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A simple digital procedure to assess facial asymmetry
TECHNO BYTES
A simple digital procedure to assess facial asymmetry Jose´ Dahan, LDS, MD, PhD Brussels, Belgium
uring the 1950s and 1960s,1-4 and again recently,5,6 skeletal asymmetry was considered to be related to joint disorders. Functional deviations of the mandible resulting from intercuspation and premature contact often are detected during clinical examination. However, screening facial skeleton asymmetries and distinguishing growth discrepancies from simple rotations of the mandible can be difficult. Conventional panoramic, frontal, and submental vertical radiographs, computed tomography (CT) scans, and magnetic resonance imaging have been used to determine facial harmony and skeletal deviation before dental treatment to avoid possible iatrogenic temporomandibular disorders.7-10 The purpose of this study was to demonstrate the usefulness of digital photography for assessing facial symmetry as well as for record keeping.11
D
THE PROCEDURE
Clinical examination, sometimes with a preliminary splint, was performed on each subject to make a differential diagnosis and to eliminate any risk of a functional shift of the mandible. A frontal view of the subject’s face was recorded with a digital camera (in this case, a Mini DV 40X Vario-Sonar, Sony, Tokyo, Japan); when useful, the subject’s frontal cephalogram was also photographed. The subject was positioned face forward with both ears clearly visible to the photographer. (A head holder was used when making frontal photographs and radiographs.) The light crystal display screen of the camera was used to find the horizontal plane of the subject and the cephalogram. PictureGear Lite 3.2 (Sony) was used to reproduce the pictures as JPEG images with a computer. This software has a built-in, adjustable, square outline that allows images of hemifaces to be cropped along sagittal and transverse planes. Professor, University of Louvain; private practice, Brussels, Belgium. Reprint requests to: Jose´ Dahan, University of Louvain/Belgium, Rue d’oultremont 1, B-1040 Brussels, Belgium; e-mail, [email protected]. Submitted, July 2001; revised and accepted, January 2002. Am J Orthod Dentofacial Orthop 2002;122:110-6 Copyright © 2002 by the American Association of Orthodontists. 0889-5406/2002/$35.00 ⫹ 0 8/1/122831 doi:10.1067/mod.2002.122831
110
The midsagittal reference plane for the frontal photograph was a vertical line that crossed the midpoint of a virtual line joining the pupils; it was located with a ruler on the screen. The vertical plane had to be perpendicular to the upper border of the computer screen and the bipupilar line (Fig 1). If the lines diverged, the nose and pupils were examined; any deviation of the nose tip with or without an irregularity in the transverse or vertical location of the pupils was considered a sign of possible upper and midface asymmetry. In such cases, no correction of head tipping to obtain parallelism between the pupils and the screen border was attempted. Instead, the reference plane that followed the nasal bone crest upward to where it joined the lower eyebrow and downward to the sideward enlargement of the nose was used (Fig 2). The horizontal reference plane was perpendicular to the vertical nasal plane and intersected at its midpoint. The reference plane for the frontal cephalogram was perpendicular to the midpoint of the intersection of a line joining the 2 lateroorbital points and the base of the crista galli12 (Fig 1). In cases of upper and midface asymmetry, a perpendicular line drawn from the base of the crista galli on the tangential projection of the planum sphenoidal defined the vertical and horizontal coordinates of the reference planes.4 Each cropped half face was then inverted to obtain an inverted right or left half face. We used photograph manipulator software such as Adobe Photo Shop (San Jose, Calif) to superimpose the half faces onto the original photograph to confirm the match along the reference (sagittal) plane (Fig 3, A and B). Next, either the half faces were merged, or 1 inverted half face was superimposed on the original photograph. To merge, each half face was combined with its inverted half (Fig 3, C and D). Both photographs were then compared with the original full photograph. For superimposition (Fig 3, E), the original photograph was outlined and transformed as a negative to produce black contours on a white background. Each half-face photograph was also outlined but kept positive with white contours on a black background. All
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Dahan 111
Fig 1. Reference lines used to define midsagittal plane in photographic (PHP) and radiographic (RHP) images. PHP is perpendicular at midpoint of line between pupils; RHP is perpendicular from base of crista galli through line joining 2 lateroorbital points.
