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A three-dimensional measuring system for the human face using three-directional photography
A three-dimensional measuring system for the human face using three-directional photography Mitsuru Motoyoshi, DDS," Shinkichi Namura, DDS, DDSc," and Harold Y. Arai, DDS, MS b ToL3"o, Japan, and Park Ridge, IlL This study was intended to develop a three-dimensional measuring system of the human face for clinical use, to ensure a high precision and a simpl e input operation by means of a personal computer and to measure the degree of its accuracy. With this system, it is possible to measure automatically two-dimensional coordinates of hundreds of gri d points on photographs of the human face with an image scanner as a reading device and to calculate their three-dimensional coordinates with a computer. An orthognathic surgical case illustrates this technique in Which the Patient's face is displayed before and after the surgery on a cathode-ray tube (CRT),.with the three-dimensional coordinates obtained with this system. A cubic plaster cast with a certain degree of irregularity has been constructed to measure the precision of this System..Comparison was then made between the three~-dimensional coordinates obtained with this system and the coordinates obtained with the contact three-dimensional measuring system. The mean of errors and the standard deviation were 0.04 _+ 0.24 mm for the X coordinate, 0.03 -- 0.16 mm for the Y coordinate, and 0.08 _ 0.23 mm for the Z coordinate. Thus the accuracy of this system is high enough for the measurement of the human face. (AM J OnTHOO DENTOFACORTHOP 1992;101:431-40.)
C o n v e n t i o n a l methods with cephalogram tracings are generally used for evaluating facial form changes as a result of growth and orthodontic treatment. The human face, however, changes its form three-dimensionally, so it would not be possible to understand these three-dimensional transformations completely with only the use of the conventional methods. Threedimensional information from the human face is therefore considered to be of vital importance for diagnosis and evaluation of treatment effects and of growth. Thus far a large varietY of thri~e-dimensional measuring methods for soft tissue have been developed and published. Major techniques include moire topography,' telecentric photography, 2-6 stereophotogrammetry, T M and laser measurement) 6'17 Each of these methods, however, involves problems, and their immediate applicability to clinical cases is questionable. Stereophotogrammetry,T M for instance, requires a special camera and a contour mapping technique, therefore is not in widespread clinical use. Measuring methods with lasers '6''7 have great potential, but the equipment is still too expensive to make its general clinical use possible. In 1970 Takasaki' was the first to report on moire topography, which uses interference of rays.
'Department of Orthodontics, Nihon Univemity School of Demistry. Tokyo, Japan. qn private practice, Park Ridge. Ill. 8/1/23138
Rgbertson 4"~ has since developed telecenti'ic photography for the three-dimensi0nal recording of the human face. In 1986 Segner3 reported on counter photography with a reflecting mirror to simplify the apparatus. The equipment for these methods is easy to obtain and is of little burden on the patients. However, most of these methods require tracings or the input by digitizer, and their reliance on human operation reduces their preci L sion, particularly when they have to deal with hundreds of measurement points. In this study, we have developed a program to systematize the process from inPut and calculation to ihreedimensional display on a cathode rfiy tube.(CRT). The precisionand usefulness of this system were measured and examined with the goal Of solving the problems of conventional moire topogral~hy and telecentric photography by the automatic reading of data, and enhancing the precision by the reduction of human error. MATERIALS AND METHOD
Fig. l shows the diagram of the computer system used in this study. First, a subject was photographed while projecting about 800 points of light onto the face with a projector. Three-directional photography was preferred to two-directional, as the former enables better measurement of the side sites (Fig. 2, A). Each of the three cameras (one from ihe front, another from 45~ to the right, and the third from 45 ~ to the left) was attached to a receiver, so that a transmitter at h-and could trip all three shutters simultaneously (Fig. 2, B). To establish reference points, five luminous diodes were set--two for the cameras from the 45~ directions on the 431
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extension line of the right and left earrods, two for the front view, and one above the h e a d - - s o that three reference points could be shown on the photograph in each direction. To correct the data, the distance between the reference points on the photograph and the distance between the reference points on the film were obtained, and then the expansion rate for the film on printing paper was calculaied and inputted into the computer. The true distance between each reference point was also measured to reduce measuring error and was applied to the correction of the final data. The three photographs obtained were then transmitted to a computer as pictorial image data by an image scanner. Resolution was fixed at 200 DPI (dots per inch), the maximum in horizontal and vertical scanning directions, and the number of pixels was fixed at 800 • 750. The input mode was monochrome.
