Journal of Medical Systems, Vol. 16, No. 4, 1992
A Visual Field Quantification System for the Goldmann Perimeter Tomohiro Odaka,* Kimihiko Fujisawa,* Kouhei Akazawa,* Maki Sakamoto,* Naoko Kinukawa,* Tatsuro Kainakura,* Yuko Nishioka,* Hidetoshi Itasaka,* Yoshiaki Watanabe,t and Yoshiaki Nose*
We have developed a visual field quantification system that can accurately quantify the measurement results by the Goldmann Perimeter (GP). This system calculates the plural indexes introduced in published papers. In recent years, several isopter quantification methods have been proposed. In these methods, the isopters are digitized and the data are input into a computer, after which a computer program evaluates the changes in the isopters quantitatively. However, each program is only able to evaluate private indexes. We have developed a system that quantifies data using multiple methods. This system used five methods that have been introduced in published papers. With this system, a physician can analyze GP data with multiple methods and can diagnose diseases accurately. We have already input about 2500 GP recording papers into the computer by this system. We then calculated the plural indexes, and visualized the temporal changes in the perimetry.
INTRODUCTION We have developed a visual field quantification system that can accurately quantify Goldmann Perimeter (GP) data. This system can calculate the various indexes previously introduced in published papers. GP is used widely as the instrument that measures kinetic visual field. ~Kinetic visual field measurement by GP is useful not only for daily clinical practice but also for research. In daily clinical practice, physicians evaluate GP data such as isopter form, isopter area, the number of scotoma and the position of scotoma qualitatively. For example, if the area of an isopter seems to be decreasing with time, it means that the visual field has become narrow, and it is understood that the disease has been aggravated. There is no standard
From the *Department of Medical lnformatics, Faculty of Medicine, Kyushu University, Japan; and the ~Department of Information Science, Faculty of Science and Engineering, Saga University, Japan. 161 0148-5598/92/0800-0161506.50/0 © 1992 Plenum Publishing Corporation
162
Odaka et al.
quantitative method for GP analysis, however. This is in contrast to the static visual field evaluation that is sufficiently computerized. In recent years, several isopter quantitative methods have been proposed. In these methods, the isopters are digitized and the data input into a computer, afterwards the computer program evaluates the changes in the isopters quantitatively. In our research, we classified the methods previously published into five types and developed a system that applies to these five types of methods individually for the same data. This system can be used not only for clinical research but also for clinical diagnosis. With this system, a physician can thus analyze GP data with multiple methods and can therefore quantitatively diagnose a disease.
METHODS Calculation Formulas GP is an instrument that measures the sensibility curve of an eye to different brightness levels. To measure such sensibility, a light source on GP projects a perimetric target of a particular size and brightness to a half spherical screen. Then the target is moved from the peripheral of the visual field to the center. The examiner plots the point where a patient answered that the light was seen. Finally, the perimetrist connects the points with a smooth curve. An example of the GP recording paper is shown in Figure 1. In Figure 1, the curve that connects the same sensibility points is called an isopter. Usually five
A--/
D i a n * ; i r mm,!l ~t
Co~ec~io
Figure 1. Exampleof an isopter.
163
A Visual Field Quantification System for the Goldman Perimeter
isopters are measured for each eye. Each isopter is called I1, I2, 13, I4, V4 from the center to the peripheral. The field shown with a diagonal has a low sensibility compared with other field of vision. This field is called a scotoma. A scotoma is measured separately from an isopter. Conventionally, a physician evaluates GP data qualitatively. A physician mainly evaluates isopter form, isopter area, the number of scotoma and position of scotoma. For example, if the area of an isopter is decreasing with time, it means that the visual field has become narrow, and it is understood that disease has been aggravated. In our system, a digitizer is used as the isopter input device. An isopter is then handled as a collection of n discrete coordinate points ( x i, Yi) (i = 1 . . . n ) as shown in Figure 3. For simplicity, we assume that ( x n + 1 , y n + 1) = ( x l , y l ) . The data are analyzed with the following methods [2-91 (Fig. 2):
Method 1 The isopter is evaluated with the area on the GP recording paper of each isopter4 (Method 1). In Method 1, five indexes corresponding to five isopters are calculated for the each GP recording paper. The Ss area of the isopter is calculated as n as : E
(xi - Xi+l)(yi q-
(l)
yi+O/2
i=1
Method 2 The coordinate of the isopter is projected to the hemispherium and the area of the isopter is calculated on the hemispherium 5 (Method 2). In Method 2, five indexes are calculated on each GP recording paper. The Sc area on the hemispherium is calculated as
S~ = ~ 0,-{1 - (cos ai + cos 13/)/2}, i=1 Methods E•aluation
(2)
!
