American Journal of Medical Genetics 39:161-166 (1991)
Photogrammetric Evaluation in Clinical Genetics: Theoretical Considerations and Experimental Results John H. DiLiberti and David P. Olson Medical Computing Research Laboratory, Department of Pediatrics, Saint Francis Hospital and Medical Center, Hartford, Connecticut and Division of Medical Genetics, Department of Pediatrics, University of Connecticut School of Medicine, Farmington, Connecticut As newer mathematical approaches are applied to the field of clinical genetics accurate methods of craniofacial measurement are increasingly necessary. If photogrammetric techniques are to be used certain theoretical and practical issues must be taken into account. Errors due to projection are particularly important, but systematic and random errors must also be considered. We discuss theoretical aspects of projection errors along with experimentalmeasurements.Systematic errors in excess of 20%were found during simulations of typical clinical conditions, although smaller errors were obtained using techniques practical in a clinical setting. Photogrammetric measurements are potentially valuable in the field of clinical genetics but must be used cautiously. KEY WORDS: dysmorphology, anthropometry, photogrammetry,congenital anomalies INTRODUCTION The diagnosis of syndromes of disordered morphogenesis, particularly those involving altered facial appearance, has historically relied heavily on relatively subjective impressions or clinical gestalts, perhaps coupled with a fairly small number of objective measurements [Smith and Jones, 1982; Ward, 19891. Although Thompson 119611suggested a mathematical approach to biological shape analysis early in this century, for a variety of reasons his suggestions and more recent recommendations by Bookstein [19781have not led to many serious attempts to transform the study of disorders of morphogenesis into a mathematical science. This situation seems to be changing as a result of the availability of more powerful digital computers and by the need for more accurate clinical diagnosis for counseling purposes and in the application of molecular techniques. Any quantitative approach to anomalies of the face requires accurate data, although the mathematical apFteceived for publication April 2,1990; revision received July 11, 1990. Address reprint requests to John H. DiLiberti, M.D., Department ofpediatrics, Saint Francis Hospital and Medical Center, 114 Woodland St., Hartford, CT 06105.
0 1991 Wiley-Liss, Inc.
proach chosen will undoubtedly determine the precision of the measurements necessary for reproducible analysis. Since the field of mathematical analysis in this area is quite new, no firm guidelines for precision of measurements have been determined. These guidelines will undoubtedly develop over the next few years as mathematical approaches becomes more common and more refined. In the meantime, research done in this field must use rigorous approaches to data collection in order to avoid potential bias in analysis. The most common approaches to craniofacial measurements include the methods of classical physical anthropology, anthropometry, as well as photogrammetry, and radiography (along with the related methods: magnetic resonance imaging, ultrasonography, etc.). Obviously only the first 2 techniques will generally be applied directly by the clinical geneticist. Although each approach has been used in the study of disorders of morphogenesis, discussions of measurement errors from theoretical and practical perspectives have been limited. We have examined the systematic errors in the photogrammetric approach and present the results below.
THEORETICAL CONSIDERATIONS Systematic and Random Errors In any quantitative system, 3 distinct classes of measurement uncertainty and their respective magnitudes must be considered-random error, systematic error, and intrinsic measurement uncertainty. For a given set of measurements the mean and standard deviation give information about systematic and random errors, respectively. If we were to measure a bar precisely 1m in length with 2 different measuring devices, one set of measurements might have a mean of 1.000001m with a standard deviation of 0.010000 m. The second device might give a mean of 1.010000m with a standard deviation of 0.000001 m. The first device has a very small systematic error and a relatively large random error. The converse is true for the second device. Under some circumstances, information obtained from estimating systematic errors may be used to make corrections in subsequent measurements. The intrinsic limitations of the measurement device must be also considered. The intrinsic measurement uncertainty of any ruled instrument is 2 ALJ2 where S is the smallest ruled interval. The most reasonable estimate of the measurement uncertainty is then given
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either by the intrinsic measurement uncertainty, or the random (statistically determined) error, whichever is larger. Note that it is possible for the random error to be smaller than the intrinsic measurement uncertainty. Finally, care must be taken when estimating random errors in the presence of a systematic error. Generally, systematic errors will be either additive or multiplicative. In a photogrammetric system the former arise from varying the distance between the camera and object, and the latter as a result of a geometric projection. Obviously, there will be some degree of uncertainty in the determination of the (additive or multiplicative) corrections to the measurement. The total measurement uncertainty will then have 2 contributions, the original measurement uncertainty, and the uncertainty in the correction due to systematic errors. For example, if we are measuring some length L with uncertainty AL and have determined a systematic correction C with uncertainty AC then for the case of an additive systematic error we may determine the corrected length L, and the total uncertainty:
L,=L+C
and
AL,=AL+AC
I-.
-
~-
-
----- -
I - ~ - -
Fig, 1. Photographic projection of three-dimensional object on twodimensional film.
12. Random and systematic errors as noted above in taking measurements from the photograph.
for the case of a multiplicative systematic error we have
L,=L.C
and
AL,=AL.C+L.AC
Note that uncertainties are always positive quantities. A photogrammetric system is far more complex than the measurement systems described above. In Figure 1a three-dimensional image is projected through a lens in 2 dimensions onto a piece of film which is then developed and printed through yet another optical system onto a piece of photographic paper. Finally one or more measurements may be taken from the print using calipers or ruler. In many cases a marker of known dimensions is attached to the face being studied. Potential sources of error are as follows: 1. If the marker is not rigid, has it molded to the shape of the face resulting in dimensional change? 2. The orientation of the camera film plane with respect to the marker and the remainder of the face, and the distance of the camera from the face altering the projection size of different regions. 3. Distortion in the optical system of the camera. 4. Imperfect flatness of the film. 5. Dimensional stability of the film during processing, i.e., was there any stretching or shrinking during the wettingldrying cycle? 6. Flatness of the film in the enlarger. 7. Parallel alignment of the film plane with the paper plane in the enlarger. 8. Distortion in the optical system of the enlarger. 9. Flatness of the photographic paper during exposure. 10. Dimensional stability of the photographic paper during processing. 11. Inaccurate focusing or poor quality film leading to blurred images.
