A Three-Dimensional Measurement of Human Head ―For the Purpose of Dummyhead Construction

J. Acoust, Soc. Jpn. (E) 4, 1 (1983)

A three-dimensional measurement of human head ―For the purpose of dummyhead construction

Kimitoshi Fukudome

Department of Acoustic Design, Kyushu Institute of Design, 226, Shiobaru, Minami-ku, Fukuoka, 815 Japan

(Received 22 May 1982)

A method is presented of describing numerically the three dimensional shape of human head. By making use of the method the statistics on the head shape are obtained in 52 male young adult Japanese. Contours of the head are drawn by an apparatus whose principle of operation is similar to that of the perigraph used in the craniometry. After the contours and the positions of reference points are processed by a digital computer, the head shape is represented in the spherical coordinate system UA(R, Θ, Φ) as well as the rectangular Cartesian coordinate system U(X, Y, Z) where the origin is at the midpoint of the right-and-left tragions, X-axis is passing through the tragions, Y-axis is on the Frankfort horizontal, and Z-axis is perpendicular to both X-axis and Y-axis. The statistics on the radius R in the direction with polar angle Θ and azimuth Φ at intervals of six degrees are obtained: the average, standard deviation, maximum, and minimum are shown. Finally, a method of generating a model head which may be used in the dummyhead-headphone system is described. The shape of the model head is based on the statistical values obtained.

PACS number: 43. 88. Md, 43. 88. Vk, 43. 66. Yw

the listener having the same head shape as the dum- 1. INTRODUCTION myhead, may be allowable without any unnatural The dummyhead-headphone system, through perception. which a listener is able to hear the same sound as To solve this problem, we must take the followings he would hear in the sound field where the dummy- into consideration: (A) to evaluate the influence of head is located, may play an important role in the shape and size of the head upon the Thevenin acoustic measurements e. g., evaluation of acoustics pressure1) at the earcanal entrance, (B) to know the of a room or evaluation of acoustical devices for the statistics on the shape of human head, and (C) to reproduction of sound. determine the specification of a standard dummy- Of the dummyhead-headphone system, a method head. In particular, it is important to evaluate the of equalization for precise reproduction of the origi- influence of the shape and size of human auricle nal sound has been studied by the author.1) It was upon the Thevenin pressure at high frequencies found that the external shape of the dummyhead since the auricle is complicated in shape. should be identical to the shape of the head of the On the other hand, the numerical study on the listener in order that the equalizer suffices the Thevenin pressure on the oblate spheroidal head, requirements irrespective of the direction of incident which has ears of point receivers located at the op- sounds. It remains, however, to be solved what posite ends of the diameter on the axis of revolution amount of deviation of the shape of a listener's of the spheroid, tells us that the Thevenin pressure head from that of the dummyhead with its proper in the shadow region is considerably influenced at equalizer, whose characteristics are determined for high frequencies by the shape and size of the head.2)