--~Sufface Area Calculation ] 2-dimensional(Method1) ] 3-dimensional(Method2) ] -~ Volume Calculation
] 2-dimensional(Method3) I
3-dimensional(Method4) I --f Form Index Calculation j
I I
[ Method5 Figure 2. Isopterevaluationmethods.
]
164
Odaka et al.
,-'"" ', ..-L.. r"'--. .... ~ ...... WT--/
.....;~.3
V4 )"~""--, Y'-.Y\ -..~x"., / X'. /:~ " X--"L_.v4
/ /' ~ ( X i + 2 , ~ ! + 2 ) ;"~~~'-~'N(xi+l,yi+l)
~ \.
.- / /f
Figure 3. Isopterdigitization. where,
Oi = tan- l(yi/xi) -- tan- l(yi+ l/Xi+ l) Ot i -~-
K~/-~i + y~
~i
K~V/x2i+l + Y2+1
:
K
Constant (depends on the reduced scale of the isopter recording paper)
Method 3
In Method 1 and Method 2, five indexes are calculated for the each recording paper. A single representative index is preferable for diagnosis. In addition, the central part of the isopter is more important than the peripheral part in the matter of diagnosis. 6'7 Therefore, the indexes of Method 1 are summed up on a weighted scale (Method 3). The volume of the solid constructed with isopters is calculated as
Vs : {K3(Sv4 + SI4) + K2(SI4 + SI3) + K2(SI3 + SI2) + K2(SI2 + (SI2 + Sn) + K1Sn}/2 (3) where, Sv4 • • • Sn K3 • . • K1
The result of Method 1 Constant
Method 4
In Method 4, the polar coordinate is applied to the recording paper. Five points on five isopters near angle O (O = 0 to 2rr [rad]) make up a plain figure according to a specific algorithm. Then the solid body of revolution is constructed with the plain figure. The volume of the solid body then becomes the index (Method 4) [8,9]. In Method 4, a point on each isopter near an angle O is found. The point (x, y) is then projected onto the u-v space according to the following expressions:
A Visual Field Quantification System for the Goldman Perimeter
165
u = Ncos ( K ~ / x 2 + y2)
(4)
v = Nsin (KWe-~ + yZ)
(5)
where, K N
constant (depending on recording paper) (I4: 4, I3: 5, I2: 6, I1: 7)
Then the points (u, v) from five isopters constitute a plan figure, and the plane figure is revolved around the v-axis to constitute the solid body of the revolution. The volume Vco of this solid body is then calculated by
Vco = Sd2rr
(6)
where d s
the distance from the revolution axis (= v-axis) to the center of gravity of the plane figure the area of the plane figure
Last, Vco is averaged out with every O. Method 5
The shape factor is one of the estimation indexes of the isopter. 8'9 To calculate the shape factor, one has to calculate the peripheral length of a real circle having the same area as a certain isopter. The shape factor PA is then calculated by the division of isopter length with the peripheral length of a real circle.