Fortunately, modern photographic methods and technology have decreased the amount of error in optical systems and film flatness to low levels resulting in optical distortions of only a few percent in high quality cameras and enlargers. Dimensional stability of most films and papers is generally considered to be high enough to neglect except for the most demanding areas where glass photographic plates may still be used. Thus, of the 11categories noted above numbers 1,2,7, and 12 remain for consideration. If a reasonably flat portion of the face is selected for a flexible marker, distortion will be relatively unlikely but still somewhat unpredictable. The more rigid the marker, the smaller the error. Unfortunately this error will be random and uncorrectable since it will vary depending on the amount of flexion in the marker. Failure to keep the film plane parallel with the paper plane during enlargement may also cause random errors which are not likely to be large unless considerable misalignment is present in the enlarger. Standard techniques are available to correct for this problem, but it is rarely considered in most cases. If a large (20 cm by 25 cm minimum) photographic print is made for obtaining measurements reasonably precise data can be obtained using calipers or a rule. Parallax errors should be avoided as much as possible. The remaining sources of measurement error, camera orientation and camera to film distance, are mathematically related and may both be considered as projection errors. They are potentially the largest in magnitude, both theoretically and practically, and warrant further discussion. Geometric Considerations One type of projection error arises from an undesired or unavoidable inclination of the film plane with respect t o a line connecting 2 points of interest on the subject. The angle of inclination 8 is defined as the angle be-
Photogrammetric Evaluation
tween the line connecting these 2 points and (its projection on) the plane of focus as shown in Figure 2 (which also illustrates the nature of the systematic error): the line projected on the film is reduced in length (compared to lines parallel with the film plane) by a factor of cos 8. In the event that the set of points of interest is not coplanar, then some degree of systematic error in measurement is unavoidable since it is then impossible for the plane of focus to be parallel to all line segments connecting the points. Figure 3 illustrates the geometric considerations in a morphometric (3 dimensional) context. Two possible planes of focus are shown, F , which lies in the vertical plane, and Fz which is inclined at an angle 8 with respect to F,. Suppose that we wish to measure the distances between points A, B , and C. If, as drawn in Figure 3, these points all lie in the plane of F , then there is a simple scaling transformation which can be applied to all measurements taken from the photograph. This implies that any ratios of measurements taken from the photograph will be equivalent (within normal measurement tolerances, i.e., random errors) to measurements taken from the original subject:
AB -LAB
AC-Lac
where mIA7 is the ratio of lengths measured from the photograph and LABILAC is the ratio of lengths measured from the subject. Next consider the photograph resulting from a plane of focus F2.At most, 2 of the 3 points of interest could lie in this new plane. We wish to measure the distances between points A, B , and C for the case shown in Figure 3. If points A and B lie in the plane of F2 but C does not, then there is no simple mathematical transformation which can be applied to all measuEmentstaken from the photograph. Measured lengths AC and BC will each be shortened by a geometricprojection factor of cos8, while the measured length AB is unaffected by geometric projection factors. Consequently, ratios of measurements taken from the photograph will be subject to a systematic error that increases (nonlinearly) with the angle of inclination 8. IMAGE
Fig. 2. Projection effects on image due to object inclination
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Fig. 3. Inclination of image plane with respect to the object plane introduces systematic measurement errors.
The fractional error in a measured length L due to an inclination of the plane of focus is given by
-AL _ - (1- cos 8 ) L
In the general case, where multiple points of interest lie in different image planes, 0 is different for each length to be measured. Consequently, each measurement suffers from a unique projection effect, i.e., its own cos 8, factor and in a n absolute sense cannot be meaningfully compared with measurements taken from a different set of points a t a different angle 8,. From a practical viewpoint, we must agree on the magnitude of acceptable error and determine if our measurements are within those bounds. Table I lists the theoretical fractional error (ALIL) 100 versus 8. A second source of projection error arises from the variation in image magnification with object distance. Morphometric studies, especially cephalometric studies, typically involve photographic images (e.g., of the head) necessitating either a short camera-object distance (with a conventional 50 mm lens) or a telephoto lens which allows photographing from a longer distance. As discussed below, the magnification (and hence the scale of the photograph) varies with the object distance from the camera and the focal length of the lens used. To illustrate how this variation in magnification can introduce measurement errors consider the following example: a photograph of a person with mountains in the background. On a bright day, with a small aperture setting (large fnumber) both the mountains and person would appear to be in focus. Since the mountains are so far in the background, knowing the height of the person would not allow calculation of the height of the mountains from the ratio measured in a photographic print. If, however, the person were standing on the mountain far away from the camera, then the ratio of measurements in the photograph would give a fairly accurate estimate of the height of the mountain. It should also be immediately apparent that exactly the same considerations apply, albeit with smaller magnitude effects, to the photographic measurement of any
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TABLE I. Fractional Projection Error hL -=.0" 2"
5" 7"
lo" 20" 30"
(%I
0.0 .06 .4
.7 2 6 13
objects which are different distances from the camera and whose images consequently lie in different image planes. It is difficult, if not impossible, to discriminate from a photograph whether or not a specific pair of objects lie in the same image plane or not-solely on the basis of sharpness of focus. While this is all intuitively reasonable, it is worthwhile to examine the relevant optics which underlie this phenomenon, and to estimate the magnitude of these effects in the context of cephalometrics. The fractional change in magnification AMIM for 2 objects at object distances o1 and o2 (assuming that the image plane is at ol) is given by
Consequently, measurement of the length of two identical objects at o1and o2from the photograph will have a fractional error:
Note that AM/M, which does not explicitly depend on the focal length f, decreases as o1 increases (with fixed o1 - 0 2 ) .From a practical viewpoint this is an implicit dependence on f since the object distance o chosen for a particular view will depend on the focal length of the lens. Thus, photographs taken with a longer focal length lens will have smaller AMIM effects than identical photographs taken with a shorter focal length lens assuming that the image on the film is the same size. Expressed differently, the fractional error is inversely proportional to the subject to film plane distance. A telephoto lens allows increased distance from the subject for the same image size and results in smaller measurement error. Alternatively, a standard (50 mm) lens used at a longer distance will produce the same effect although with a smaller image. This can be adjusted in the enlarging process within a fairly broad range of magnifications. Errors may also result from variations in the relative position of the camera for each photograph. Photogrammetric evaluation of a 2D object such as a painting is easy to standardize in this regard. If the camera (actually the film) is parallel to the object plane, no distortion will occur. Angular movement of the camera results in foreshortening proportional to the cosine of the angular change. When dealing with 3D objects the situation becomes somewhat more complicated. Specifyingan ab-
solute camera position is only possible if certain conditions of symmetry prevail. This works well for the Platonic solids and their relatives but the human head has only (imperfect) bilateral symmetry. Constraining the film plane to be perpendicular to the mid-sagittal plane may be established as an absolute specification within the limits of the degree of bilateral symmetry and positioning technique. The camera may still be turned in an infinite number of positions relative to the face, however. Several different approaches have been used to deal with this problem, including an unwieldy mechanical device which holds the head in a fixed position. Since heads and faces all differ in shape and have no symmetry beyond the bilateral it may be shown mathematically that it is impossible to specify an absolute, invariant camera position which will eliminate this type of distortion when measuring multiple subjects. All is not lost, however, since the laws of geometry greatly reduce the potential magnitude of this type of error. If the camera is positioned 3 m from the subject, foreshortening error will be less than 1.5%if the camera is no more than 52 cm from the horizontal plane, a very generous margin. The specification of the horizontal plane cannot be accomplished absolutely, because of the absence of symmetry, as noted above, but reasonable compromises may be made. Except in the presence of low-set ears, aiming the camera so that the outer canthus and superior attachment of the external ear to the head are aligned will give reasonable consistency. If other conventions are used it is unlikely that the rotation of the head between the 2 camera orientations will be greater than 10". Since the cosine of lo" is ,985 the difference in measurements will be 1.5%.Even an extremely large relative angular rotation of 20" will result in measurement differences no greater than 6%.Therefore, as long as reasonable care is taken aiming the camera, measurement differences as a consequence of foreshortening are likely to be relatively small. In the absence of symmetry beyond the bilateral, complete elimination of this type of error is impossible.
METHODS We constructed a device for measuring projection scaling errors by attaching 2 flat rigid pieces of aluminum to a device which allowed parallel movement through the desired range of distances (Fig. 4). A regularly ruled strip of white paper was firmly attached to each piece of aluminum, which was about 25 cm long, approximately the length of an adult human face. After consulting anthropometric tables we decided that 12 cm would be the greatest distance between two regions of an adult face that might be considered for photogrammetric evaluation. In most cases the distances involved would be considerably smaller. We therefore made photographs at 3, 6, 9, and 12 cm distances to simulate a range relevant t o typical craniofacial structures of children and adults. Note that we are only interested in the distance between planes containing 2 regions if both can appear simultaneously in a photograph. Thus the ears can both be seen in the same plane in a frontal photograph but will not be visible in a lateral view. Photographs were taken on Kodak T-Max 400 black
Photogrammetric Evaluation
Fig. 4. Experimental setup for measuring scaling errors
and white film using a Nikon 35 mm camera with 24,50, 105, and 200 mm Nikkor lenses at subject to film plane distances ranging from 31.3 to 211.8 cm in order to obtain a nearly full frame image. The film was processed in Kodak T-Max developer and fixer according to the manufacturers recommendations. Prints were made using a n Omega D-2V enlarger with Nikkor 50 lens on Kodak Polycontrast RC “paper,” which actually has a polymer base and is more stable dimensionally than fiber. It was developed and fixed according to the manufacturers recommendations. Measurements were taken using a metric rule to the nearest 0.5 mm.
RESULTS As can be seen in Figure 5 the observed scaling error is nearly a straight line and for the smaller object separatiodobject distance (OS/OD) ratios coincides quite nicely with the predicted (theoretical) line. Thus for a n OS/OD ratio of 0.1 the predicted error was 10% and the observed error was 10.2%.At larger OS/OD ratios the observed error was somewhat less than the predicted error, especially for the 24 mm lens. This is almost certainly the result of the rather different (retrofocus)
optical design used in this lens. The lenses using telephoto designs gave error measurements much closer to predicted values. DISCUSSION Although it might be argued that the results of our experiment were predictable from elementary optics, real-world systems, in fact, often deviate from theory. The deviations seen for the measurements made using the wide angle lens emphasize the difference between ideal theoretical models and the performance of operational systems. The laws of optics are only relatively straightforward for simple, thin lenses, whereas modern camera lenses involve complex optical design, the mathematics of which is beyond the scope of this paper. Thus, we designed our experiment to examine the “output” from a complex, multistage optical system using readily available components. Our results should therefore be applicable to clinical settings where comparable components are used. We have not made any a priori assumptions about which points on the face will prove to be most useful for formal analysis of syndromes. Landmarks derived from physical anthropology, such as those advocated by Farkas [1981], appear to us to have been selected because they are convenient to measure. We know of no theoretical or practical reasons why the points currently measured will be more useful for analysis than others such as the point of maximum convexity of the cheek. This location may be determined using computerized shape analysis of photographs but would almost certainly escape the most skilled anthropometrician using classical methodology. We believe, therefore, that clinical geneticists interested in the formal analysis of syndromes should strive to use a general approach to data collection and not be constrained by arbitrary conventions based on other disciplines.
