Verification and standardization of cephalometric coordinate data

212

Computer Programs in Biomedicine 12 (1980) 212-216 Elsevier/North-Holland Biomedical Press

VERIFICATION

AND STANDARDIZATION

OF CEPHALOMETRIC

COORDINATE

DATA

Ellen A. BeGOLE University o f Illinois at the Medical Center, College of Dentistry, Department of Orthodontics, P.O. Box 6998, Chicago, IL 60680, USA

This paper presents the details and logic of two FORTRAN computer programs designed to verify the accuracy of digitized coordinate data arising from cephalometric radiographs, prior to entry into a databank. In addition, the software accounts for varying magnifications of the radiographs which result from the use of different cephalometers. Finally, data from all records are oriented in the same coordinate system, thus standardization of the data has been accomplished. As a result of the two programs, the user may be guaranteed accurate and comparable data for any or all records contained in the databank. Orthodontics

Digitizing

FORTRAN

Magnification

1. Introduction In [1], BeGole outlined the need for a computerbased system designed for the management of cephalometric radiographic data. The data arise from a variety of radiographs, having somewhat different characteristics, and are used primarily in research studies carried out within the University of Illinois, Departhaent of Orthodontics. The major goals of the system developed to manage the data were efficient storage of data from studies presently being conducted, and retrieval of the data for future research. Presently, X - Y coordinates for a set of 37 standardized landmarks found on cephalometric radiographs, as described by BeGole [ 1 ] and Chebib et al. [2], are obtained by use of a Graf/Pen (Science Accessories Corp., Southport, CT) sonic digitizing apparatus which is interfaced to an IBM (International Business Machines, Don Mills, Ontario) keypunch. Thus, the coordinate values are recorded directly on punched cards for subsequent entry into an on-line disk file called DATABANK. To date, a set of three assembler language programs, outlined in [1 ], have been developed to manage the data entered into the system. The program, DATACK, checks all fields in the input data for valid entries prior to entering data into the system; INDEX prints an organized listing of the records contained in the file; and SELECT allows the user to retrieve

Cephalometric radiograph

Standardization

specified records for research use. As the system evolved, certain problems became apparent. Of primary concern was the accuracy of the coordinate data being stored for future use. The program, DATACK, checked coordinate data for positive numeric values only. Such a check was obviously limited in its usefulness, as it did not ascertain the relationship between the digitized numeric data and the landmarks on the radiograph. As a means of verifying this relationship, a program named PLOT was devised to graphically portray the digitized data by connecting various points to simulate a face. The resulting plot, based on numeric data, could then be superimposed over the radiograph to verify accuracy of the data. An additional problem which required resolution related to the cephalometers with which the radiographs were exposed and the radiographic techniques employed. Because the source of X-rays is a small area, divergence of the rays produces enlargement of the image on the film. The degree of enlargement is determined by the ratio of the targetobject distance to the target-film distance, as shown in fig. 1. In the usual cephalometer, the target-object distance is fixed, whereas the object-firm distance is free to vary, so that the fdm is positioned as close to the lateral aspect of the head as possible. Thus, the placement of the fdm is determined by the size of the head. As the object-film distance increases, or as

0010-468x/80]0000-0000/$02.25 O Elsevier/North-Holland Biomedical Press

213 TABLE 1 Enlargement data for samples included in DATABANK TARGET

Code

Sampledescription

01 02

Universityof Illinois Clinc Universityof Illinois Archives (before 1976) University of Illinois Archives (1976 only) Bolton Denver Michigan Winnipeg AndriaOffice (before 1970) Andria Office (1970 to present) Haas Office Unknown Minnesota(before 1952) Minnesota (1952 to present)

%

Multiplier

FILM POSITION

Fig. 1. Relationship between source of X-rays, object and film.

the head becomes larger with age, a correspondingly greater enlargement of the image results. This is the usual technique employed with the use of the Broadbent [3] cephalometer. Ideally, for each radiograph, the variable distance between the object and the film should be recorded, however, such a recording is not always made. Thus, it becomes impossible to accurately compute the precise degree of magnification for these radiographs. As a reasonable compromise for the databank, an average magnification value for sample data obtained using Broadbent [3] cephalometers was used. The figure was based on the usual range of object-film distances, which is 7 - 1 4 cm, and a fixed five-foot target-object distance. Details of computational methods for determining magnification multipliers are given by Adams [4], and more recently by Bergesen [5]. The magnification multiplier, M, is given by: M = TO/TF

where TO represents the target-object distance, and TF the target-film distance. The percentage enlargement is given by: % = 100(TO - TF)/TF Magnification factors and percentage enlargement for each of the samples presently included in the databank are shown in table 1. Magnifications used for the University of Illinois Clinic (01) and the University of Illinois Archives (02) were computed for various cephalometers used within the department over a period of years. Further details on the techniques and equipment used in radiographing the Bolton (03) sample are given by Broadbent et al. [6] ; information on the Denver (04) sample from the University of Colorado School of Medicine is presented by Waldo [7] and McDowell [8]. The Michigan (05) sample is described by Riolo et al.