35 J. Acoust. Soc. Jpn. (E) 4, 1 (1983)

In evaluating the influence of the shape and size measurement of contour lines on the surface of of human head, therefore, we adopt an experimental human head is made by an apparatus whose principle scheme consisting of two steps: (1) to determine the of operation is similar to the perigraph used in the specification of the head shape without the auricle, craniometry. Coordinates of contours and reference the nose and hair, and (2) to examine the effect of points such as tragion, orbitale, subnasale, and so them being attached to the dummyhead with this on are fed into a computer through a data tablet specification. digitizer. Of the positions of the auricles on both Many studies on the anthropometric measure- sides of the head, the right-and-left tragions are ment of human head have been made by the method chosen as fiducial points. The eye-ear plane, which established by Martin.3) This method provides is defined as a plane containing the tragions and the one dimensional data such as length, breadth, left orbitale, is chosen as a fiducial plane (When the height, and arc length between landmarks by the eye-ear plane is held horizontally, this fiducial plane use of the standard anthropometer: the sliding is called the Frankfort horizontal). Further the and spreading calipers for the direct measurement median-sagittal plane, which is defined as a plane of distances, and a steel tape for the arc length perpendicular to both the eye-ear plane and a line measurement. For example, to examine the change passing through the tragions, is chosen as another in head shape due to the age and the sex, Roe fiducial plane. A spherical coordinate system as measured head length, head breadth, auricular well as a rectangular Cartesian coordinate system height, head circumference, bi-auricular breadth, are defined by the origin at the midpoint of the longitudinal arc, and transverse arc of adults living tragions and the fiducial planes. The expression of in Tokyo Metropolis. In the Martin method, how- the head shape in this spherical coordinate system ever, there exists no measurement on the positions develops the possibility of getting the statistics on of auricles on both sides of the head. For designing the three-dimensional shape of human head. By of helmets, glasses, binoculars, goggles, and so on, making use of this method the statistics on the head Uchimura and Takeichi5) measured sizes of head shapes of 52 male young adult Japanese are ob- and face of Japanese males and females on 23 items tained. by the Martin method. Among these items, eight Since another method of describing the shape of are Martin's specified items and 15 are items such the auricles and nose is under investigation, it is not as otobasion superius to opistocranion, bi-otobasion included in this paper. superius-inion arc, bi-otobasion superius-subnasale arc, bi-otobasion superius-gnathion arc, and 2. MATERIALS so on. The anthropometric measurement of the head Subjects are 52 male young adult Japanese. Their has greatly contributed to an inter-population com- ages range from 20 to 25. They are students or parison in physical anthropology, or to the design- graduate students at Dept. of Acoustic Design, ing of head-worn equipments for aid and safeguard Kyushu Institute of Design. The number of sub- in human engineering. But a number of items of jects from their native districts in Japan is shown in measures on head by the method mentioned above Appendix (Table A. 1). are not enough to reproduce an actual shape of a 3. METHOD particular head and determine the positions of auricles on both sides of the head with the sufficient 3.1 Drawing of Contours of a Head accuracy for our acoustic purpose The method of An apparatus for drawing contours of a head was measuring the human skull in three-dimensional assembled. Its principle of operation is similar to relationship has been developed recently by the use that of the perigraph used in the craniometry. The of the Moire contourography.6) This method, how- subject was requested to sit on a chair under this ever, can not reveal an exact shape of the human apparatus, and to look at his image in a mirror head under hair. placed vertically in front of him. Further he was In this paper, a method which is more suitable for asked to retain his head position during the mea- dummyhead construction is presented of describing surement with the help of a chin-rest and four posi- numerically the three-dimensional shape of human tioning pointers; the chin-rest was adjusted up to head except the auricles, nose, and hair. The the height of the subject's gnathion, and the pointer

36 K. FUKUDOME: A THREE-DIMENSIONAL MEASUREMENT OF HUMAN HEAD

Fig. 1 The configuration of the measurement apparatus. was used to fit its chip to the mark on the face or on the temple. The configuration of the measurement apparatus is shown in Fig. 1. Contours were measured at intervals of 20mm, except for 10mm in the vicinity of the parietal or the chin; these intervals may be reasonable choice for describing those irregularities on a human head except the auricles and nose which have the Fig. 2 A block diagram of the contour data effect on the sound field of audible frequency range processing. up to 10kHz around the head. The positions of the reference points were also measured: tragion, or- a least-squares fitting is carried out to decrease the bitale, subnasale, vertex, and gnathion. fluctuations due to the head with the soft surface. An algorithm for the smoothing and the interpola- 3.2 The Spherical Coordinate Representation of tion is described in Appendix (C). the Head Shape In the fifth and sixth blocks of the figure, an algo- After the processing of the above data by a digital rithm of the isotropic four-point interpolation7) is computer, the head shapes were represented by the used jointly with the golden section search method spherical coordinate system whose origin is at the for optimization.8) midpoint of the right-and-left tragions and whose Thus the head shape was represented in terms of polar axis is perpendicular to the Frankfort hori- the radius R in the direction with polar angle Θ and zontal. azimuth Φ at intervals of six degrees. A block diagram of the data processing is shown in Fig. 2, where the rectangular Cartesian coordinate 4. RESULTS AND DISCUSSIONS system S, T, U, the cylindrical coordinate system 4.1 Statistics on Head Shape in Terms of Spherical TA and the spherical coordinate system UA are Coordinates used. Their definitions are described in Appendix The head shape of each subject is represented in (B). the spherical coordinate system UA with origin at In the third block of the figure, the smoothing by the midpoint of the subject's tragions, and with the

37 J. Acoust. Soc. Jpn. (E) 4, 1 (1983)

polar axis perpendicular to the Frankfort horizontal.

Then statistics on the radius R in the direction with polar angle Θ and azimuth Φ are obtained: average R(Θ,Φ), variance VR(Θ,Φ), standard deviation

σR(Θ,Φ), maximum value Rmax(Θ,Φ), and minimum value Rmin(Θ,Φ).

The average, variance, and standard deviation are calculated from the following equations:

where Ri(Θ,Φ) is the radius R in the direction with polar angle Θ and azimuth Φ of the i-th subject, and N is the total number of the subjects.