Percent Error 60
50 40
30 20
10
0 0
0.1
0.2 0.3 0.4 Object Separation / Object Distance
0.5
Lens Focal Length *
24 rnrn
+
50 mrn
165
*
105 rnrn
0
200 rnm
Fig. 5. Experimental results for several different focal length lenses,
0.6
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Our results indicate that in applying photogrammetric evaluations to clinical genetics, projection errors may be unacceptably large unless efforts based on knowledge of photogrammetry are made t o reduce them. Many clinicians use lenses of approximately 50 mm focal length for routine photographs. As may be seen in Figure 5, using a marker placed on the forehead, measurements taken from an area of interest 3 cm further from the camera plane will have a measurement error of nearly 10% based on the typical camera to subject distance for a full face photograph. With a 200 mm telephoto lens at a distance of 212 cm the error is reduced to about 1.5%.Alternatively if the 50 mm lens were used at this same distance and the negative enlarged proportionately the error would also be about 1.5%.Note that this is for objects in planes no more than 3 cm apart. In order to reduce measurement errors to about 1%for object planes 6 cm apart the film plane must be 6 m from the subject, perhaps the practical upper limit because of room size considerations. Farkas [19811discusses what he calls “photogrammetry of the face” including a brief history of this technique up to that time and a comparison with his anthropometric methodology. He used a camera to subject distance of 3352.8 mm and claims that this is 2.2 times the minimum distance recommended by Gavan et al. [19521 to reduce photographic error to less than 1%.This was determined using the average ear to ear distance of adult men of 153 mm. According to optical theory and our experimental results we calculate a nearly 5%maximum error for this configuration, not the less than 0.5% apparently implied by Farkas. (Gavan seems to have misunderstood photographic projection principles and Farkas apparently repeated this error.) He then goes on to compare the photogrammetric method with his anthropometric method and finds the photogrammetric approach deficient. Unfortunately, he gives no data regarding systematic or random errors using either method and appears to assume that the anthropometric method has no error. His rejection of the photographic method because it differs from his favored anthropometric approach seems to be unwarranted. It is entirely possible for the 2 methods to give results which differ significantly systematically but not randomly. In this case a correction factor could be determined which would make anthropometric and photogrammetric measurements compatible and interchangeable. Farkas seems more concerned with landmarks of interest for surgical procedures. Thus, even if his conjecture about photogrammetric landmarks is correct regarding their accuracy related to their anthropometric correlates, it may be of no concern to clinical geneticists. Obviously this must be studied more carefully before reaching any definitive conclusions about the relative merits of either technique when applied to clinical genetics. In our opinion, for some regions of interest such as the distance between bony prominences easily palpated but difficult to identify in photographs, the anthropometric approach may be superior, whereas measurements based
on soft tissue landmarks may be more amenable to photogrammetric assessment. Stengel-Rutkowski et al. [ 19841attempted to use photogrammetric evaluation of minor facial anomalies. Unfortunately they fail to describe their photogrammetric method and used ratios rather than absolute measurements. In their measurements of 10 photographs of the same child the variance ranged from 2.06 to 11.25%. This is of interest since it is virtually identical to our experimental results for photographs taken from a distance of 107 cm (Fig. 51, a typical camera to subject distance for a modest telephoto lens. Clarren et al. [19871 describe the application of the photogrammetric approach to the fetal alcohol syndrome. Unfortunately, they also fail to describe the photogrammetric method employed. The possibility that systematic measurement errors affected their conclusions remains uncertain.
CONCLUSIONS We have demonstrated that large systematic errors may result from the improper use of photogrammetric techniques to clinical genetics. These results do not address the issue of whether photographs taken under controlled circumstances will be useful in the mathematical analysis of craniofacial syndromes. In order to discover whether this is feasible both anthropometric and photogrammetric techniques must be applied to a group of subjects by a number of trained clinical geneticists with careful statistical comparison of the results. Even if the photogrammetric technique is lacking in overall accuracy it may still be practical for selected applications in clinical genetics. Prior to this determination we recommend that all papers using photogrammetric approaches carefully describe their experimental methodology and strongly encourage using subject to camera distances long enough to reduce projection errors to low levels based on the OS/OD ratio described above.
REFERENCES Bookstein FL (1978):“The Measurement of Biological Shape and Shape Change.” Lecture Notes in Biomathematics Volume 24. Berlin: Springer-Verlag. Clarren SK, Sampson PD, Larsen J , Donne11 DH, Barr HM, Bookstein FL, Martin DC, Streissguth AP (1987):Facial effects offetal alcohol exposure: Assessment of photographs and morphometric analysis. Am J Med Gen 26:651-666. Farkas LG (1981):“Anthropometryofthe Head and Face in Medicine,” New York: Elsevier North Holland. Gavan JA, Washburn SL, Lewis PH (1952):Photography: An anthropometric tool. Am J Phys Anthro 10:331-353. Smith DW, Jones KL (1982):“Recognizable Patterns of HumanMalformation,” Major Problems in Clinical Pediatrics, Volume VII. Philadelphia: W.B. Saunders. Stengel-Rutkowski S, Schimanek P, Wernheimer A (1984): Anthropometric definitions of dysmorphic facial signs. Hum Genet 67:272-295. Thompson DW (1961): “On Growth and Form.” Cambridge: Cambridge University Press. Ward RE (1989):Facial morphology as determined by anthropometry: Keeping it simple. J Craniof Genet Dev Biol 9:45-60.