03 04 05 06 07 08 09 10

9.35

0.9145

7.00

0.9346

8.80 5.73 7.00 11.00 7.00 15.00

0.9191 0.9458 0.9346 0.9009 0.9346 0.8969

10.00 12.35

0.9091 0.8900

8.00 7.00

0.9259 0.9346

[9] ; Chebib et al. [2] present further information on the Winnipeg (06) sample. Office (07) (Louis M. Andria, 206 W. State, Rockford, IL 61101) and Office (08) (Andrew J. Haas, 1234 Portage Trail, Cuyahoga Falls, OH 44223) records arise from offices of two private practitioners of orthodontics, both of whom have provided details of magnification related to their cephalometers. Relevant information regarding the Minnesota (10) sample was provided by the Department of Orthodontics at the University of Minnesota (Department of Orthodontics, Morrill Hall, Minneapolis, MN 55455). Because of the variety of magnifications used for data in the databank, it was deemed appropriate to develop software which would account for this factor, and at the same time, orient the data in a common manner for all records. A program, TRANSFORM, was designed to carry out these tasks related to the cephalometric data prior to entry into the file, DATABANK. Both of these programs, PLOT and TRANSFORM, are described in the present paper. Both are currently implemented on an IBM 370 computer at the University of Illinois, Chicago Circle Campus Computing Center. The programs are coded in FORTRAN, and detailed descriptions follow.

214

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ng

Transform ] cOordinate data

volt

99~

I

I Value. ~ rar ge = Out

Check ranger

of

'or

99.00

~

X~: . . . . . . .

--~ . . . . . . . . . . . . ~-~:--~;. , :. ~. / .

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•

(/j

I

I 17 .14 15~y

Yes

Fig. 2. Cephalometric landmarks digitized from radiographs.

Plot

characters -÷,,

I

NO

Print

Error

report

2. Description of the program, PLOT The program, PLOT, was designed to produce a graphical display of coordinate values in order to verify the accuracy of data taken from cephalometric radiographs. A set of 37 landmarks deemed clinically useful [1,2] is digitized from the radiogiaphs, and is shown in the form of a schematic diagram in fig. 2. The first 80 byte record, along with entries in the first 14 bytes of succeeding records, completely identifies the subject from whom the data were taken. Coordinate data, corresponding to the 37 landmarks, appear as a set of 37 eight digit values on the data cards, as shown in fig. 3. Program logic is shown in fig. 4. Primarily, data for one subject are read by the program. Missing data, denoted on input by coordinate values 9999, are handled by the routine, so that such values do not

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Fig. 3. Inpu(example ~rtheprogramsPLOTandTRANSFORM.

g Fig. 4. Logic of the program, PLOT• appear in the graphics. Likewise, values which are beyond the logical limits of the plotter paper are handled in a similar manner. Data are transformed so that the sella-nasion line, determined by coordinates 2 and 4, becomes the horizontal axis, with the origin of the system at sella. This is readily accomplished through the use of an orthogonal transformation matrix, so that the relation between

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215 3 0 4 0 I R 0 ! 04F" Z NISSING Pf'JINTS P O ! N T S OUT OF R ~ N G E

2

34 0

35

36

.'47

Fig. 6. Printed report output from the program, PLOT.

331

25

8

16 Fig. 5. Simulated face produced as graphical output by the program, PLOT.

the original and transformed coordinates is given by:

F cos0

L-sin0

sin01 cos 0J

Ix]

= [ X c o s 0 + Ysin0 1 L-Xsin0 +Ycos0 " Following the data transformation, a simulated face, as shown in fig. 5, is produced using a Versatec (Sunnyvale, CA) plotting device. Coordinates are connected using straight lines, as follows: 1-6; 2-4; 3-4-5; 7-8-9-10-11-12-13-14; 28-33-32-15-16-17-18; 19-21;20-22; 23-24-25; 27-29-28-2. In addition, a centered '+' sign is drawn at the location of coordinates 26, 30, 31,34, 35, 36 and 37. In this manner, all digitized coordinates appear either as the endpoint of a straight line segment, or at the center of the '+' character. Comparison of fig. 2 and 5 shows the relationship of the data to the landmarks. Once the plot is available, it is an easy matter to superimpose it with the original radiograph to ascertain if the numeric data correspond with the radiographic landmarks. Thus, the accuracy of the data may readily be verified prior to entry into a permanent databank for future use. In addition, a short printed report, shown in fig. 6, is produced and is used to indicate to the user those points which for one reason or another were not digitized, and also those points which are beyond the logical limits of the plotter page.