To illustrate these statistics on the head shape with figure, let us imagine the following five heads.

(1) Maximum head (designated by "MX" head): a head whose radius R(Θ,Φ) is equal to Rmax(Θ,Φ).

(2) Minimum head ("MN" head): a head with radius R(Θ,Φ), where R(Θ,Φ)=Rmin(Θ,Φ).

(3) Average head ("AV" head): a head with radius R(Θ,Φ),where R(Θ,Φ)=R(Θ,Φ).

(4) Head which is larger than the average by the Fig. 3 The statistics on the radius R as the standard deviation ("LS" head): a head with radius sectional views of the five heads ("MX", "LS R(Θ,Φ), where R(Θ,Φ)=R(Θ,Φ)+σR(Θ,Φ). ," "AV," "SS," and "MN" head) cut by the vertical plane α, where the α- (5) Head which is smaller than the average by the standard deviation ("SS" head): a head with plane intersects with the median-sagittal plane on the line along the polar axis. radius R(Θ,Φ), where R(Θ,Φ)=R(Θ,Φ)-σR(Θ, Five broken lines in the top left-hand Φ). show the statistics on the gnathion height. Sectional views of these heads cut by the vertical plane α which intersects with the median-sagittal by the standard deviation, the average, the value smaller than the average by the standard deviation, plane on the line along the polar axis is shown in Fig. 3. Figure 4 shows sectional views of the heads and the minimum value. cut by the oblique plane β which intersects with the Table 1 shows the statistics on some measure-

Frankfort horizontal on the line through the tragi- ments defined in the sectional views at α=90° and ons. In Figs. 3 and 4, the interval of intersecting 0° of Fig. 5. angle is chosen as 30°.

The lower jaw is missing out of Figs. 3 and 4 4.2 Statistics on the Arc Length in the Oblique because that part could not be measured accurately. Section

Since the smallest height difference between the In the oblique section cut by the β-plane shown tragion and the gnathion was 79.5mm, the shapes in Fig. 6, lengths of an upper arc au(β), a lower arc of the upper part of the heads above -70.0mm in al(β), and a circumference s(β) are taken into con- height are shown. sideration. Their statistics are shown in Table 2,

Five broken lines in the top left-hand of Fig. 3 with β 0° to 150° at intervals of 30°. Note that the show the statistics on the gnathion height: the al(β) and s(β) are missing at β=60°, 90°, and 120° maximum value, the value larger than the average for lack of accurate observation of lower jaw.

38 K. FUKUDOME: A THREE-DIMENSIONAL MEASUREMENT OF HUMAN HEAD

Table 1 The statistics on some measurements defined in the sectional views at α=90° and 0° of Fig. 5.

(a) (b)

Fig. 5 Some measurements and landmarks in the sectional views cut by the α-plane.

(a) α=90° and (b) α=0°.

Fig. 4 The statistics on the radius R as the Fig. 6 Arc lengths in the sectional views cut sectional views of the five heads cut by the by the oblique plane β. oblique plane β where the β-plane intersects with the Frankfort horizontal on the line through the tragions. for the time difference is a remarkably good ap- proximation9): 4.3 Path Length Difference between the Tragions Dt=Ds/c from a Distant Source where A distant sound source generates sound waves Ds=aΦ+asinΦ arriving at the two ears at different times because of the difference in path length from the source to and Ds is the difference in length between sound each ear. For transient signals, which contain wide paths, c the speed of sound in air, a the radius of the band frequency components, the following formula spherical head, and Φ the azimuthal angle in radians

39 J. Acoust. Soc. Jpn. (E) 4, 1 (1983)

Table 2 The statistics on the arc length and the circumference length in the oblique section cut by the β-plane.

Table 3 The statisticson the path length difference between the tragions from a distant source located in the δ direction on the oblique plane β.

of the source. This formula is derived from the

case where the ears are located at the ends of a

diameter of a rigid spherical head.10)

On the other hand, the Ds can be regarded as a

diffbrence in length between two acoustic rays. One is a direct ray to the irradiated ear, and the other is a ray which is tangent to the head and travels to the shadowed ear along the surface of the head.