PA-
4"rrS 12
(7)
where, S l
is the area of isopter is the peripheral length of the isopter
We designed the isopter quantification system using the above five methods. The system can evaluate each recording paper using all five methods. Hardware and Software
The constitution of the system is shown in Figure 4. The system is constructed of a digitizer DT4513 (Seiko electron) and a personal computer PS/55 model 5551 S (IBM). The hardware used is broadly available and no special devices are used at all. The isopter is digitized by the digitizer and the patient identification data is input from the keyboard. The software of PS/55 operates on OS/2. A compiler of C language C/2 was used for the system development. The source program consists of about 2700 lines. The software system is composed of four sub-systems. The input subsystem controls the input from the digitizer. The indexes are calculated by three subsystems: an isopter surface area calcu-
166
Odaka et al.
Visual Field Quantification System IBM PS/55 Coordinate Input
i
TM
SEIKO DigitizerDF3213
Calculation
File
NN~
8
File Transmisson
Mainframe Comput~
Macintosh personal computer
Statistical Software Packages
Graph Package
Figure 4. Software and hardware.
lation sub-system, a volume calculation sub-system and a shape factor calculation subsystem. The results of all five methods are then summarized into one file. After the calculation by the PS/55, the file is then transmitted to a mainframe computer 3081/4381 (IBM) and analyzed by various kinds of statistical analysis software packages (SAS, BMDP). The results are then printed out on a Macintosh personal computer.
RESULTS We input about 2500 sheets of data into the computer using this system. About 2 minutes were required to input the data from each recording paper. About 20 seconds were required for the calculations of the area, volume and shape factors on each sheet. The size of the coordinate data consisted of about 3K byte on each data sheet. Figure 5 shows an example of the indexes that have been calculated using this system. Figure 5 shows the temporal changes of the perimetry. The graph of Method 1 shows that the isopter area was decreasing gradually, i.e., the visual field was decreasing gradually. Similarly, the graph of Methods 2 and 3 shows a decrease in the visual field, but the graph of Methods 4 and 5 does not show this trend clearly.
A Visual Field Quantification System for the Goldman Perimeter
167
9O00
150 o-*
I1 I2
8006
~100
70oo 4
600O 50 5000
1/1988
5/1988
10/1988 date(month/year)
4000 6/1989
3]1989 _______.~ _ _
2- - K 3 - -
O,
j
a~
1/1988
5/1988
m
10/1988 date(month/year)
I1 I2 I3 I4 V4
--if3/1989
i
6/t989
26000
2000 t
24000
~
~
[] --,*------~
Method 3 Method4
1600
22000 c~
20000
1200
18000
8OO
16000 400
14000 12000 1/1988
5/1988
10/1988 date(month/year)
~-------a-1"0 1 0.8 "~
0 6/1989
3/1989 I1 v4
0.6-
0.40.20.0
1/1988
5/1988
10/1988 date(month/year) Figure 5. Trend of indices.
3/1989
6/1989
168
Odaka et al.
Discussion In this study, we developed a visual field evaluation system that quantifies the result of Goldmann Perimeter (GP) measurements. This system calculates the indexes of visual fields in five ways. This system can digitize the isopter in order to calculate the area, volume and the shape factors, to visualize the results, and to analyze these results statistically. In a previous study, 4-9 only private indexes could be evaluated by each program. On the other hand, a physician can use multiple indexes with our system. Each index has both merits and demerits. As a result, this system is considered to be quite useful. A physician can also estimate the efficiency of each index using this system. This is a general-purpose system. For example, this system can be used for research, clinical diagnosis and group examinations. For a clinical diagnosis, a physician can use a trend graph of the change of visual field. As a result, a physician can make a quantitative diagnosis. For group examinations, a physician can accurately and efficiently diagnose patients by using a statistical analysis on a large quantity of GP data. We used a mainframe computer for the statistical analysis since some statistical software packages on the mainframe (such as SAS, BMDP) are very popular and easier to use than other packages on personal computers. However, it is also possible to use a personal computer for statistical analysis. For isopter digitization, this system is slightly tedious. One reference 1° reports a trial with automated digitization. In this trial, they put a potentiometer on GP and measured the coordinates of the isopters directly. For digitizing isopters that have already been measured, we chose a manual digitization method. However in the future, it is believed that automated digitization will make this system even more convenient.