3. Description of the program, TRANSFORM The purpose of the program, TRANSFORM, is to transform and demagnify the coordinate data, orienting it one the sella-nasion line. The procedure is necessary so that all records contained within the sample are comparable. The radiographs have been exposed on a variety of cephalometers, all of which produce a magnified image of the head on the film. Since the extent of the magnification produced by the different cephalometers is not identical, the films are not directly comparable for use in research studies. If the magnification is considered, and the coordinates are adjusted to reflect it, this problem is circumvented. Data from any of the various sources should then be life-size, hence comparable for statistical purposes. In addition, the transformation orients all data in the same coordinate system which is centered at sella (coor-

? values = 9999

ma( nif

Re(1~ anc E n d o ~ Y e s file ?

(5 Fig. 7. Logic of the program, TRANSFORM.

Print transformed

216

dinate 2) and oriented on the sella-nasion line (coordinates 2 and 4). Logic of the program, TRANSFORM, is shown in fig. 7. The program initially reads the magnification factor, M, followed by a set of data, as shown in fig. 3. Each X and Y coordinate is then multiplied by M so that:

in the same coordinate system, thus standardization of the data has been accomplished. 4. Mode of availability For further details on the system, please write to the author at the above address. Acknowledgements

The de-magnified coordinate values are then transformed using a transformation matrix to obtain the values for permanent storage, as follows:

p4:r

Computing services used in this research were provided by the Computer Center, University of Illinois, Chicago Circle Campus, Chicago, IL.

cos0

L-sin 0

cos O_H_MY_J

References

= r cos 0 + 0] [-MX sin 0 +MY cos 0U The values are rounded and converted to integer data so that ultimately when retrieved for use, the data will be accurate to two decimal places which corresponds to the accuracy of the original digitized coordinate data. Missing values orignally denoted by 9999 are not transformed, hence these values are maintained throughout the transformation, and appear as such in the transformed data. Once the transformation is carried out, the new values are listed at the line printer, as shown in fig. 8, and in addition, are written into a disk file for subsequent entry into the databank. For any future studies, as a result of the programs PLOT and TRANSFORM, accuracy of the coordinate data can be guaranteed to the user. Additionally, since the varying magnifications of the object on the film resulting from the use of different cephalometers have been accounted for, the user may be assured of comparable data for any or all records contained in the databank. Finally, all records are oriented

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Fig. 8. Listing of transformed values.

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[1] E.A. BeGole, Software development for the management of cephalometric radiographic data, Comput. Prog. Biomed. 11 (1980) 175-182. [2] F.S. Chebib, J.F. Cleall and K.J. Carpenter, On-line computer system for the analysis of cephalometric radiographs, Angle Orthod. 46 (1976) 305-311. [3] B.H. Broadbent, A new X-ray technique and its application to orthodontia, Angle Orthod. 1 (1931) 45-66. [4] J.W. Adams, Correction of error in cephatometric roentgenograms, Angle Orthod. 10 (1940) 3-13. [5] E.O. Bergesen, Enlargement and distortion in cephalometric radiography: Compensation tables for linear measurements, Angle Orthod. 50 (1980) 230-244. [6] B.H. Broadbent, St, B.H. Broadbent, Jr and W.H. Golden, Bolton Standards of Dentofacial Developmental Growth (C.V. Mosby, St Louis, MO, 1975). [7] C.M. Waldo, Orthodontic research as a component part of a balanced longitudinal study of 100 children, Int. J. Orthod. Oral Surg. 22 (1936) 659-673. [8] R.M. McDoweU, The use of lateral head radiographs for evaluating orthodontic results as distinguished from growth changes, Am. J. Orthod. Oral Surg. 27 (1941) 59-74. [9] M.L. Riolo, R.E. Moyers, J.A. McNamara, Jr and W.S. Hunter, An Atlas of Craniofacial Growth (Center for Human Growth and Development, Ann Arbor MI, 1974).

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