Now let us consider a new measurement. A path length difference between the tragions from a distant source located in the δ direction on the oblique β- Fig. 7 The path length diffbrence between plane would be the measurement associated with the tragions from a distant source located acoustic property. Let us assume that the path in the δ direction on the oblique plane β. length difference between the tragions Ds(β, δ) is Here, the left tragion is in the shadow given as follows: region. The point T is the tangential point to the contour. The point A and B are Ds(β,δ)=ELT+(OB-OA) the projection of the point T and the where the left tragion EL is in the shadow region as tragion ER on the line incident to the shown in Fig. 7. Then the Ds(β, δ) can be calculated point O, respectively. from the sectional data cut by the oblique plane β.

The statistics on the Ds(β, δ) is shown in Table 3. system, a model head based on the statistics on R,

e.g., a "XSR" head, can be easily realized. Here, 4.4 Generation of Model Heads the "XSR" head denotes the head whose radius Since the head shape has been represented in R(Θ, Φ) is equal to the quantity "R(Θ, Φ)+xσR terms of the radius R in the spherical coordinate (Θ, Φ)", where x is a real number.

40 K. FUKUDOME: A THREE-DIMENSIONAL MEASUREMENT OF HUMAN HEAD

Now, let us consider how to generate a model head based on the statistics on the arc length or the path length difference between the tragions. As- sume that such desired model head is realized as the "XSR" head with an appropriate x. Let a(βj) be the arc length in the oblique section with β=βj. Let a(βj) be the value of a(βj) of the desired model head, and let a(βj) be the actual value of a(βj) of the "XSK" head. And let {βj,j=1,2,…, Fig. 8 The root-mean-squared error between the values of the "XSR" head and M} be the discrete set of angles at which the error the desired head with respect to the fol- between a(βj) and a(βj) is evaluated. lowing measurement as a function of x:

Then, the root-mean-squared error in angle (as (○) the upper arc length and (●) the path a function of x) can be expressed as length difference between the tragions.

Assuming that the distribution of the measure- To minimize the root-mean-squared error implies ment a is the normal distribution with average a

finding the optimum value of x, say x*, such that and variance σa2, we can determine two limit heads

for x≠x*. with respect to 75% of distribution of the measure- Evaluating the root-mean-squared error Q(x=0), ment a: for the lower limit head, a=a-1.15σa we can examine whether an average head with re- and for the upper limit head, a=a+1.15σa. Then spect to the upper arc length au or an average head the desired head is realized by finding the optimum with respect to the path length difference Ds is value of x.

identical to the "AV" head with radius R(Θ,Φ), The Qau(x) and QDs(x) are shown in Fig. 8, with

where R(Θ,Φ)=R(Θ,Φ). βj=30° ×j (j=0,1,…,5) and δk=30° ×k (k=

For the upper arc length au, by choosing β= 1,2,3), where

30° ×j, (j=0,1,…,5), we obtain

and

where au(βj) is the actual value of au(βj) of the "AV" head and a u(βj) is the average of au(βj) for all subjects. Therefore, the limit heads with respect to 75% of For the path length difference Ds, by choosing distribution of the upper arc length and those of the βj=30° ×j (j=0,1,…,5) and δk=30° ×k (k=1,2,3), path length difference are determined as the "XSR" we obtain head with x=±1.0 and the "XSR" head with x =±0.9, respectively.

5. CONCLUSION

where Ds(βj,δk) is the actual value of Ds(βj,δk) of A method of measuring the head shape three-

the head "AV", and Ds(βj, δk) is the average of dimensionally has been described and the statistics Ds(βj,δk) for all subjects. on the head shape has been obtained in 52 male Since both Qau(0) and QDs(0) are within the order young adult Japanese. The head shape has been of standard deviation of au(βj) and that of Ds(βj,δk) represented in terms of the radius R in the direction respectively, we can regard the "AV" head as the with polar angle Θ and azimuth Φ in the spherical average head with respect to both the upper arc coordinate system whose origin is at the midpoint length and the path length difference. Note that of the right-and-left tragions and whose polar axis from Tables 3 and 4 the order of standard deviation is perpendicular to the Frankfort horizontal. With of au(βj) and that of Ds(βj,δk) are 10/√52 and the result, a model head based on the statistics on 5/√52, respectively. the radius R, e. g., an average head, can be easily

41 J. Acoust. Soc. Jpn. (E) 4, 1 (1983)

Table A.1 The number of subjects from their native districts in Japan.

realized. Further a model head based on the the line passing through the tragions, and y'-axis statistics on the other measurement such as the perpendicular to both x'-axis and z'-axis. arc length between the tragions on the contour cut The rectangular coordinate system U is defined by the oblique plane can be realized as the "XSR" by the same origin as the T-system, X-axis passing head with radius R(Θ,Φ) (where R(Θ,Φ)=R(Θ, through the tragions, Y-axis perpendicular to X- Φ)+xσR(Θ,Φ)) with an optimum x by minimizing axis and on the Frankfort horizontal, and Z-axis the root-mean-squared error with respect to the arc perpendicular to both X-axis and Y-axis. length. The cylindrical coordinate system TA is defined

