doctoral Degree of Engineering, University of Tokyo.
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