Photogrammetric Evaluation in Clinical Genetics: Theoretical Considerations and Experimental Results John H. DiLiberti and David P. Olson Medical Computing Research Laboratory, Department of Pediatrics, Saint Francis Hospital and Medical Center, Hartford, Connecticut and Division of Medical Genetics, Department of Pediatrics, University of Connecticut School of Medicine, Farmington, Connecticut As newer mathematical approaches are applied to the field of clinical genetics accurate methods of craniofacial measurement are increasingly necessary. If photogrammetric techniques are to be used certain theoretical and practical issues must be taken into account. Errors due to projection are particularly important, but systematic and random errors must also be considered. We discuss theoretical aspects of projection errors along with experimentalmeasurements.Systematic errors in excess of 20%were found during simulations of typical clinical conditions, although smaller errors were obtained using techniques practical in a clinical setting. Photogrammetric measurements are potentially valuable in the field of clinical genetics but must be used cautiously. KEY WORDS: dysmorphology, anthropometry, photogrammetry,congenital anomalies INTRODUCTION The diagnosis of syndromes of disordered morphogenesis, particularly those involving altered facial appearance, has historically relied heavily on relatively subjective impressions or clinical gestalts, perhaps coupled with a fairly small number of objective measurements [Smith and Jones, 1982; Ward, 19891. Although Thompson 119611suggested a mathematical approach to biological shape analysis early in this century, for a variety of reasons his suggestions and more recent recommendations by Bookstein [19781have not led to many serious attempts to transform the study of disorders of morphogenesis into a mathematical science. This situation seems to be changing as a result of the availability of more powerful digital computers and by the need for more accurate clinical diagnosis for counseling purposes and in the application of molecular techniques. Any quantitative approach to anomalies of the face requires accurate data, although the mathematical apFteceived for publication April 2,1990; revision received July 11, 1990. Address reprint requests to John H. DiLiberti, M.D., Department ofpediatrics, Saint Francis Hospital and Medical Center, 114 Woodland St., Hartford, CT 06105.
0 1991 Wiley-Liss, Inc.
proach chosen will undoubtedly determine the precision of the measurements necessary for reproducible analysis. Since the field of mathematical analysis in this area is quite new, no firm guidelines for precision of measurements have been determined. These guidelines will undoubtedly develop over the next few years as mathematical approaches becomes more common and more refined. In the meantime, research done in this field must use rigorous approaches to data collection in order to avoid potential bias in analysis. The most common approaches to craniofacial measurements include the methods of classical physical anthropology, anthropometry, as well as photogrammetry, and radiography (along with the related methods: magnetic resonance imaging, ultrasonography, etc.). Obviously only the first 2 techniques will generally be applied directly by the clinical geneticist. Although each approach has been used in the study of disorders of morphogenesis, discussions of measurement errors from theoretical and practical perspectives have been limited. We have examined the systematic errors in the photogrammetric approach and present the results below.
THEORETICAL CONSIDERATIONS Systematic and Random Errors In any quantitative system, 3 distinct classes of measurement uncertainty and their respective magnitudes must be considered-random error, systematic error, and intrinsic measurement uncertainty. For a given set of measurements the mean and standard deviation give information about systematic and random errors, respectively. If we were to measure a bar precisely 1m in length with 2 different measuring devices, one set of measurements might have a mean of 1.000001m with a standard deviation of 0.010000 m. The second device might give a mean of 1.010000m with a standard deviation of 0.000001 m. The first device has a very small systematic error and a relatively large random error. The converse is true for the second device. Under some circumstances, information obtained from estimating systematic errors may be used to make corrections in subsequent measurements. The intrinsic limitations of the measurement device must be also considered. The intrinsic measurement uncertainty of any ruled instrument is 2 ALJ2 where S is the smallest ruled interval. The most reasonable estimate of the measurement uncertainty is then given
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either by the intrinsic measurement uncertainty, or the random (statistically determined) error, whichever is larger. Note that it is possible for the random error to be smaller than the intrinsic measurement uncertainty. Finally, care must be taken when estimating random errors in the presence of a systematic error. Generally, systematic errors will be either additive or multiplicative. In a photogrammetric system the former arise from varying the distance between the camera and object, and the latter as a result of a geometric projection. Obviously, there will be some degree of uncertainty in the determination of the (additive or multiplicative) corrections to the measurement. The total measurement uncertainty will then have 2 contributions, the original measurement uncertainty, and the uncertainty in the correction due to systematic errors. For example, if we are measuring some length L with uncertainty AL and have determined a systematic correction C with uncertainty AC then for the case of an additive systematic error we may determine the corrected length L, and the total uncertainty:
L,=L+C
and
AL,=AL+AC
I-.
-
~-
-
----- -
I - ~ - -
Fig, 1. Photographic projection of three-dimensional object on twodimensional film.
12. Random and systematic errors as noted above in taking measurements from the photograph.
for the case of a multiplicative systematic error we have
L,=L.C
and
AL,=AL.C+L.AC
Note that uncertainties are always positive quantities. A photogrammetric system is far more complex than the measurement systems described above. In Figure 1a three-dimensional image is projected through a lens in 2 dimensions onto a piece of film which is then developed and printed through yet another optical system onto a piece of photographic paper. Finally one or more measurements may be taken from the print using calipers or ruler. In many cases a marker of known dimensions is attached to the face being studied. Potential sources of error are as follows: 1. If the marker is not rigid, has it molded to the shape of the face resulting in dimensional change? 2. The orientation of the camera film plane with respect to the marker and the remainder of the face, and the distance of the camera from the face altering the projection size of different regions. 3. Distortion in the optical system of the camera. 4. Imperfect flatness of the film. 5. Dimensional stability of the film during processing, i.e., was there any stretching or shrinking during the wettingldrying cycle? 6. Flatness of the film in the enlarger. 7. Parallel alignment of the film plane with the paper plane in the enlarger. 8. Distortion in the optical system of the enlarger. 9. Flatness of the photographic paper during exposure. 10. Dimensional stability of the photographic paper during processing. 11. Inaccurate focusing or poor quality film leading to blurred images.