The problems which remain are as follows: (1) by the following relation: z'=z', x'=rcosφ, and to obtain the statistics on the three-dimensional y'=rsinφ. shape of human auricles and nose that protrude The spherical coordinate system UA is defined by from the wall of the head, (2) to examine the influ- the following relation: Z=RcosΘ, X=RsinΘcosΦ, ence of their shape and size including those of the and Y=RsinΘsinΦ. head upon the Thevenin pressure at the earcanal (C) The algorithm for the smoothing and the entrance. In this paper the statistics have been ob- interpolation used in the third block of Fig. 2. tained for only male subjects. Since the average The algorithm is as follows: value of the male head circumference is about the Step 1: Set the azimuth φint, where the interpo- value of the standard deviation larger than the lation is to be performed, to zero. female one,4) it should be separately done in the Step 2: For φint, find a data point (ri, φi), case of males and females to examine precisely the where the difference between φint and φi is smallest. influence of the shape and size of the head and the Step 3: Take a least-squares fit on five consecu- auricles upon the Thevenin pressure. Therefore a tive data points (ri+j, φi+j), (j=-2,-1,0,1,2), study similar to the present one remains for females. whose middle point has been found in Step 2, using

a quadratic, say a+bφ+cφ2; minimize ACKNOWLEDGEMENTS The auther would like to express his appreciation to Emertus Prof. Yasuo Makita and Prof. Hikaru

Date of Kyushu Institute of Design for their sus- Step 4: Calculate a value of this quadratic at tained guidance and encouragement. the azimuth φint; take this value to be the "Smoothed

This work was partially supported by a Grant-in- and interpolated value."

Aid for Scientific Research 565119 from the Ministry Step 5: Proceed to Step 6 until the φint reaches of Education, Science and Culture of Japan. to 360.

Step 6: Increase the φint by six degrees. APPENDIX Step 7: Return to Step 2. (A) The table of the number of subjects from their native districts in Japan. (Table A. 1) REFERENCES (B) The definition of the coordinate systems. 1) K. Fukudome, "Equalization for the dummy-head- The rectangular coordinate system S is defined by headphone system capable of reproducing true the rectangular coordinates (x, y) given by the directional information," J. Acoust. Soc. Jpn. (E) 1, 59-67 (1980). digitizer and the prescribed height z of the contour. 2) K. Fukudome and M. Yamada, "Relations be- The rectangular coordinate system T is defined by tween the geometrical dimension of the oblate the origin at the midpoint of the right-and-left spheroidal dummyhead and the Thevenin pressure," tragions, z'-axis parallel to z-axis of the S-system, Proc. Spring Meeting of Acoust. Soc. Jpn., 289- x'-axis along the projection on the plane z'=0 of 290 (1982) (in Japanese).

42 K. FUKUDOME: A THREE-DIMENSIONAL MEASUREMENT OF HUMAN HEAD

3) R. Martin and K. Saller, Lehrbuch der Anthropologie 7) J. E. Midgley, "Isotropic four-point interpolation," Band I (Gustav Fischer Verlag, Stuttgart, 1957), Comput. Graphics Image Process. 11, 192-196 pp.273-385. (1977). 4) M. Itou, "A somatometrical study on the shape of 8) J. Kowalik and M. R. Osbone, Methods for Un- adult head," St. Marianna Kenkyujo Gyohou 7, 1- constrained Optimization Problems (American Else- 172 (1954) (in Japanese). vier Publishing Company Inc., New York, 1968), 5) Y. Uchimura and K. Takeichi, "Anthropometric pp.10-17. survey of human figure measurement of head and 9) W. E. Feddersen, T. T. Sandel, D. C. Teas, and L. face," Bull. Ind. Prod. Res. Inst. 62, 57-64 (1970) A. Jeffres, "Localization of high-frequency tones," (in Japanese). J. Acoust. Soc. Am. 29, 988-991 (1957). 6) H. Terada and E. Kanazawa, "The position of 10) R. S. Woodworth and H. Schlosberg, Experimental euryon on the human skull analyzed three-dimen- Psychology, Revised Ed. (Holt, Rinehart and sionally by Moire contourography," J. Anthropol. Winston, New York, 1954), pp.349-353. Soc. Nippon 82, 10-19 (1974).