From the transmitted pictorial image data, two-dimensional coordinates at each point shown on the screen were obtained. Fig. 3 shows the method to recognize the boundary at each point, which is read by an image scanner and consists of several pixels as shown here. The coordinates in the middle of this group of pixels become the two-dimensional coordinates of each point. The recognition of boundary is done row by ro w from the left side of the figure. The left boundary is where the first pixel was discovered. While continuing with the search for an upper boundary and a lower one, we come to a row where the last pixel disappears, the one before is recognized as the boundary on the right. After recognizing one group of pixels and obtaining its coordinates by taking an average value of the coordinates of each pixel as a central point, the search for other groups of pixels begins. The co-
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Three-tfimensional measuring system of the human face
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ordinates of each point obtained from the photographs taken from the front and the two 45 ~ angles are ranked at random in the array because of the irregular order of discovery. Each point is shown in both photographs taken from the front and from either of the 45 ~ angles, but to acknowledge two points appearing on two different photos as the same point, it is necessary to rearrange in order the coordinates of each point in the array. Therefore for this system two arrays with orderly
ranks were arranged to calculate the three-dimensional coordinates of each point. The coordinates are calculated on the basis of two-dimensional data given at the same position in these two arrays. In the case of the photograph of the face taken at 45 ~ on the right, for example, the point at the farthest -upper.right is ranked at 11, which is followed by, in searching toward the left, the point ranked 12 and 13, as shown on Fig. 4. This ranking is repeatcd to the left until there are no
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more points to be found. When a nonexistent point is acknowledged in the leftward direction, the operation moves onto the second row, ranking the array as21, 22, and 23, in that order. The same process is repeated with the right half of the photograph taken from the front. After ranking all the points in two arrays, three-dimensional coordinates are calculated on the basis of two-dimensional coordinates of the same ranking number. The principle for calculating threedimensional coordinates is given in the Appendix. The three-dimensional coordinates obtained were given final correction on the basis of the actual distance between the reference points for storage onto the hard disk. Precision test Fig. 5 shows a piaster cast used for the precision test. The three-dimensional coordinates were obtained with threedirectional photography, after projecting points (with a projector) on a total of 70 measurement points on the plaster. These three-dimensional coordinate values were compared with the coordinate values obtained by the contact threedimensional measuring system (Fig. 6). Coordinate values of each point marked on the plaster cast were measured by this contact three-dimensional me 9
suring system three times, and their average was established as a reference value. The difference between these values and the coordinate values at each measuring point obtained by three-directional photography was considered error. Three-dimensional display We conducted a three-dimensional measurement of a face--an orthognathic surgical case--with this system, then displayed it three-dimensionally. A display with the use of a wire frame provided with hidden-line elimination or with shading was also possible. The same computer and programming language were used for the measurement of coordinates. This system, which is intended for clinical application, requires only a simple operation with a mouse commanding the reading of photographs, the calculation of the three-dimensional coordinates, and the three-dimensional display. RESULTS Precision Table I s h o w s errors at each measurement point. The average value and standard deviation of errors at all the measurement points are as follows:
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X coordinate: 0.04 • 0.24 mm Y coordinate: - 0 . 0 3 • 0.16 mm Z coordinate: 0.08 • 0.23 mm The measurement limit of this system is 2000 measurement points and a 1.5 mm interval between points. Three-dimensional
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Figs. 7 through 9 are three-dimensional images of the actual subject who underwent orthognathic surgical treatment. Fig. 7 uses a wire-frame display, whereas Fig. 8 is provided with shading. Fig. 9 is a threedimensional display of the same subject about ! month after surgery. DISCUSSION
Two possible factors that affect the precision of this system are those related to the photography and those related to the process of measurement with the computer and the reading device. Factors related to photography include accuracy of the camera position, structure of the camera, and pos-
Fig. 5. Plaster cast used for precision test.
sible inadequate enlargement from film to printing paper. Accuracy of the camera position should be achieved with utmost care as it directly affects the image distance
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Am. J. Orthod. Dentofac. Orthop. May 1992
Fig. 8. Shading image of patient shown in Fig. 9.
Fig. 6. Contact three-dimensional measuring system (Tristation 400M CNC) determined reference values of coordinates at each point on plaster cast.
Fig. 9. Image of same patient measured by this system about 1 month after surgery.
Fig. 7. Three-dimensional image represented by wire frame.
and the object distance. Therefore a plastic disk in the contact three-dimensional measuring system was measured in advance, and with this as a subject, the accuracy of the conditions for the camera position was confirmed. Image distance requires other factors to be taken into consideration. Image distance consists of focal distance and focusing extension, of which focal distance is a nominal value.allowing ---5% deviation in the case of a Japanese-made camera. For this reason, in this
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Three-dimensional measuring system of the human face
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Table I. Errors in the measuring of each point on the plaster Coordinate (ram)
Points
X -0.26 -0.22 -0.03 0.06 0.10 0.27 -0.14
-0.27 0.06 -0.10 -0.08 0.41 0.22 -0.27
-0.16 0.16 -0.02 -0.15 -0.24 0.22 0.12
-0.32 0.37 -0.41 0.47 -0.05 -0.13 -0.11
-0.30 0.09 0.06 -0.05 -0.20 0.12 0.31
0.19 -0.12 0.34 0.13 0.04 0.29 0.00
0.06 -0.39 -0.05 0.22 -0.12 0.27 0.29
-0.46 0.10 0.08 0.13 -0.03 0.21 0.68
0.46 -0.03 0.31 0.18 0.39 -0.09 0.05
0.11 0.48 -0.01 -0.27 -0.09 0.19 -0.06
0.19 0.22 0.17 0.13 -0.19 0.08 0.16
0.05 -0.21 0.24 0.30 0.22 0.02 0.21
-0.05 0.20 -0.13 -0.04 0.30 0.10 0.00
-0.02 -0.22 -0.06 -0.15 -0.18 -0.02 0.05
-0.01 0.01 -0.10 -0.02 0.04 -0.23 0.02
-0.01 -0.03 -0.20 -0.28 -0.02 0.02 0.01
-0.10 -0.14 -0.25 -0.10 -0.04 -0.28 -0.01
-0.27 -0.02 -0.08 -0.07 -0.12 -0.23 -0.28
0.09 -0.39 -0.04 0.06 0.30 -0.08 0.07
-0.04 -0.11 -0.09 -0.29 -0.05 -0.09 -0.17
0.38 0.50 -0.02 0.11 -0.07 0.09 -0.03
0.17 0.21 0.10 0.21 0.11 -0.06 0.02
0.27 -0.08 0.11 -0.09 0.14 0.20 0.22
-0.09 0.18 -0.02 -0.03 -0.13 0.02 0.18
0.48 0.17 0.43 0.17 -0.39 -0.09 -0.40
0.10 -0.18 0.46 0.21 -0.09 0.16 -0.13
-0.09 0.18 0.15 -0.13 0.04 0.42 -0.05
-0.49 .0.20 -0.18 0.12 0.06 -0.08 -0.04
0.51 0.43 0.15 0.02 -0.16 -0.42 -0.05
0.20 0.44 -0.46 0.46 0.19 0.35 0.37
Y
Z
Ranking of values corresponds to ranking of points on the plaster cast shown in Fig. 7.