ACKNOWLEDGMENTS The author is greatly indebted to Mr. Brian Quinn, Kyushu University, for his careful critique of this manuscript.
REFERENCES 1. Werner, E.B., Manual of Visual Fields. Churchill Livingstone, pp. 7-37, 1991. 2. Watanabe, Y., A Method for Volume Estimation by Using Vector Areas and Centroids of Serial Cross Sections. IEEE Tran. on BME, Vol. BME-29, No. 3, pp. 202-205, 1982. 3. Watanabe, Y., Nose, Y., Sanefuji, S., Yokota, M., and Nakamura, M., A Method to Estimate Cardiac Volume by Two-dimensional Echocardiograms Recorded from One Extracorporeal Point. J. Biomed. Eng. 4:125-128, 1982. 4. Endo, N., Goldmann Perimeter, ganka MOOK, Vol. 36, pp. 31--43, 1988. 5. Baba, H., Quantitative Evaluation of the Visual Field Measured by Goldmann Perimetry as a Solid Angle. nichigan kaishi, Vol. 90, No. 1, pp. 210-214, 1985. 6. Kani, K., Principles of the kinetic perimetry, ganka rinsyou ihou, Vol. 77, No. 10, pp. 1561-1565, 1983.
A Visual Field Quantification System for the Goldman Perimeter
169
7. Nakatani, H., Kosaki, H., A New Method for Numerical Expression of Visual Field. nichigan kaisi, Vol. 78, No. 11, pp. 1202-1207, 1974. 8. Matsuo, H., On practice in perimetry, ringan, Vol. 37(3), pp. 263-277, 1983. 9. Suzurnura, H., Furuno, F., and Matsuo, H., Volume of 3-Dimensional Visual Field and Its Objective Evaluation by Shape Coefficient: Normal Values by Age and Abnormal Visual Field. gamki, Vol. 34, pp. 2448-2457, 1983. 10. Mori, K., Sonoda, Y., Futa, R., On-Line Processing of Goldmann Perimeter. IEtCE technical report, Vol. MBE-91, pp. 31-38, 1991.
A Visual Field Quantification System for the Goldmann Perimeter Tomohiro Odaka,* Kimihiko Fujisawa,* Kouhei Akazawa,* Maki Sakamoto,* Naoko Kinukawa,* Tatsuro Kainakura,* Yuko Nishioka,* Hidetoshi Itasaka,* Yoshiaki Watanabe,t and Yoshiaki Nose*
We have developed a visual field quantification system that can accurately quantify the measurement results by the Goldmann Perimeter (GP). This system calculates the plural indexes introduced in published papers. In recent years, several isopter quantification methods have been proposed. In these methods, the isopters are digitized and the data are input into a computer, after which a computer program evaluates the changes in the isopters quantitatively. However, each program is only able to evaluate private indexes. We have developed a system that quantifies data using multiple methods. This system used five methods that have been introduced in published papers. With this system, a physician can analyze GP data with multiple methods and can diagnose diseases accurately. We have already input about 2500 GP recording papers into the computer by this system. We then calculated the plural indexes, and visualized the temporal changes in the perimetry.
INTRODUCTION We have developed a visual field quantification system that can accurately quantify Goldmann Perimeter (GP) data. This system can calculate the various indexes previously introduced in published papers. GP is used widely as the instrument that measures kinetic visual field. ~Kinetic visual field measurement by GP is useful not only for daily clinical practice but also for research. In daily clinical practice, physicians evaluate GP data such as isopter form, isopter area, the number of scotoma and the position of scotoma qualitatively. For example, if the area of an isopter seems to be decreasing with time, it means that the visual field has become narrow, and it is understood that the disease has been aggravated. There is no standard
From the *Department of Medical lnformatics, Faculty of Medicine, Kyushu University, Japan; and the ~Department of Information Science, Faculty of Science and Engineering, Saga University, Japan. 161 0148-5598/92/0800-0161506.50/0 © 1992 Plenum Publishing Corporation
162
Odaka et al.
quantitative method for GP analysis, however. This is in contrast to the static visual field evaluation that is sufficiently computerized. In recent years, several isopter quantitative methods have been proposed. In these methods, the isopters are digitized and the data input into a computer, afterwards the computer program evaluates the changes in the isopters quantitatively. In our research, we classified the methods previously published into five types and developed a system that applies to these five types of methods individually for the same data. This system can be used not only for clinical research but also for clinical diagnosis. With this system, a physician can thus analyze GP data with multiple methods and can therefore quantitatively diagnose a disease.