Fig 2. In cases of severe upper face and midface asymmetry, sagittal reference plane should follow upper portion of nasal crest. Horizontal plane is perpendicular to nasal line through its midpoint.
outlined photographs were made 30% to 40% less opaque to achieve good superimposition. Inverted outlined half faces were superimposed separately on the inverted, contoured, and negatively transformed originals. Contouring, negative transformation, and transparency incrementation are options available on photograph manipulator software.
When necessary, cephalograms were examined by merging the half faces with or without inversion and with or without transformation from negative to positive. Cephalometric tracings are unnecessary but can be used for postural analysis. A simple traced polygon superimposed on merged photographs can help the examiner visualize differences in bilateral structures.
112 Dahan
American Journal of Orthodontics and Dentofacial Orthopedics July 2002
Fig 3. Schematic representation of procedure. Picture is split virtually in half along midsagittal plane (S) and reconstructed without and with inversion of opposite side. B, Right side (R) is larger than left side (L); therefore, C is larger than D. E, Superimposition of reversed right half (RI) on original left half. F, Difference between magnification and distortion. G, How object rotation can distort photograph. Beam’s incidence reduces structures displaced to rotation side and enlarges counterparts.
INTERPRETING THE PICTURES
Frontal photographs indicate existing facial symmetry, dissymmetry, and asymmetry13 (Fig 4). Dissymmetry is a slight but harmonious width or length difference between the halves of the face. Asymmetry is defined as a noticeable disharmony between the halves of the face in at least 1 dimension. All imaging results in both magnification and distortion of the subject14 (Fig 3, F), but digital photography allows different sized enlargements to be compared because photographs can be processed to the same scale. However, distortion can occur in digital photography just as in radiography or film photography. It results from the angle of the subject relative to the projection device (ie, the incident beam and the recording plane). Distortion can be caused by poor head posture during exposure or by the parallax effect of noncentric camera orientation. Head rotation, tipping, and inclination distort frontal views differently. Rotation most affects assessment of the transverse dimension. Tipping can be corrected by computer processing. Inclination, which shortens the face, can influence the symmetric comparison of a single case. Frontal view images require evaluation for possible distortion,15 and all images of subjects (before
and after treatment) should be carefully compared. Distortion resulting from rotation causes an altered reproduction of both sides of the subject’s head (Fig 3, G); the rotated side appears narrow in the front, and the opposite side appears narrow in the back (Fig 5). This distortion can be easily detected when the halves are merged with their respective inverted photographs. The reconstructed photographs show different facial shapes; by examining anterior and posterior structures, the examiner can distinguish rotation caused by poor head posture from a true partial or total facial asymmetry. If asymmetry is indicated, whether cranial base deformations are detected on clinical examination, further radiographs or other imaging methods are required. CASE DESCRIPTIONS
Case 1. An 18-year-old man sought a third opinion regarding possible orthodontic treatment (Figs 6 and 7). He had been advised that his facial asymmetry, first diagnosed 8 years before, could be corrected only with surgery on both jaws. Frontal photographs and radiographs were taken and analyzed according to the method described earlier. The photographs showed that the asymmetry was caused by reduced transverse growth of the maxilla combined with a
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Dahan 113
Fig 4. Merged photographs of symmetric and asymmetric half faces. In asymmetric face, narrow right side (R) merged with its inverted picture (RI) results in narrow face, whereas wider left side (L) merged with its inverted homologue (LI) results in larger face.
Fig 5. Photographs and radiographs of skull showing how rotation can influence perspective and lead to misinterpretation. Central beam targeted midsagittal plane of middle images. Images on left and right show rotation of skull to left or right side. Front structures show less distortion than those in back. Rotation to left is more discrete than rotation to right and could remain undetected if photograph is not processed as described in text.
right-side rotation of the mandible. The CT scan and the submental-vertex radiographs confirmed the diagnosis. The patient is now being treated nonsurgically.
Case 2. A 37-year-old man sought orthodontic treatment to correct malocclusion and to improve his appearance (Figs 8 and 9). Frontal photographs and radiographs taken in April 1994 showed asymmetry of
114 Dahan
American Journal of Orthodontics and Dentofacial Orthopedics July 2002
Fig 6. Reconstructed photographs of patient (case 1) with unilateral crossbite right and reduced transverse dimension of right half face. Superimposition of transparent original and inverted half faces helps to define this growth deficit. Original outline is black, and inverted outline is white.