study we used the previously mentioned disk that was photographed by each camera first. An image distance was then obtained from the ratio of the diameter of the disk on the film to the actual diameter. From this and the focusing extension, the focal distance of each lens was obtained. Finally, an image distance was corrected to 55 mm by adjusting the focusing extension. Regarding the camera structure, lens aberrations seem to particularly affect precision. There are six types of lens aberrations: chromatic aberration, spherical aberration, coma, astigmatism, curvature of field, and distortion. To enhance precision, a survey camera with good correction of aberrations is ideal, but even with an ordinary camera, it is possible to increase precision by correcting aberrations to the degree possible. This system, which is intended for widespread application to clinical cases, used an ordinary 35 mm camera, which is the most popular type in Japan. It was corrected for distortion, which affects precision to a greater degree than the other types of aberrations. The other aberrations can be improved to some extent by setting a large diaphragm. To reduce errors during the process of reading coordinates, the film should be enlarged. Therefore we used an enlargement on 8 • 12 cm printing paper as
the original reading paper in this study. There was concern however, that errors during the enlargement might affect the precision of the final data, so we measured the positions between each reference point in advance to use for the correction of the final data. There are other minor problems, such as distortion and elasticity on the film surface at the time of photographing, but we believe they do not affect the precision of measurement of the human face and therefore do not need correction. For want of any appropriate way of solving this problem, we did not provide any correction in this study. The resolution of the image scanner is the factor that most affects the precision of measurement in use of the computer and reading device. The degree of error depends on the efficiency of the selected image scanner. The resolution of the scanner used in this study was fixed at a maximum 200 • 200 DPI for reading. We then had to consider the precision of the extraction process of the points from the image data read from the photographs. Since the greater the number of pixels read by the scanner, the higher the precision, the numbeL.of vertical pixels was fixed at 750, the maximum value allowed by the vertical resolution (750 lines) of the CRT, and the number of horizontal pixels was 800,
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Motoyoshi, Namura, and Arai
the maximum value of the scanner. To study the repeatability of the extraction process of the points, the readings and calculations of the coordinates using the same photographs were conducted several times. The fact that the same results could be obtained each time leads us to conclude that the extraction process of the points in this system always finds the same conditions, reducing deviation more than in the case where a digitizer was used. Yet another factor believed to affect precision is error resulting from calculation by the computer, but this is thought to be extremely minor compared with the aforementioned factor. The results of the precision tests show that the measurement precision of this system is higher than other measuring methods, such as telecentric photography, moire topography, stereophotogrammetry, and laser measurement. The measurement speed was also fast enbugh to be clinically applicable. ! Furthermore, this system is capable of a wire-frame display with hidden-line elimination and of a display of i'evolving images with shading. In the case of a wire: frame display with arrays of each measurement poini au!omatically ranked by a computer, there is no need to input just the relationship between each surface .and point for a three-dimensional display. Moreover, the time required for shading is approximately 20 seconds, with a marginal difference depending on the revolving angle, whereas the wire-frame display takes approximately I0 seconds, which means that this system is highly applicable to clinical cases that demand highspeed processing. To evaluate surgery and to measure the changed values, it is necessary to develop a system capable of accurate superimposition. For this purpose, constant reference points on the face before and after the surgery must be established for the correction of revolution or divergence of the face at the time the photograph is taken. We are also considering the development of a new system that would enable the simulation of prediction of results after orthognathic surgery, by combining it with measuring systems of the maxillomandibular structure. ~s.~9 CONCLUSION
The four conditions necessary for a clinically applicable three-dimensional measuring system are (1) a small burden on the patient at the time of measurement, (2) the simple input operation and high-precision measurement, (3) the calculation of coordinates for a substantial number of measuring points, and (4) a highspeed three-dimensional display based on the threedimensional coordinates Obtained. For the development of a system that meets all these conditions, this study has made the following conclusions:
Am. J. Orthod. Dentofac. Orthop. May 1992
1. In this study a projector for measurement was used because it reduced the burden on the patient and allowed for easy operation. For this purpos.e, we developed an apparatus capable of simultaneous, three-directional photography. 2. For a simplified input operation, automatic analysis is indispensable. It is also vital for the reduction of human manipulation and the improvement of precision. Therefore a three-dimensional measuring system was developed in which an image scanner directly reads the photographs obtained. The phot~raphs are transmitted to a computer as image data, and the coordinates of each measuring point are automatically calculated. This almost completely eliminates complex human manipulation. Input operation to a scanner was all that was necessary. This also ensured high precision. 3. The development of this system, capable of treating many measuring points, is expected to contribute to a more detailed three-dimensional understanding of the shape of the human face. 4. This system is believed to be functionally applicable to clinical cases that require high-speed processing. REFERENCES 1. Takasaki H. Moire topography. Applied Optics 1970;9:t45772. 2. Lovesey El. A simple photogrammetric technique for recording three dimensional head shape. Med Biol lllus 1973;23:210-3. 3. Segner D. The shape of the human face recorded by use of contour photography and spline function interpolation. Eur J Orthod 1986;8:112-7. 4. Robertson NRE. Contour photography. Br J Orthod 1976;3: 105-9. 5. Robertson NRE. Telecentde photogrammetry. AM J Or'mop 1981;80:623-37. 6. Sassouni V, Nanda S. Analysis of dentofacial vertical proportions. AM J OrmoP 1964;50:801-23. 7. Burke PH, Beard LFH. Stereophotograntmetry of the face. AM J ORtttOD 1967;53:769-82. 8. Berkowits S. Stereophotogrammetrie analysis of each of normal and abnormal palates. AM J OR'mOP 1971;60:1-18. 9. Berkowits S, Cuzzi J. Biostereometfic analysis of surgically corrected abnormal faces. AM J OrroOD 1977;72:526-38. 10. Savara BS. Applications of photogrametry for quantitative study of tooth and face morphology. Am J Phys Anthropol 1965;23:427-34. 1 I. Macgregor AR, Newton 1, Gilder RS. A sterophotogrammetrie method of investigating facial changes following the loss of teeth. Meal Biol Illus 1971;71:75-82. 12. tlaga M, Koshihara Y, Ota Y. Stereophotogrammetfic study of the face. Bull Tokyo Meal Dent Univ 1964;5:10-24. 13. Beard LFH, Burke PIt. Evolution of a system of stereophotogrammetry for the study of facial morphology. Med Biol lllus 1967; 17:20-5. 14. Chaya tl, Ishiakawa H, lmai T, Nakamura S. A three-dimensional analyzing system of face using stereophotogrammetry and computergraphics. Jpn J Orthod Soc 1988;47:560-78.
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15. Baumrind S, Moffitt FH. Stereophotogrammett3' of the face. A.',t J ORrnoo 1967;53:769-82. 16. Arridge SR, Moss JP, Linney AD, et al. Three dimensional digitization of the face and skull. J Maxillofac Surg 1985;I 3:13643. 17. Moss JP, Grindrod SR, Linney AD, Arridge SR, James D. A computer system for the interactive planning and prediction of maxillofacial surgeD,. Ast J ORTtlOD DENI'OFACORTIIOP 1988;94, 469-75. 18. Motoyoshi M, Yamazaki T, Inoue K, Kura M, Yoshida T, Na-
mera S. Studies on three dimensional evaluation of maxillomandibular morphok~gy. Jpn J Onhod Soc 1986;45:181-95. 19. lnoue K, Yamazaki T, Motoyoshi M. Matsunaga S, ttayashi M, Namura S. Studies on 3-dimensional prediction of orth~nathic surgery cases. Jpn J Orthod Soc 1986;45:658-66.
Reprint requests to: Dr. Harold Y. Arai 101 S. Washington Park Ridge, IL 60068
APPENDIX
Y/XF = (d - x)/e Z/YF = (d - x)/e
The principle for calculating three-dimensional coordinates is as follows: XY coordinates on the film can be obtained by dividing XY coordinates on the photograph by L, ~,vhere L is the enlargement ratio from film to printing paper. The value of L is obtained by measuring the distance between the reference points shown on the printing paper and those on the film. The XY coordinates on the film that are obtained in the direction of the front, 45 ~ to the right, and 45 ~ to the left are referred to as XF, YF, XR, YR, XL, and YL; whereas the object distance, i.e., the distance between the lens principal point and the midpoint of the ear-rods, is referred to as d; the image distance or distance between the lens principal point and the film, e; and three-dimensional coordinates on the subject, X,Y, and Z. We then obtained the following formula from the conditions of camera position when the photograph of a front view of the subject was taken.
In the case of a photograph taken at an angle of 45 ~ the following formula was obtained from the ratio of the real distance, indicated by an arrow (Y/X/-2 x/X/2) on Fig. A1, to the photograph distance, taking the left side as an example. (y -
x)/x/~
z
XL
YR
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Am. J. Orthod. Dentofac. Orthop.