METHODS Calculation Formulas GP is an instrument that measures the sensibility curve of an eye to different brightness levels. To measure such sensibility, a light source on GP projects a perimetric target of a particular size and brightness to a half spherical screen. Then the target is moved from the peripheral of the visual field to the center. The examiner plots the point where a patient answered that the light was seen. Finally, the perimetrist connects the points with a smooth curve. An example of the GP recording paper is shown in Figure 1. In Figure 1, the curve that connects the same sensibility points is called an isopter. Usually five
A--/
D i a n * ; i r mm,!l ~t
Co~ec~io
Figure 1. Exampleof an isopter.
163
A Visual Field Quantification System for the Goldman Perimeter
isopters are measured for each eye. Each isopter is called I1, I2, 13, I4, V4 from the center to the peripheral. The field shown with a diagonal has a low sensibility compared with other field of vision. This field is called a scotoma. A scotoma is measured separately from an isopter. Conventionally, a physician evaluates GP data qualitatively. A physician mainly evaluates isopter form, isopter area, the number of scotoma and position of scotoma. For example, if the area of an isopter is decreasing with time, it means that the visual field has become narrow, and it is understood that disease has been aggravated. In our system, a digitizer is used as the isopter input device. An isopter is then handled as a collection of n discrete coordinate points ( x i, Yi) (i = 1 . . . n ) as shown in Figure 3. For simplicity, we assume that ( x n + 1 , y n + 1) = ( x l , y l ) . The data are analyzed with the following methods [2-91 (Fig. 2):
Method 1 The isopter is evaluated with the area on the GP recording paper of each isopter4 (Method 1). In Method 1, five indexes corresponding to five isopters are calculated for the each GP recording paper. The Ss area of the isopter is calculated as n as : E
(xi - Xi+l)(yi q-
(l)
yi+O/2
i=1
Method 2 The coordinate of the isopter is projected to the hemispherium and the area of the isopter is calculated on the hemispherium 5 (Method 2). In Method 2, five indexes are calculated on each GP recording paper. The Sc area on the hemispherium is calculated as
S~ = ~ 0,-{1 - (cos ai + cos 13/)/2}, i=1 Methods E•aluation
(2)
!
--~Sufface Area Calculation ] 2-dimensional(Method1) ] 3-dimensional(Method2) ] -~ Volume Calculation
] 2-dimensional(Method3) I
3-dimensional(Method4) I --f Form Index Calculation j
I I
[ Method5 Figure 2. Isopterevaluationmethods.
]
164
Odaka et al.
,-'"" ', ..-L.. r"'--. .... ~ ...... WT--/
.....;~.3
V4 )"~""--, Y'-.Y\ -..~x"., / X'. /:~ " X--"L_.v4
/ /' ~ ( X i + 2 , ~ ! + 2 ) ;"~~~'-~'N(xi+l,yi+l)
~ \.