Fig 7. Reconstructed frontal radiographs of patient (case 1) indicate reduced transverse dimension of right upper face and midface and rotation of mandible to right without structural deformation of halves. Axial, submental vertex view, and frontal scan confirm subject’s deformed appearance resulting from mandibular rotation.
the face because of mandibular rotation on the left side, indicated by the shift of the lower midline and the medial chin point. Treatment, completed in July 1996, corrected tooth crowding, open bite, and deviation of the lower jaw.
Digital evaluation of frontal radiographs confirmed the presence and subsequent correction of mandibular rotation, which was also observed on intraoral photographs.
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Fig 8. Photographs of patient (case 2) before and after correction of midline deviation and mandibular rotation to left.
Fig 9. Frontal radiographs of patient (case 2) showing quadrangular tracings performed before (1994) and after (1996) treatment. Pretreatment tracing is superimposed on original frontal cephalogram (A) on original left side merged with inversion (B), and on a second virtual radiograph created by merging right side with its inversion (C). Radiographs demonstrate rotation of mandible to left. B, Medial situation of left gonial area in relation to tracing of right side, which is superimposed on it. C, Lateral position of inverted right gonion (reproduced as positive) compared with original tracing of left side. D, Tracings made before and after treatment and superimposed on original cephalogram confirm clinically observed correction of mandibular rotation.
116 Dahan
CONCLUSIONS
Frontal imaging is a useful diagnostic tool for assessing facial asymmetry. Before a treatment plan can be devised, the site of asymmetry must be located and the severity determined. This can usually be accomplished by using readily available computer software to analyze digital photographs, cephalograms, and radiographs. Distortion resulting from poor head posture must be discerned from skeletal rotation. If craniofacial deformation is suspected, supplemental radiographs or other imaging methods are indicated. The author thanks Ashur Chavoor, DDS, for reviewing this article and Marc Baiolla and Daniel Lelangue for technical support. REFERENCES 1. Potter JW, Meredith HV. A comparison of two methods of obtaining biparietal and bigonial measurements. J Dent Res 1948;27:459-65. 2. Harvold EP. The asymmetries of the upper facial skeleton and their morphological significance. Trans Eur Orthod Soc 1951;27: 63-81. 3. Mulick J. Clinical use of the frontal head film. Angle Orthod 1965;35:299-307. 4. Dahan J. The diagnosis of jaw and face asymmetries: a cephalometric problem. Fortschr Kieferorthop 1968;27:289-333.
American Journal of Orthodontics and Dentofacial Orthopedics July 2002
5. Tallents RH, Guay JA, Katzberg RW, Murphy W, Proskin H. Angular and linear comparisons with unilateral mandibular asymmetry. J Craniomandib Disord Facial Oral Pain 1991;5:13542. 6. Bishara SE, Burkey PS, Kharouf JG. Dental and facial asymmetries: a review. Angle Orthod 1994;64:89-98. 7. Kobayashi T, Honma K. Temporomandibular joint symptoms and disc displacement in patients with mandibular prognathism. Br J Oral Maxillofac Surg 1999;37:455-8. 8. Miller VJ, Yoeili Z, Barnea E, Zeltser C. The effect of parafunction on condylar asymmetry in patients with temporomandibular disorders. J Oral Rehabil 1998;25:721-4. 9. Inui M, Fushima K, Sato S. Facial asymmetry in temporomandibular disorders. J Oral Rehabil 1999;26:402-6. 10. Pirttiniemi P, Raustia A, Kantomaa T, Pyhtinen J. Relationships of bicondylar position to occlusal asymmetry. Eur J Orthod 1991;13:441-5. 11. Stuts WF. Clinical photography in orthodontic practice. Am J Orthod 1978;74:1-31. 12. Sassouni VA. Roentgenographic cephalometric analysis of cephalo-facio-dental relationships. Am J Orthod 1955;41: 735-7. 13. Meredith G. Facial photography for the orthodontic office. Am J Orthod Dentofacial Orthop 1997;11:463-70. 14. Ahlqvist J, Eliasson S, Welander U. The cephalographic projection. Part II. Principles of image distortion in cephalography. Dentomaxillofac Radiol 1983;12:101-8. 15. Major PW, Johnson DE, Hesse KL, Glover KE. Landmark identification error in posterior anterior cephalometrics. Angle Orthod 1994;64:447-54.