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M a y 1992
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The coordinates of X, Y, and Z on the subject can be obtained from the formulas given. Incidentally, the distance between the midpoint of the eatrods and the surface of the film was fixed at 700 ram. When the
focal distance of the lens in use was 50 mm, lens extension for focusing on the subject was 5 mm. Consequently, the object distance was 645 ram, and the image distance was 55 mm, both of which are known values. Since it was convenient to keep the image distance constant for calculation, the subject was photographed with the diaphragm set at 11 for large depth of field and the focusing extension fixed at 5 ram.
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C o n v e n t i o n a l methods with cephalogram tracings are generally used for evaluating facial form changes as a result of growth and orthodontic treatment. The human face, however, changes its form three-dimensionally, so it would not be possible to understand these three-dimensional transformations completely with only the use of the conventional methods. Threedimensional information from the human face is therefore considered to be of vital importance for diagnosis and evaluation of treatment effects and of growth. Thus far a large varietY of thri~e-dimensional measuring methods for soft tissue have been developed and published. Major techniques include moire topography,' telecentric photography, 2-6 stereophotogrammetry, T M and laser measurement) 6'17 Each of these methods, however, involves problems, and their immediate applicability to clinical cases is questionable. Stereophotogrammetry,T M for instance, requires a special camera and a contour mapping technique, therefore is not in widespread clinical use. Measuring methods with lasers '6''7 have great potential, but the equipment is still too expensive to make its general clinical use possible. In 1970 Takasaki' was the first to report on moire topography, which uses interference of rays.
'Department of Orthodontics, Nihon Univemity School of Demistry. Tokyo, Japan. qn private practice, Park Ridge. Ill. 8/1/23138
Rgbertson 4"~ has since developed telecenti'ic photography for the three-dimensi0nal recording of the human face. In 1986 Segner3 reported on counter photography with a reflecting mirror to simplify the apparatus. The equipment for these methods is easy to obtain and is of little burden on the patients. However, most of these methods require tracings or the input by digitizer, and their reliance on human operation reduces their preci L sion, particularly when they have to deal with hundreds of measurement points. In this study, we have developed a program to systematize the process from inPut and calculation to ihreedimensional display on a cathode rfiy tube.(CRT). The precisionand usefulness of this system were measured and examined with the goal Of solving the problems of conventional moire topogral~hy and telecentric photography by the automatic reading of data, and enhancing the precision by the reduction of human error. MATERIALS AND METHOD
Fig. l shows the diagram of the computer system used in this study. First, a subject was photographed while projecting about 800 points of light onto the face with a projector. Three-directional photography was preferred to two-directional, as the former enables better measurement of the side sites (Fig. 2, A). Each of the three cameras (one from ihe front, another from 45~ to the right, and the third from 45 ~ to the left) was attached to a receiver, so that a transmitter at h-and could trip all three shutters simultaneously (Fig. 2, B). To establish reference points, five luminous diodes were set--two for the cameras from the 45~ directions on the 431
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Motoyoshi, Namura, and Arai
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extension line of the right and left earrods, two for the front view, and one above the h e a d - - s o that three reference points could be shown on the photograph in each direction. To correct the data, the distance between the reference points on the photograph and the distance between the reference points on the film were obtained, and then the expansion rate for the film on printing paper was calculaied and inputted into the computer. The true distance between each reference point was also measured to reduce measuring error and was applied to the correction of the final data. The three photographs obtained were then transmitted to a computer as pictorial image data by an image scanner. Resolution was fixed at 200 DPI (dots per inch), the maximum in horizontal and vertical scanning directions, and the number of pixels was fixed at 800 • 750. The input mode was monochrome.
From the transmitted pictorial image data, two-dimensional coordinates at each point shown on the screen were obtained. Fig. 3 shows the method to recognize the boundary at each point, which is read by an image scanner and consists of several pixels as shown here. The coordinates in the middle of this group of pixels become the two-dimensional coordinates of each point. The recognition of boundary is done row by ro w from the left side of the figure. The left boundary is where the first pixel was discovered. While continuing with the search for an upper boundary and a lower one, we come to a row where the last pixel disappears, the one before is recognized as the boundary on the right. After recognizing one group of pixels and obtaining its coordinates by taking an average value of the coordinates of each pixel as a central point, the search for other groups of pixels begins. The co-
Voh,,e 101
Three-tfimensional measuring system of the human face
Number 5
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ordinates of each point obtained from the photographs taken from the front and the two 45 ~ angles are ranked at random in the array because of the irregular order of discovery. Each point is shown in both photographs taken from the front and from either of the 45 ~ angles, but to acknowledge two points appearing on two different photos as the same point, it is necessary to rearrange in order the coordinates of each point in the array. Therefore for this system two arrays with orderly