.- / /f
Figure 3. Isopterdigitization. where,
Oi = tan- l(yi/xi) -- tan- l(yi+ l/Xi+ l) Ot i -~-
K~/-~i + y~
~i
K~V/x2i+l + Y2+1
:
K
Constant (depends on the reduced scale of the isopter recording paper)
Method 3
In Method 1 and Method 2, five indexes are calculated for the each recording paper. A single representative index is preferable for diagnosis. In addition, the central part of the isopter is more important than the peripheral part in the matter of diagnosis. 6'7 Therefore, the indexes of Method 1 are summed up on a weighted scale (Method 3). The volume of the solid constructed with isopters is calculated as
Vs : {K3(Sv4 + SI4) + K2(SI4 + SI3) + K2(SI3 + SI2) + K2(SI2 + (SI2 + Sn) + K1Sn}/2 (3) where, Sv4 • • • Sn K3 • . • K1
The result of Method 1 Constant
Method 4
In Method 4, the polar coordinate is applied to the recording paper. Five points on five isopters near angle O (O = 0 to 2rr [rad]) make up a plain figure according to a specific algorithm. Then the solid body of revolution is constructed with the plain figure. The volume of the solid body then becomes the index (Method 4) [8,9]. In Method 4, a point on each isopter near an angle O is found. The point (x, y) is then projected onto the u-v space according to the following expressions:
A Visual Field Quantification System for the Goldman Perimeter
165
u = Ncos ( K ~ / x 2 + y2)
(4)
v = Nsin (KWe-~ + yZ)
(5)
where, K N
constant (depending on recording paper) (I4: 4, I3: 5, I2: 6, I1: 7)
Then the points (u, v) from five isopters constitute a plan figure, and the plane figure is revolved around the v-axis to constitute the solid body of the revolution. The volume Vco of this solid body is then calculated by
Vco = Sd2rr
(6)
where d s
the distance from the revolution axis (= v-axis) to the center of gravity of the plane figure the area of the plane figure
Last, Vco is averaged out with every O. Method 5
The shape factor is one of the estimation indexes of the isopter. 8'9 To calculate the shape factor, one has to calculate the peripheral length of a real circle having the same area as a certain isopter. The shape factor PA is then calculated by the division of isopter length with the peripheral length of a real circle.
PA-
4"rrS 12
(7)
where, S l
is the area of isopter is the peripheral length of the isopter
We designed the isopter quantification system using the above five methods. The system can evaluate each recording paper using all five methods. Hardware and Software
The constitution of the system is shown in Figure 4. The system is constructed of a digitizer DT4513 (Seiko electron) and a personal computer PS/55 model 5551 S (IBM). The hardware used is broadly available and no special devices are used at all. The isopter is digitized by the digitizer and the patient identification data is input from the keyboard. The software of PS/55 operates on OS/2. A compiler of C language C/2 was used for the system development. The source program consists of about 2700 lines. The software system is composed of four sub-systems. The input subsystem controls the input from the digitizer. The indexes are calculated by three subsystems: an isopter surface area calcu-
166
Odaka et al.
Visual Field Quantification System IBM PS/55 Coordinate Input
i
TM
SEIKO DigitizerDF3213
Calculation
File
NN~
8
File Transmisson
Mainframe Comput~
Macintosh personal computer
Statistical Software Packages
Graph Package
Figure 4. Software and hardware.
lation sub-system, a volume calculation sub-system and a shape factor calculation subsystem. The results of all five methods are then summarized into one file. After the calculation by the PS/55, the file is then transmitted to a mainframe computer 3081/4381 (IBM) and analyzed by various kinds of statistical analysis software packages (SAS, BMDP). The results are then printed out on a Macintosh personal computer.
RESULTS We input about 2500 sheets of data into the computer using this system. About 2 minutes were required to input the data from each recording paper. About 20 seconds were required for the calculations of the area, volume and shape factors on each sheet. The size of the coordinate data consisted of about 3K byte on each data sheet. Figure 5 shows an example of the indexes that have been calculated using this system. Figure 5 shows the temporal changes of the perimetry. The graph of Method 1 shows that the isopter area was decreasing gradually, i.e., the visual field was decreasing gradually. Similarly, the graph of Methods 2 and 3 shows a decrease in the visual field, but the graph of Methods 4 and 5 does not show this trend clearly.