A simple digital procedure to assess facial asymmetry Jose´ Dahan, LDS, MD, PhD Brussels, Belgium
uring the 1950s and 1960s,1-4 and again recently,5,6 skeletal asymmetry was considered to be related to joint disorders. Functional deviations of the mandible resulting from intercuspation and premature contact often are detected during clinical examination. However, screening facial skeleton asymmetries and distinguishing growth discrepancies from simple rotations of the mandible can be difficult. Conventional panoramic, frontal, and submental vertical radiographs, computed tomography (CT) scans, and magnetic resonance imaging have been used to determine facial harmony and skeletal deviation before dental treatment to avoid possible iatrogenic temporomandibular disorders.7-10 The purpose of this study was to demonstrate the usefulness of digital photography for assessing facial symmetry as well as for record keeping.11
D
THE PROCEDURE
Clinical examination, sometimes with a preliminary splint, was performed on each subject to make a differential diagnosis and to eliminate any risk of a functional shift of the mandible. A frontal view of the subject’s face was recorded with a digital camera (in this case, a Mini DV 40X Vario-Sonar, Sony, Tokyo, Japan); when useful, the subject’s frontal cephalogram was also photographed. The subject was positioned face forward with both ears clearly visible to the photographer. (A head holder was used when making frontal photographs and radiographs.) The light crystal display screen of the camera was used to find the horizontal plane of the subject and the cephalogram. PictureGear Lite 3.2 (Sony) was used to reproduce the pictures as JPEG images with a computer. This software has a built-in, adjustable, square outline that allows images of hemifaces to be cropped along sagittal and transverse planes. Professor, University of Louvain; private practice, Brussels, Belgium. Reprint requests to: Jose´ Dahan, University of Louvain/Belgium, Rue d’oultremont 1, B-1040 Brussels, Belgium; e-mail, [email protected]. Submitted, July 2001; revised and accepted, January 2002. Am J Orthod Dentofacial Orthop 2002;122:110-6 Copyright © 2002 by the American Association of Orthodontists. 0889-5406/2002/$35.00 ⫹ 0 8/1/122831 doi:10.1067/mod.2002.122831
110
The midsagittal reference plane for the frontal photograph was a vertical line that crossed the midpoint of a virtual line joining the pupils; it was located with a ruler on the screen. The vertical plane had to be perpendicular to the upper border of the computer screen and the bipupilar line (Fig 1). If the lines diverged, the nose and pupils were examined; any deviation of the nose tip with or without an irregularity in the transverse or vertical location of the pupils was considered a sign of possible upper and midface asymmetry. In such cases, no correction of head tipping to obtain parallelism between the pupils and the screen border was attempted. Instead, the reference plane that followed the nasal bone crest upward to where it joined the lower eyebrow and downward to the sideward enlargement of the nose was used (Fig 2). The horizontal reference plane was perpendicular to the vertical nasal plane and intersected at its midpoint. The reference plane for the frontal cephalogram was perpendicular to the midpoint of the intersection of a line joining the 2 lateroorbital points and the base of the crista galli12 (Fig 1). In cases of upper and midface asymmetry, a perpendicular line drawn from the base of the crista galli on the tangential projection of the planum sphenoidal defined the vertical and horizontal coordinates of the reference planes.4 Each cropped half face was then inverted to obtain an inverted right or left half face. We used photograph manipulator software such as Adobe Photo Shop (San Jose, Calif) to superimpose the half faces onto the original photograph to confirm the match along the reference (sagittal) plane (Fig 3, A and B). Next, either the half faces were merged, or 1 inverted half face was superimposed on the original photograph. To merge, each half face was combined with its inverted half (Fig 3, C and D). Both photographs were then compared with the original full photograph. For superimposition (Fig 3, E), the original photograph was outlined and transformed as a negative to produce black contours on a white background. Each half-face photograph was also outlined but kept positive with white contours on a black background. All
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Dahan 111
Fig 1. Reference lines used to define midsagittal plane in photographic (PHP) and radiographic (RHP) images. PHP is perpendicular at midpoint of line between pupils; RHP is perpendicular from base of crista galli through line joining 2 lateroorbital points.