Fortunately, modern photographic methods and technology have decreased the amount of error in optical systems and film flatness to low levels resulting in optical distortions of only a few percent in high quality cameras and enlargers. Dimensional stability of most films and papers is generally considered to be high enough to neglect except for the most demanding areas where glass photographic plates may still be used. Thus, of the 11categories noted above numbers 1,2,7, and 12 remain for consideration. If a reasonably flat portion of the face is selected for a flexible marker, distortion will be relatively unlikely but still somewhat unpredictable. The more rigid the marker, the smaller the error. Unfortunately this error will be random and uncorrectable since it will vary depending on the amount of flexion in the marker. Failure to keep the film plane parallel with the paper plane during enlargement may also cause random errors which are not likely to be large unless considerable misalignment is present in the enlarger. Standard techniques are available to correct for this problem, but it is rarely considered in most cases. If a large (20 cm by 25 cm minimum) photographic print is made for obtaining measurements reasonably precise data can be obtained using calipers or a rule. Parallax errors should be avoided as much as possible. The remaining sources of measurement error, camera orientation and camera to film distance, are mathematically related and may both be considered as projection errors. They are potentially the largest in magnitude, both theoretically and practically, and warrant further discussion. Geometric Considerations One type of projection error arises from an undesired or unavoidable inclination of the film plane with respect t o a line connecting 2 points of interest on the subject. The angle of inclination 8 is defined as the angle be-
Photogrammetric Evaluation
tween the line connecting these 2 points and (its projection on) the plane of focus as shown in Figure 2 (which also illustrates the nature of the systematic error): the line projected on the film is reduced in length (compared to lines parallel with the film plane) by a factor of cos 8. In the event that the set of points of interest is not coplanar, then some degree of systematic error in measurement is unavoidable since it is then impossible for the plane of focus to be parallel to all line segments connecting the points. Figure 3 illustrates the geometric considerations in a morphometric (3 dimensional) context. Two possible planes of focus are shown, F , which lies in the vertical plane, and Fz which is inclined at an angle 8 with respect to F,. Suppose that we wish to measure the distances between points A, B , and C. If, as drawn in Figure 3, these points all lie in the plane of F , then there is a simple scaling transformation which can be applied to all measurements taken from the photograph. This implies that any ratios of measurements taken from the photograph will be equivalent (within normal measurement tolerances, i.e., random errors) to measurements taken from the original subject:
AB -LAB
AC-Lac
where mIA7 is the ratio of lengths measured from the photograph and LABILAC is the ratio of lengths measured from the subject. Next consider the photograph resulting from a plane of focus F2.At most, 2 of the 3 points of interest could lie in this new plane. We wish to measure the distances between points A, B , and C for the case shown in Figure 3. If points A and B lie in the plane of F2 but C does not, then there is no simple mathematical transformation which can be applied to all measuEmentstaken from the photograph. Measured lengths AC and BC will each be shortened by a geometricprojection factor of cos8, while the measured length AB is unaffected by geometric projection factors. Consequently, ratios of measurements taken from the photograph will be subject to a systematic error that increases (nonlinearly) with the angle of inclination 8. IMAGE
Fig. 2. Projection effects on image due to object inclination
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I
, ,
Fig. 3. Inclination of image plane with respect to the object plane introduces systematic measurement errors.
The fractional error in a measured length L due to an inclination of the plane of focus is given by
-AL _ - (1- cos 8 ) L
In the general case, where multiple points of interest lie in different image planes, 0 is different for each length to be measured. Consequently, each measurement suffers from a unique projection effect, i.e., its own cos 8, factor and in a n absolute sense cannot be meaningfully compared with measurements taken from a different set of points a t a different angle 8,. From a practical viewpoint, we must agree on the magnitude of acceptable error and determine if our measurements are within those bounds. Table I lists the theoretical fractional error (ALIL) 100 versus 8. A second source of projection error arises from the variation in image magnification with object distance. Morphometric studies, especially cephalometric studies, typically involve photographic images (e.g., of the head) necessitating either a short camera-object distance (with a conventional 50 mm lens) or a telephoto lens which allows photographing from a longer distance. As discussed below, the magnification (and hence the scale of the photograph) varies with the object distance from the camera and the focal length of the lens used. To illustrate how this variation in magnification can introduce measurement errors consider the following example: a photograph of a person with mountains in the background. On a bright day, with a small aperture setting (large fnumber) both the mountains and person would appear to be in focus. Since the mountains are so far in the background, knowing the height of the person would not allow calculation of the height of the mountains from the ratio measured in a photographic print. If, however, the person were standing on the mountain far away from the camera, then the ratio of measurements in the photograph would give a fairly accurate estimate of the height of the mountain. It should also be immediately apparent that exactly the same considerations apply, albeit with smaller magnitude effects, to the photographic measurement of any
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TABLE I. Fractional Projection Error hL -=.0" 2"
5" 7"
lo" 20" 30"
(%I
0.0 .06 .4
.7 2 6 13
objects which are different distances from the camera and whose images consequently lie in different image planes. It is difficult, if not impossible, to discriminate from a photograph whether or not a specific pair of objects lie in the same image plane or not-solely on the basis of sharpness of focus. While this is all intuitively reasonable, it is worthwhile to examine the relevant optics which underlie this phenomenon, and to estimate the magnitude of these effects in the context of cephalometrics. The fractional change in magnification AMIM for 2 objects at object distances o1 and o2 (assuming that the image plane is at ol) is given by
Consequently, measurement of the length of two identical objects at o1and o2from the photograph will have a fractional error:
Note that AM/M, which does not explicitly depend on the focal length f, decreases as o1 increases (with fixed o1 - 0 2 ) .From a practical viewpoint this is an implicit dependence on f since the object distance o chosen for a particular view will depend on the focal length of the lens. Thus, photographs taken with a longer focal length lens will have smaller AMIM effects than identical photographs taken with a shorter focal length lens assuming that the image on the film is the same size. Expressed differently, the fractional error is inversely proportional to the subject to film plane distance. A telephoto lens allows increased distance from the subject for the same image size and results in smaller measurement error. Alternatively, a standard (50 mm) lens used at a longer distance will produce the same effect although with a smaller image. This can be adjusted in the enlarging process within a fairly broad range of magnifications. Errors may also result from variations in the relative position of the camera for each photograph. Photogrammetric evaluation of a 2D object such as a painting is easy to standardize in this regard. If the camera (actually the film) is parallel to the object plane, no distortion will occur. Angular movement of the camera results in foreshortening proportional to the cosine of the angular change. When dealing with 3D objects the situation becomes somewhat more complicated. Specifyingan ab-
solute camera position is only possible if certain conditions of symmetry prevail. This works well for the Platonic solids and their relatives but the human head has only (imperfect) bilateral symmetry. Constraining the film plane to be perpendicular to the mid-sagittal plane may be established as an absolute specification within the limits of the degree of bilateral symmetry and positioning technique. The camera may still be turned in an infinite number of positions relative to the face, however. Several different approaches have been used to deal with this problem, including an unwieldy mechanical device which holds the head in a fixed position. Since heads and faces all differ in shape and have no symmetry beyond the bilateral it may be shown mathematically that it is impossible to specify an absolute, invariant camera position which will eliminate this type of distortion when measuring multiple subjects. All is not lost, however, since the laws of geometry greatly reduce the potential magnitude of this type of error. If the camera is positioned 3 m from the subject, foreshortening error will be less than 1.5%if the camera is no more than 52 cm from the horizontal plane, a very generous margin. The specification of the horizontal plane cannot be accomplished absolutely, because of the absence of symmetry, as noted above, but reasonable compromises may be made. Except in the presence of low-set ears, aiming the camera so that the outer canthus and superior attachment of the external ear to the head are aligned will give reasonable consistency. If other conventions are used it is unlikely that the rotation of the head between the 2 camera orientations will be greater than 10". Since the cosine of lo" is ,985 the difference in measurements will be 1.5%.Even an extremely large relative angular rotation of 20" will result in measurement differences no greater than 6%.Therefore, as long as reasonable care is taken aiming the camera, measurement differences as a consequence of foreshortening are likely to be relatively small. In the absence of symmetry beyond the bilateral, complete elimination of this type of error is impossible.
METHODS We constructed a device for measuring projection scaling errors by attaching 2 flat rigid pieces of aluminum to a device which allowed parallel movement through the desired range of distances (Fig. 4). A regularly ruled strip of white paper was firmly attached to each piece of aluminum, which was about 25 cm long, approximately the length of an adult human face. After consulting anthropometric tables we decided that 12 cm would be the greatest distance between two regions of an adult face that might be considered for photogrammetric evaluation. In most cases the distances involved would be considerably smaller. We therefore made photographs at 3, 6, 9, and 12 cm distances to simulate a range relevant t o typical craniofacial structures of children and adults. Note that we are only interested in the distance between planes containing 2 regions if both can appear simultaneously in a photograph. Thus the ears can both be seen in the same plane in a frontal photograph but will not be visible in a lateral view. Photographs were taken on Kodak T-Max 400 black
Photogrammetric Evaluation
Fig. 4. Experimental setup for measuring scaling errors
and white film using a Nikon 35 mm camera with 24,50, 105, and 200 mm Nikkor lenses at subject to film plane distances ranging from 31.3 to 211.8 cm in order to obtain a nearly full frame image. The film was processed in Kodak T-Max developer and fixer according to the manufacturers recommendations. Prints were made using a n Omega D-2V enlarger with Nikkor 50 lens on Kodak Polycontrast RC “paper,” which actually has a polymer base and is more stable dimensionally than fiber. It was developed and fixed according to the manufacturers recommendations. Measurements were taken using a metric rule to the nearest 0.5 mm.
RESULTS As can be seen in Figure 5 the observed scaling error is nearly a straight line and for the smaller object separatiodobject distance (OS/OD) ratios coincides quite nicely with the predicted (theoretical) line. Thus for a n OS/OD ratio of 0.1 the predicted error was 10% and the observed error was 10.2%.At larger OS/OD ratios the observed error was somewhat less than the predicted error, especially for the 24 mm lens. This is almost certainly the result of the rather different (retrofocus)
optical design used in this lens. The lenses using telephoto designs gave error measurements much closer to predicted values. DISCUSSION Although it might be argued that the results of our experiment were predictable from elementary optics, real-world systems, in fact, often deviate from theory. The deviations seen for the measurements made using the wide angle lens emphasize the difference between ideal theoretical models and the performance of operational systems. The laws of optics are only relatively straightforward for simple, thin lenses, whereas modern camera lenses involve complex optical design, the mathematics of which is beyond the scope of this paper. Thus, we designed our experiment to examine the “output” from a complex, multistage optical system using readily available components. Our results should therefore be applicable to clinical settings where comparable components are used. We have not made any a priori assumptions about which points on the face will prove to be most useful for formal analysis of syndromes. Landmarks derived from physical anthropology, such as those advocated by Farkas [1981], appear to us to have been selected because they are convenient to measure. We know of no theoretical or practical reasons why the points currently measured will be more useful for analysis than others such as the point of maximum convexity of the cheek. This location may be determined using computerized shape analysis of photographs but would almost certainly escape the most skilled anthropometrician using classical methodology. We believe, therefore, that clinical geneticists interested in the formal analysis of syndromes should strive to use a general approach to data collection and not be constrained by arbitrary conventions based on other disciplines.