ranks were arranged to calculate the three-dimensional coordinates of each point. The coordinates are calculated on the basis of two-dimensional data given at the same position in these two arrays. In the case of the photograph of the face taken at 45 ~ on the right, for example, the point at the farthest -upper.right is ranked at 11, which is followed by, in searching toward the left, the point ranked 12 and 13, as shown on Fig. 4. This ranking is repeatcd to the left until there are no
434
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Am. J. Orthod. Dentofac. Orthop. May 1992
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more points to be found. When a nonexistent point is acknowledged in the leftward direction, the operation moves onto the second row, ranking the array as21, 22, and 23, in that order. The same process is repeated with the right half of the photograph taken from the front. After ranking all the points in two arrays, three-dimensional coordinates are calculated on the basis of two-dimensional coordinates of the same ranking number. The principle for calculating threedimensional coordinates is given in the Appendix. The three-dimensional coordinates obtained were given final correction on the basis of the actual distance between the reference points for storage onto the hard disk. Precision test Fig. 5 shows a piaster cast used for the precision test. The three-dimensional coordinates were obtained with threedirectional photography, after projecting points (with a projector) on a total of 70 measurement points on the plaster. These three-dimensional coordinate values were compared with the coordinate values obtained by the contact threedimensional measuring system (Fig. 6). Coordinate values of each point marked on the plaster cast were measured by this contact three-dimensional me 9
suring system three times, and their average was established as a reference value. The difference between these values and the coordinate values at each measuring point obtained by three-directional photography was considered error. Three-dimensional display We conducted a three-dimensional measurement of a face--an orthognathic surgical case--with this system, then displayed it three-dimensionally. A display with the use of a wire frame provided with hidden-line elimination or with shading was also possible. The same computer and programming language were used for the measurement of coordinates. This system, which is intended for clinical application, requires only a simple operation with a mouse commanding the reading of photographs, the calculation of the three-dimensional coordinates, and the three-dimensional display. RESULTS Precision Table I s h o w s errors at each measurement point. The average value and standard deviation of errors at all the measurement points are as follows:
Volume i01
Three-dimensional mea.sttring system af the human fiwe
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X coordinate: 0.04 • 0.24 mm Y coordinate: - 0 . 0 3 • 0.16 mm Z coordinate: 0.08 • 0.23 mm The measurement limit of this system is 2000 measurement points and a 1.5 mm interval between points. Three-dimensional
display
Figs. 7 through 9 are three-dimensional images of the actual subject who underwent orthognathic surgical treatment. Fig. 7 uses a wire-frame display, whereas Fig. 8 is provided with shading. Fig. 9 is a threedimensional display of the same subject about ! month after surgery. DISCUSSION
Two possible factors that affect the precision of this system are those related to the photography and those related to the process of measurement with the computer and the reading device. Factors related to photography include accuracy of the camera position, structure of the camera, and pos-
Fig. 5. Plaster cast used for precision test.
sible inadequate enlargement from film to printing paper. Accuracy of the camera position should be achieved with utmost care as it directly affects the image distance
436
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Am. J. Orthod. Dentofac. Orthop. May 1992
Fig. 8. Shading image of patient shown in Fig. 9.
Fig. 6. Contact three-dimensional measuring system (Tristation 400M CNC) determined reference values of coordinates at each point on plaster cast.
Fig. 9. Image of same patient measured by this system about 1 month after surgery.
Fig. 7. Three-dimensional image represented by wire frame.
and the object distance. Therefore a plastic disk in the contact three-dimensional measuring system was measured in advance, and with this as a subject, the accuracy of the conditions for the camera position was confirmed. Image distance requires other factors to be taken into consideration. Image distance consists of focal distance and focusing extension, of which focal distance is a nominal value.allowing ---5% deviation in the case of a Japanese-made camera. For this reason, in this
Volume 101 Number 5
Three-dimensional measuring system of the human face
437
Table I. Errors in the measuring of each point on the plaster Coordinate (ram)
Points
X -0.26 -0.22 -0.03 0.06 0.10 0.27 -0.14
-0.27 0.06 -0.10 -0.08 0.41 0.22 -0.27
-0.16 0.16 -0.02 -0.15 -0.24 0.22 0.12
-0.32 0.37 -0.41 0.47 -0.05 -0.13 -0.11
-0.30 0.09 0.06 -0.05 -0.20 0.12 0.31
0.19 -0.12 0.34 0.13 0.04 0.29 0.00
0.06 -0.39 -0.05 0.22 -0.12 0.27 0.29
-0.46 0.10 0.08 0.13 -0.03 0.21 0.68
0.46 -0.03 0.31 0.18 0.39 -0.09 0.05
0.11 0.48 -0.01 -0.27 -0.09 0.19 -0.06
0.19 0.22 0.17 0.13 -0.19 0.08 0.16
0.05 -0.21 0.24 0.30 0.22 0.02 0.21
-0.05 0.20 -0.13 -0.04 0.30 0.10 0.00
-0.02 -0.22 -0.06 -0.15 -0.18 -0.02 0.05
-0.01 0.01 -0.10 -0.02 0.04 -0.23 0.02
-0.01 -0.03 -0.20 -0.28 -0.02 0.02 0.01
-0.10 -0.14 -0.25 -0.10 -0.04 -0.28 -0.01
-0.27 -0.02 -0.08 -0.07 -0.12 -0.23 -0.28
0.09 -0.39 -0.04 0.06 0.30 -0.08 0.07
-0.04 -0.11 -0.09 -0.29 -0.05 -0.09 -0.17
0.38 0.50 -0.02 0.11 -0.07 0.09 -0.03
0.17 0.21 0.10 0.21 0.11 -0.06 0.02
0.27 -0.08 0.11 -0.09 0.14 0.20 0.22
-0.09 0.18 -0.02 -0.03 -0.13 0.02 0.18
0.48 0.17 0.43 0.17 -0.39 -0.09 -0.40
0.10 -0.18 0.46 0.21 -0.09 0.16 -0.13
-0.09 0.18 0.15 -0.13 0.04 0.42 -0.05
-0.49 .0.20 -0.18 0.12 0.06 -0.08 -0.04
0.51 0.43 0.15 0.02 -0.16 -0.42 -0.05
0.20 0.44 -0.46 0.46 0.19 0.35 0.37
Y
Z
Ranking of values corresponds to ranking of points on the plaster cast shown in Fig. 7.