Fig 2. In cases of severe upper face and midface asymmetry, sagittal reference plane should follow upper portion of nasal crest. Horizontal plane is perpendicular to nasal line through its midpoint.
outlined photographs were made 30% to 40% less opaque to achieve good superimposition. Inverted outlined half faces were superimposed separately on the inverted, contoured, and negatively transformed originals. Contouring, negative transformation, and transparency incrementation are options available on photograph manipulator software.
When necessary, cephalograms were examined by merging the half faces with or without inversion and with or without transformation from negative to positive. Cephalometric tracings are unnecessary but can be used for postural analysis. A simple traced polygon superimposed on merged photographs can help the examiner visualize differences in bilateral structures.
112 Dahan
American Journal of Orthodontics and Dentofacial Orthopedics July 2002
Fig 3. Schematic representation of procedure. Picture is split virtually in half along midsagittal plane (S) and reconstructed without and with inversion of opposite side. B, Right side (R) is larger than left side (L); therefore, C is larger than D. E, Superimposition of reversed right half (RI) on original left half. F, Difference between magnification and distortion. G, How object rotation can distort photograph. Beam’s incidence reduces structures displaced to rotation side and enlarges counterparts.
INTERPRETING THE PICTURES
Frontal photographs indicate existing facial symmetry, dissymmetry, and asymmetry13 (Fig 4). Dissymmetry is a slight but harmonious width or length difference between the halves of the face. Asymmetry is defined as a noticeable disharmony between the halves of the face in at least 1 dimension. All imaging results in both magnification and distortion of the subject14 (Fig 3, F), but digital photography allows different sized enlargements to be compared because photographs can be processed to the same scale. However, distortion can occur in digital photography just as in radiography or film photography. It results from the angle of the subject relative to the projection device (ie, the incident beam and the recording plane). Distortion can be caused by poor head posture during exposure or by the parallax effect of noncentric camera orientation. Head rotation, tipping, and inclination distort frontal views differently. Rotation most affects assessment of the transverse dimension. Tipping can be corrected by computer processing. Inclination, which shortens the face, can influence the symmetric comparison of a single case. Frontal view images require evaluation for possible distortion,15 and all images of subjects (before
and after treatment) should be carefully compared. Distortion resulting from rotation causes an altered reproduction of both sides of the subject’s head (Fig 3, G); the rotated side appears narrow in the front, and the opposite side appears narrow in the back (Fig 5). This distortion can be easily detected when the halves are merged with their respective inverted photographs. The reconstructed photographs show different facial shapes; by examining anterior and posterior structures, the examiner can distinguish rotation caused by poor head posture from a true partial or total facial asymmetry. If asymmetry is indicated, whether cranial base deformations are detected on clinical examination, further radiographs or other imaging methods are required. CASE DESCRIPTIONS
Case 1. An 18-year-old man sought a third opinion regarding possible orthodontic treatment (Figs 6 and 7). He had been advised that his facial asymmetry, first diagnosed 8 years before, could be corrected only with surgery on both jaws. Frontal photographs and radiographs were taken and analyzed according to the method described earlier. The photographs showed that the asymmetry was caused by reduced transverse growth of the maxilla combined with a
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Dahan 113
Fig 4. Merged photographs of symmetric and asymmetric half faces. In asymmetric face, narrow right side (R) merged with its inverted picture (RI) results in narrow face, whereas wider left side (L) merged with its inverted homologue (LI) results in larger face.
Fig 5. Photographs and radiographs of skull showing how rotation can influence perspective and lead to misinterpretation. Central beam targeted midsagittal plane of middle images. Images on left and right show rotation of skull to left or right side. Front structures show less distortion than those in back. Rotation to left is more discrete than rotation to right and could remain undetected if photograph is not processed as described in text.
right-side rotation of the mandible. The CT scan and the submental-vertex radiographs confirmed the diagnosis. The patient is now being treated nonsurgically.
Case 2. A 37-year-old man sought orthodontic treatment to correct malocclusion and to improve his appearance (Figs 8 and 9). Frontal photographs and radiographs taken in April 1994 showed asymmetry of
114 Dahan
American Journal of Orthodontics and Dentofacial Orthopedics July 2002
Fig 6. Reconstructed photographs of patient (case 1) with unilateral crossbite right and reduced transverse dimension of right half face. Superimposition of transparent original and inverted half faces helps to define this growth deficit. Original outline is black, and inverted outline is white.