Percent Error 60
50 40
30 20
10
0 0
0.1
0.2 0.3 0.4 Object Separation / Object Distance
0.5
Lens Focal Length *
24 rnrn
+
50 mrn
165
*
105 rnrn
0
200 rnm
Fig. 5. Experimental results for several different focal length lenses,
0.6
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Our results indicate that in applying photogrammetric evaluations to clinical genetics, projection errors may be unacceptably large unless efforts based on knowledge of photogrammetry are made t o reduce them. Many clinicians use lenses of approximately 50 mm focal length for routine photographs. As may be seen in Figure 5, using a marker placed on the forehead, measurements taken from an area of interest 3 cm further from the camera plane will have a measurement error of nearly 10% based on the typical camera to subject distance for a full face photograph. With a 200 mm telephoto lens at a distance of 212 cm the error is reduced to about 1.5%.Alternatively if the 50 mm lens were used at this same distance and the negative enlarged proportionately the error would also be about 1.5%.Note that this is for objects in planes no more than 3 cm apart. In order to reduce measurement errors to about 1%for object planes 6 cm apart the film plane must be 6 m from the subject, perhaps the practical upper limit because of room size considerations. Farkas [19811discusses what he calls “photogrammetry of the face” including a brief history of this technique up to that time and a comparison with his anthropometric methodology. He used a camera to subject distance of 3352.8 mm and claims that this is 2.2 times the minimum distance recommended by Gavan et al. [19521 to reduce photographic error to less than 1%.This was determined using the average ear to ear distance of adult men of 153 mm. According to optical theory and our experimental results we calculate a nearly 5%maximum error for this configuration, not the less than 0.5% apparently implied by Farkas. (Gavan seems to have misunderstood photographic projection principles and Farkas apparently repeated this error.) He then goes on to compare the photogrammetric method with his anthropometric method and finds the photogrammetric approach deficient. Unfortunately, he gives no data regarding systematic or random errors using either method and appears to assume that the anthropometric method has no error. His rejection of the photographic method because it differs from his favored anthropometric approach seems to be unwarranted. It is entirely possible for the 2 methods to give results which differ significantly systematically but not randomly. In this case a correction factor could be determined which would make anthropometric and photogrammetric measurements compatible and interchangeable. Farkas seems more concerned with landmarks of interest for surgical procedures. Thus, even if his conjecture about photogrammetric landmarks is correct regarding their accuracy related to their anthropometric correlates, it may be of no concern to clinical geneticists. Obviously this must be studied more carefully before reaching any definitive conclusions about the relative merits of either technique when applied to clinical genetics. In our opinion, for some regions of interest such as the distance between bony prominences easily palpated but difficult to identify in photographs, the anthropometric approach may be superior, whereas measurements based
on soft tissue landmarks may be more amenable to photogrammetric assessment. Stengel-Rutkowski et al. [ 19841attempted to use photogrammetric evaluation of minor facial anomalies. Unfortunately they fail to describe their photogrammetric method and used ratios rather than absolute measurements. In their measurements of 10 photographs of the same child the variance ranged from 2.06 to 11.25%. This is of interest since it is virtually identical to our experimental results for photographs taken from a distance of 107 cm (Fig. 51, a typical camera to subject distance for a modest telephoto lens. Clarren et al. [19871 describe the application of the photogrammetric approach to the fetal alcohol syndrome. Unfortunately, they also fail to describe the photogrammetric method employed. The possibility that systematic measurement errors affected their conclusions remains uncertain.
CONCLUSIONS We have demonstrated that large systematic errors may result from the improper use of photogrammetric techniques to clinical genetics. These results do not address the issue of whether photographs taken under controlled circumstances will be useful in the mathematical analysis of craniofacial syndromes. In order to discover whether this is feasible both anthropometric and photogrammetric techniques must be applied to a group of subjects by a number of trained clinical geneticists with careful statistical comparison of the results. Even if the photogrammetric technique is lacking in overall accuracy it may still be practical for selected applications in clinical genetics. Prior to this determination we recommend that all papers using photogrammetric approaches carefully describe their experimental methodology and strongly encourage using subject to camera distances long enough to reduce projection errors to low levels based on the OS/OD ratio described above.
REFERENCES Bookstein FL (1978):“The Measurement of Biological Shape and Shape Change.” Lecture Notes in Biomathematics Volume 24. Berlin: Springer-Verlag. Clarren SK, Sampson PD, Larsen J , Donne11 DH, Barr HM, Bookstein FL, Martin DC, Streissguth AP (1987):Facial effects offetal alcohol exposure: Assessment of photographs and morphometric analysis. Am J Med Gen 26:651-666. Farkas LG (1981):“Anthropometryofthe Head and Face in Medicine,” New York: Elsevier North Holland. Gavan JA, Washburn SL, Lewis PH (1952):Photography: An anthropometric tool. Am J Phys Anthro 10:331-353. Smith DW, Jones KL (1982):“Recognizable Patterns of HumanMalformation,” Major Problems in Clinical Pediatrics, Volume VII. Philadelphia: W.B. Saunders. Stengel-Rutkowski S, Schimanek P, Wernheimer A (1984): Anthropometric definitions of dysmorphic facial signs. Hum Genet 67:272-295. Thompson DW (1961): “On Growth and Form.” Cambridge: Cambridge University Press. Ward RE (1989):Facial morphology as determined by anthropometry: Keeping it simple. J Craniof Genet Dev Biol 9:45-60.
