Approximate surface development of the left side half-trunk by a free-formed model.код для вставкиСкачать
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 Econ. Jpn. 30521526. Ashizawa, K, and Tsurumaki, K (1979) Application of moire-photogrammetry to the human hips. Bull. MQm. Soc. Anthropol. Paris t6 XZZE373-384. Ashizawa, K, and Tarumi, Y (1979) Somatological observation by moire topography (Part 1).Sway of points on the anteroposterior median lines in standing position. (Japanese text with English summary.) J. Home Econ. Jpn. 3Ot711-719. Ashizawa, K, Tsutsumi, E, Kurihara, S, Yoshizawa, T, Matsuyama, Y, and Yanagisawa, S (1983) Installation of moire cameras for somatometrical use. (Japanese text with English summary.) Bull. Fac. Domestic Ski. 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 topography. J. Hum. Ergol. 15:167-169. the stretched posture. Thus stretching en- Bezier, P (1970) Emploi des Machines a Commande larges the back skin more than it does the Numerique. Paris: Masson et Cie. frontal skin (back, 109%,front, 107%). Boyd, E (1975) The Growth of the Surface Area of the Human Body. Westport. Greenwood Press. 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 gart: Gustav Fischer Verlag. technique should have a wide range of appli- Endo, B, and Baba, H (1985)Examination of nonmetrical cations, such as ergonomics in the clothing characters of the form of innominate bones from pleistocene in Japan. Part I: Description. J. Anthropol. Soc. industry, analysis of deformities in orthopedNippon 93:461-486. ics and plastic surgery, a s well as morphologK, and Nishio, F (1982) Diurnal change of the ical comparison of ethnic groups and in body- Hattori, relief on the body back surface. (Japanese text with building sports. English summary.) Jpn. J. Hum. Posture 273-78. Hosaka, M, and Kimura, F (1978) Synthesis methods of 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. 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