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