SIMPLE METHOD FOR MEASURING OF
RECOGNITION ACUITY WITH A COMPUTER
Bogusława Dubik, Marek Zając
Institute of Physics, Wrocław University of Technology
♦
WHAT FOR?
•
desease / treatment development monitoring
•
określanie przydatnosci zawodowej / stopnia inwalidztwa
♦
DO I SEE CORRECTLY?
•
quality of retinal image
∗
point spread function,
∗
aberrations
∗
transfer function
∗
two-point resolution
•
visual acuity
∗
quality of retinal image,
∗
retina as a detector
∗
visual path
♦
RESOLUTUION VS RECOGNITION
♦
VISUAL ACUITY TESTS - OPTOTYPES (SNELLEN)
∗
optotype "E"
∗
optotype "C" (Landolt ring)
∗
letter optotypes
∗
bar tests
∗
...
• MEASURES OF VISUAL ACUITY -
•
visus
∗
standard:
distance 6 m (5 m)
whole optotype angle of view 5' (detail 1')
visus=6/6
∗
definition:
V
L
D
=
L - examination distance [m]
D - 5 arc min distance [m]
E
L
ω
•
recognition acuity
∗
MAR (minumum angle of resolution)
2
• MEASUREMENT METHOD
•
Optotype is presented on the computer screen
∗
random orientation (up, down, right, left)
∗
different angular size
•
Subject indicates the optotype orientation
(or onswers "cannot recognize") by pressing the appropriate key
∗
correct recognition - the following optotype smaller
∗
false recognition - the following optotype greater
∗
random drawing procedure assuring uniform distribution of optotype sizes
•
The results
∗
ordering according to the optotype size
∗
counting the percent of correct recognitions in particular angular
intervals
∗
result: psychometric function
0
2
4
6
8
10
12
14
16
18
20
0
50
100
angular size of optotype [arc min]
percent of
correct
recognitions
∗
approximation:
Weibull function
−
−
−
=
β
α
γ
c
c
P
exp
)
1
(
1
)
(
tanh function
(
)
[
]
(
)
{
}
(
)
{
}
(
)
{
}
(
)
{
}
+
+
⋅
−
+
+
⋅
+
⋅
−
−
+
⋅
=
+
+
⋅
=
1
exp
exp
exp
exp
2
1
1
2
1
)
(
1
0
1
0
1
0
1
0
1
0
a
c
a
a
c
a
a
c
a
a
c
a
a
c
a
th
c
P
∗
numerical parameters:
K50
K100
3
EXAMPLES OF PSYCHOMETRIC FUNCTIONS
Subject: BOG12E
0
2
4
6
8
10
12
14
16
18
20
0
50
100
angular size of optotype [arc min]
correct
%
K50=3.532
K100=5.164
Subject: KRZYS12
0
2
4
6
8
10
12
14
16
18
20
0
50
100
angular size of optotype [arc min]
%
correct
K50=10.856
K100=13.552
4
POSSIBLE APPROXIMATIONS - COMPARISON
TANH FUNCTION & WEIBULL FUNCTION
Subject EWA24
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0
50
100
angular size of optotype(arc min)
tanh
Weibull
%
correct
tanh function approximation
K50 =6.824
K100=9.632
Weibull function approximation
K50=6.791
GROUPING METHOD
&
NUMBER OF OBSERVATIONS IN A SERIES
NUMBER OF OBSERVATIONS
•
Random choice of 100, 200, 300, ..., 900 observations from 1000
observation's series
GROUPING
•
Equal angular interval, different number of observations in each,
•
Equal number of observations, different angular intervals,
Institute of Physics, Wroc³aw Technical University
EXAMPLE MAR6
100
200
300
400
500
600
700
800
900 1000
5
6
7
8
9
number of observations
MAR
K100
K50
EXAMPLE BOG8
100
200
300
400
500
600
700
800
900 1000
5
6
7
8
number of observations
MAR
K100
K50
CONCLUSION:
•
number of observatioons not less than 500
•
grouping method does not matter
Institute of Physics, Wroc³aw Technical University
PARTICULAR MEASUREMENT ACCURACY
one measurement = one series of 1000 observations
random choice of 500 observations
Example MAREK6
6
7
8
9
10
11
12
13
14
15
K50
K100
number of "measurement"
=
sr50 11.992
=
sr100 10.057
=
dev50 0.034
=
dev100 0.025
Example EWA4
6
7
8
9
10
11
12
13
14
15
number of "measurement"
=
sr50 11.033
=
sr100 8.188
=
dev50 0.046
=
dev100 0.04
Example KRZYS12
6
7
8
9
10
11
12
13
14
15
i
number of "measurement"
=
sr50 13.564
=
sr100 10.808
=
dev50 0.055
=
dev100 0.044
Example BOGUSIA8
6
7
8
9
10
11
12
13
14
15
number of "measurement"
=
sr50 11.992
=
sr100 7.489
=
dev50 0.034
=
dev100 0.034
CONCLUSION
•
Measurement accuracy is not worse than
±0.15
Institute of Physics, Wroc³aw Technical University
LONG TERM CHANGES IN VISUAL ACUITY
Subject BOGUSIA, test E
0
2
4
6
8
10
12
0
1
2
3
4
5
6
7
8
9
10
number of measurement (day)
MAR
K100
K50
Subject: MAREK, test E
0
2
4
6
8
10
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
number of measurement (day)
MAR
K100
K50
Institute of Physics, Wroc³aw Technical University
VISUAL ACUITY MEASURED WITH "E" TEST & "C" TEST
Subject: MAREK
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
K100/E
K100/C
K50/E
K50/C
number of measurement
MAR
Subject: BOGUSIA
5
6
7
8
9
10
11
12
13
0
1
2
3
4
5
6
7
MAR
number of measurement
K50/E
K50/C
K100/E
K100/C
Institute of Physics, Wroc³aw Technical University
VERTICAL & HORIZONTAL TESTS
(INFLUENCE OF ASTIGMATISM)
0
1
2
3
4
5
6
7
8
9
10
0.8
0.9
1
1.1
1.2
1.3
1.4
MAR(hor)
MAR(ver)
_________
MAREK
BOGUSIA
number of measurement
SUBJECT: MAREK
<K100 v/h> = 1,003 <K50v/h> = 0,976
dev(K100v/h) = 0.015 dev(K50v/h) = 0.017
Subject: BOGUSIA
<K100v/h> = 1,165 <K50v/h> = 1,138
dev(K100v/h) = 0.014 dev(K50v/h) = 0,022
Institute of Physics, Wroc³aw Technical University
INCREASING / DECREASING TEST
COMPARISON TO PSYCHOMETRIC FUNCTION
Example KASIA0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0
50
100
angular optotype size [arc min]
MAR
K1=3,9
K2=4,7
K50=6,6
K100=8,3
Example KRZYS12
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0
50
100
angular optotype size [arc min]
MAR
K1=7,2 K2=7,7
K50=10,9
K100=13,5