Fig 7. Reconstructed frontal radiographs of patient (case 1) indicate reduced transverse dimension of right upper face and midface and rotation of mandible to right without structural deformation of halves. Axial, submental vertex view, and frontal scan confirm subject’s deformed appearance resulting from mandibular rotation.
the face because of mandibular rotation on the left side, indicated by the shift of the lower midline and the medial chin point. Treatment, completed in July 1996, corrected tooth crowding, open bite, and deviation of the lower jaw.
Digital evaluation of frontal radiographs confirmed the presence and subsequent correction of mandibular rotation, which was also observed on intraoral photographs.
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Fig 8. Photographs of patient (case 2) before and after correction of midline deviation and mandibular rotation to left.
Fig 9. Frontal radiographs of patient (case 2) showing quadrangular tracings performed before (1994) and after (1996) treatment. Pretreatment tracing is superimposed on original frontal cephalogram (A) on original left side merged with inversion (B), and on a second virtual radiograph created by merging right side with its inversion (C). Radiographs demonstrate rotation of mandible to left. B, Medial situation of left gonial area in relation to tracing of right side, which is superimposed on it. C, Lateral position of inverted right gonion (reproduced as positive) compared with original tracing of left side. D, Tracings made before and after treatment and superimposed on original cephalogram confirm clinically observed correction of mandibular rotation.
116 Dahan
CONCLUSIONS
Frontal imaging is a useful diagnostic tool for assessing facial asymmetry. Before a treatment plan can be devised, the site of asymmetry must be located and the severity determined. This can usually be accomplished by using readily available computer software to analyze digital photographs, cephalograms, and radiographs. Distortion resulting from poor head posture must be discerned from skeletal rotation. If craniofacial deformation is suspected, supplemental radiographs or other imaging methods are indicated. The author thanks Ashur Chavoor, DDS, for reviewing this article and Marc Baiolla and Daniel Lelangue for technical support. REFERENCES 1. Potter JW, Meredith HV. A comparison of two methods of obtaining biparietal and bigonial measurements. J Dent Res 1948;27:459-65. 2. Harvold EP. The asymmetries of the upper facial skeleton and their morphological significance. Trans Eur Orthod Soc 1951;27: 63-81. 3. Mulick J. Clinical use of the frontal head film. Angle Orthod 1965;35:299-307. 4. Dahan J. The diagnosis of jaw and face asymmetries: a cephalometric problem. Fortschr Kieferorthop 1968;27:289-333.
American Journal of Orthodontics and Dentofacial Orthopedics July 2002
5. Tallents RH, Guay JA, Katzberg RW, Murphy W, Proskin H. Angular and linear comparisons with unilateral mandibular asymmetry. J Craniomandib Disord Facial Oral Pain 1991;5:13542. 6. Bishara SE, Burkey PS, Kharouf JG. Dental and facial asymmetries: a review. Angle Orthod 1994;64:89-98. 7. Kobayashi T, Honma K. Temporomandibular joint symptoms and disc displacement in patients with mandibular prognathism. Br J Oral Maxillofac Surg 1999;37:455-8. 8. Miller VJ, Yoeili Z, Barnea E, Zeltser C. The effect of parafunction on condylar asymmetry in patients with temporomandibular disorders. J Oral Rehabil 1998;25:721-4. 9. Inui M, Fushima K, Sato S. Facial asymmetry in temporomandibular disorders. J Oral Rehabil 1999;26:402-6. 10. Pirttiniemi P, Raustia A, Kantomaa T, Pyhtinen J. Relationships of bicondylar position to occlusal asymmetry. Eur J Orthod 1991;13:441-5. 11. Stuts WF. Clinical photography in orthodontic practice. Am J Orthod 1978;74:1-31. 12. Sassouni VA. Roentgenographic cephalometric analysis of cephalo-facio-dental relationships. Am J Orthod 1955;41: 735-7. 13. Meredith G. Facial photography for the orthodontic office. Am J Orthod Dentofacial Orthop 1997;11:463-70. 14. Ahlqvist J, Eliasson S, Welander U. The cephalographic projection. Part II. Principles of image distortion in cephalography. Dentomaxillofac Radiol 1983;12:101-8. 15. Major PW, Johnson DE, Hesse KL, Glover KE. Landmark identification error in posterior anterior cephalometrics. Angle Orthod 1994;64:447-54.