study we used the previously mentioned disk that was photographed by each camera first. An image distance was then obtained from the ratio of the diameter of the disk on the film to the actual diameter. From this and the focusing extension, the focal distance of each lens was obtained. Finally, an image distance was corrected to 55 mm by adjusting the focusing extension. Regarding the camera structure, lens aberrations seem to particularly affect precision. There are six types of lens aberrations: chromatic aberration, spherical aberration, coma, astigmatism, curvature of field, and distortion. To enhance precision, a survey camera with good correction of aberrations is ideal, but even with an ordinary camera, it is possible to increase precision by correcting aberrations to the degree possible. This system, which is intended for widespread application to clinical cases, used an ordinary 35 mm camera, which is the most popular type in Japan. It was corrected for distortion, which affects precision to a greater degree than the other types of aberrations. The other aberrations can be improved to some extent by setting a large diaphragm. To reduce errors during the process of reading coordinates, the film should be enlarged. Therefore we used an enlargement on 8 • 12 cm printing paper as
the original reading paper in this study. There was concern however, that errors during the enlargement might affect the precision of the final data, so we measured the positions between each reference point in advance to use for the correction of the final data. There are other minor problems, such as distortion and elasticity on the film surface at the time of photographing, but we believe they do not affect the precision of measurement of the human face and therefore do not need correction. For want of any appropriate way of solving this problem, we did not provide any correction in this study. The resolution of the image scanner is the factor that most affects the precision of measurement in use of the computer and reading device. The degree of error depends on the efficiency of the selected image scanner. The resolution of the scanner used in this study was fixed at a maximum 200 • 200 DPI for reading. We then had to consider the precision of the extraction process of the points from the image data read from the photographs. Since the greater the number of pixels read by the scanner, the higher the precision, the numbeL.of vertical pixels was fixed at 750, the maximum value allowed by the vertical resolution (750 lines) of the CRT, and the number of horizontal pixels was 800,
438
Motoyoshi, Namura, and Arai
the maximum value of the scanner. To study the repeatability of the extraction process of the points, the readings and calculations of the coordinates using the same photographs were conducted several times. The fact that the same results could be obtained each time leads us to conclude that the extraction process of the points in this system always finds the same conditions, reducing deviation more than in the case where a digitizer was used. Yet another factor believed to affect precision is error resulting from calculation by the computer, but this is thought to be extremely minor compared with the aforementioned factor. The results of the precision tests show that the measurement precision of this system is higher than other measuring methods, such as telecentric photography, moire topography, stereophotogrammetry, and laser measurement. The measurement speed was also fast enbugh to be clinically applicable. ! Furthermore, this system is capable of a wire-frame display with hidden-line elimination and of a display of i'evolving images with shading. In the case of a wire: frame display with arrays of each measurement poini au!omatically ranked by a computer, there is no need to input just the relationship between each surface .and point for a three-dimensional display. Moreover, the time required for shading is approximately 20 seconds, with a marginal difference depending on the revolving angle, whereas the wire-frame display takes approximately I0 seconds, which means that this system is highly applicable to clinical cases that demand highspeed processing. To evaluate surgery and to measure the changed values, it is necessary to develop a system capable of accurate superimposition. For this purpose, constant reference points on the face before and after the surgery must be established for the correction of revolution or divergence of the face at the time the photograph is taken. We are also considering the development of a new system that would enable the simulation of prediction of results after orthognathic surgery, by combining it with measuring systems of the maxillomandibular structure. ~s.~9 CONCLUSION
The four conditions necessary for a clinically applicable three-dimensional measuring system are (1) a small burden on the patient at the time of measurement, (2) the simple input operation and high-precision measurement, (3) the calculation of coordinates for a substantial number of measuring points, and (4) a highspeed three-dimensional display based on the threedimensional coordinates Obtained. For the development of a system that meets all these conditions, this study has made the following conclusions:
Am. J. Orthod. Dentofac. Orthop. May 1992