A Visual Field Quantification System for the Goldman Perimeter
167
9O00
150 o-*
I1 I2
8006
~100
70oo 4
600O 50 5000
1/1988
5/1988
10/1988 date(month/year)
4000 6/1989
3]1989 _______.~ _ _
2- - K 3 - -
O,
j
a~
1/1988
5/1988
m
10/1988 date(month/year)
I1 I2 I3 I4 V4
--if3/1989
i
6/t989
26000
2000 t
24000
~
~
[] --,*------~
Method 3 Method4
1600
22000 c~
20000
1200
18000
8OO
16000 400
14000 12000 1/1988
5/1988
10/1988 date(month/year)
~-------a-1"0 1 0.8 "~
0 6/1989
3/1989 I1 v4
0.6-
0.40.20.0
1/1988
5/1988
10/1988 date(month/year) Figure 5. Trend of indices.
3/1989
6/1989
168
Odaka et al.
Discussion In this study, we developed a visual field evaluation system that quantifies the result of Goldmann Perimeter (GP) measurements. This system calculates the indexes of visual fields in five ways. This system can digitize the isopter in order to calculate the area, volume and the shape factors, to visualize the results, and to analyze these results statistically. In a previous study, 4-9 only private indexes could be evaluated by each program. On the other hand, a physician can use multiple indexes with our system. Each index has both merits and demerits. As a result, this system is considered to be quite useful. A physician can also estimate the efficiency of each index using this system. This is a general-purpose system. For example, this system can be used for research, clinical diagnosis and group examinations. For a clinical diagnosis, a physician can use a trend graph of the change of visual field. As a result, a physician can make a quantitative diagnosis. For group examinations, a physician can accurately and efficiently diagnose patients by using a statistical analysis on a large quantity of GP data. We used a mainframe computer for the statistical analysis since some statistical software packages on the mainframe (such as SAS, BMDP) are very popular and easier to use than other packages on personal computers. However, it is also possible to use a personal computer for statistical analysis. For isopter digitization, this system is slightly tedious. One reference 1° reports a trial with automated digitization. In this trial, they put a potentiometer on GP and measured the coordinates of the isopters directly. For digitizing isopters that have already been measured, we chose a manual digitization method. However in the future, it is believed that automated digitization will make this system even more convenient.
ACKNOWLEDGMENTS The author is greatly indebted to Mr. Brian Quinn, Kyushu University, for his careful critique of this manuscript.
REFERENCES 1. Werner, E.B., Manual of Visual Fields. Churchill Livingstone, pp. 7-37, 1991. 2. Watanabe, Y., A Method for Volume Estimation by Using Vector Areas and Centroids of Serial Cross Sections. IEEE Tran. on BME, Vol. BME-29, No. 3, pp. 202-205, 1982. 3. Watanabe, Y., Nose, Y., Sanefuji, S., Yokota, M., and Nakamura, M., A Method to Estimate Cardiac Volume by Two-dimensional Echocardiograms Recorded from One Extracorporeal Point. J. Biomed. Eng. 4:125-128, 1982. 4. Endo, N., Goldmann Perimeter, ganka MOOK, Vol. 36, pp. 31--43, 1988. 5. Baba, H., Quantitative Evaluation of the Visual Field Measured by Goldmann Perimetry as a Solid Angle. nichigan kaishi, Vol. 90, No. 1, pp. 210-214, 1985. 6. Kani, K., Principles of the kinetic perimetry, ganka rinsyou ihou, Vol. 77, No. 10, pp. 1561-1565, 1983.
A Visual Field Quantification System for the Goldman Perimeter
169
7. Nakatani, H., Kosaki, H., A New Method for Numerical Expression of Visual Field. nichigan kaisi, Vol. 78, No. 11, pp. 1202-1207, 1974. 8. Matsuo, H., On practice in perimetry, ringan, Vol. 37(3), pp. 263-277, 1983. 9. Suzurnura, H., Furuno, F., and Matsuo, H., Volume of 3-Dimensional Visual Field and Its Objective Evaluation by Shape Coefficient: Normal Values by Age and Abnormal Visual Field. gamki, Vol. 34, pp. 2448-2457, 1983. 10. Mori, K., Sonoda, Y., Futa, R., On-Line Processing of Goldmann Perimeter. IEtCE technical report, Vol. MBE-91, pp. 31-38, 1991.