1. In this study a projector for measurement was used because it reduced the burden on the patient and allowed for easy operation. For this purpos.e, we developed an apparatus capable of simultaneous, three-directional photography. 2. For a simplified input operation, automatic analysis is indispensable. It is also vital for the reduction of human manipulation and the improvement of precision. Therefore a three-dimensional measuring system was developed in which an image scanner directly reads the photographs obtained. The phot~raphs are transmitted to a computer as image data, and the coordinates of each measuring point are automatically calculated. This almost completely eliminates complex human manipulation. Input operation to a scanner was all that was necessary. This also ensured high precision. 3. The development of this system, capable of treating many measuring points, is expected to contribute to a more detailed three-dimensional understanding of the shape of the human face. 4. This system is believed to be functionally applicable to clinical cases that require high-speed processing. REFERENCES 1. Takasaki H. Moire topography. Applied Optics 1970;9:t45772. 2. Lovesey El. A simple photogrammetric technique for recording three dimensional head shape. Med Biol lllus 1973;23:210-3. 3. Segner D. The shape of the human face recorded by use of contour photography and spline function interpolation. Eur J Orthod 1986;8:112-7. 4. Robertson NRE. Contour photography. Br J Orthod 1976;3: 105-9. 5. Robertson NRE. Telecentde photogrammetry. AM J Or'mop 1981;80:623-37. 6. Sassouni V, Nanda S. Analysis of dentofacial vertical proportions. AM J OrmoP 1964;50:801-23. 7. Burke PH, Beard LFH. Stereophotograntmetry of the face. AM J ORtttOD 1967;53:769-82. 8. Berkowits S. Stereophotogrammetrie analysis of each of normal and abnormal palates. AM J OR'mOP 1971;60:1-18. 9. Berkowits S, Cuzzi J. Biostereometfic analysis of surgically corrected abnormal faces. AM J OrroOD 1977;72:526-38. 10. Savara BS. Applications of photogrametry for quantitative study of tooth and face morphology. Am J Phys Anthropol 1965;23:427-34. 1 I. Macgregor AR, Newton 1, Gilder RS. A sterophotogrammetrie method of investigating facial changes following the loss of teeth. Meal Biol Illus 1971;71:75-82. 12. tlaga M, Koshihara Y, Ota Y. Stereophotogrammetfic study of the face. Bull Tokyo Meal Dent Univ 1964;5:10-24. 13. Beard LFH, Burke PIt. Evolution of a system of stereophotogrammetry for the study of facial morphology. Med Biol lllus 1967; 17:20-5. 14. Chaya tl, Ishiakawa H, lmai T, Nakamura S. A three-dimensional analyzing system of face using stereophotogrammetry and computergraphics. Jpn J Orthod Soc 1988;47:560-78.
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Three-dintensional measuring system o f the Imman face
15. Baumrind S, Moffitt FH. Stereophotogrammett3' of the face. A.',t J ORrnoo 1967;53:769-82. 16. Arridge SR, Moss JP, Linney AD, et al. Three dimensional digitization of the face and skull. J Maxillofac Surg 1985;I 3:13643. 17. Moss JP, Grindrod SR, Linney AD, Arridge SR, James D. A computer system for the interactive planning and prediction of maxillofacial surgeD,. Ast J ORTtlOD DENI'OFACORTIIOP 1988;94, 469-75. 18. Motoyoshi M, Yamazaki T, Inoue K, Kura M, Yoshida T, Na-
mera S. Studies on three dimensional evaluation of maxillomandibular morphok~gy. Jpn J Onhod Soc 1986;45:181-95. 19. lnoue K, Yamazaki T, Motoyoshi M. Matsunaga S, ttayashi M, Namura S. Studies on 3-dimensional prediction of orth~nathic surgery cases. Jpn J Orthod Soc 1986;45:658-66.
Reprint requests to: Dr. Harold Y. Arai 101 S. Washington Park Ridge, IL 60068
APPENDIX
Y/XF = (d - x)/e Z/YF = (d - x)/e
The principle for calculating three-dimensional coordinates is as follows: XY coordinates on the film can be obtained by dividing XY coordinates on the photograph by L, ~,vhere L is the enlargement ratio from film to printing paper. The value of L is obtained by measuring the distance between the reference points shown on the printing paper and those on the film. The XY coordinates on the film that are obtained in the direction of the front, 45 ~ to the right, and 45 ~ to the left are referred to as XF, YF, XR, YR, XL, and YL; whereas the object distance, i.e., the distance between the lens principal point and the midpoint of the ear-rods, is referred to as d; the image distance or distance between the lens principal point and the film, e; and three-dimensional coordinates on the subject, X,Y, and Z. We then obtained the following formula from the conditions of camera position when the photograph of a front view of the subject was taken.
In the case of a photograph taken at an angle of 45 ~ the following formula was obtained from the ratio of the real distance, indicated by an arrow (Y/X/-2 x/X/2) on Fig. A1, to the photograph distance, taking the left side as an example. (y -
x)/x/~
z
XL
YR
Similarly with the photograph taken from the right side, the relationship is . (Y + X ) / V ~
XR
Z
YR
Furthermore, the following formula is obtained from the ratio of the image distance to the object distance, as Fig. A2 shows.
MID-POINT OF EAR-RODS '~,~
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440
Motovoshi, N a m u r a , a n d Arai
Am. J. Orthod. Dentofac. Orthop.
"
M a y 1992
"HE MID-POINT OF EAR-RODS
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d - (Y + X)/X/-2 e
Z YL
d - (X - Y)/X/'2~ e
Z YR
The coordinates of X, Y, and Z on the subject can be obtained from the formulas given. Incidentally, the distance between the midpoint of the eatrods and the surface of the film was fixed at 700 ram. When the
focal distance of the lens in use was 50 mm, lens extension for focusing on the subject was 5 mm. Consequently, the object distance was 645 ram, and the image distance was 55 mm, both of which are known values. Since it was convenient to keep the image distance constant for calculation, the subject was photographed with the diaphragm set at 11 for large depth of field and the focusing extension fixed at 5 ram.
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