14th Congress of the International Society of Photogrammetry
Hamburg 1980
Commission V - Working Group 6
Presented Paper
Elena BAJ
Full assistant at the Chair of Topography, Politecnico of Milano
Assistant professor, Institute of Geodesy, Topography and Photo
grammetry , University of Pisa, Italy
Title
Remarks about the monocular and stereoscopic observation of whi
te strips on a zebra crossing .
Abstract
Observing white strip images on a zebra crossing with both mono
cular and stereoscopic method, it seems that their width is dif
ferent, and precisely their width looks larger with stereoscopic
observation than it looks with the monocular one . In order to e
stablish if it is only a sensorial appearance we have tried tomeasure the width of the strips, always on the same photogram ,
with monocular as well as stereoscopic observation : the result
was that the width obtained by stereoscopic observation is some
micron larger . The measures have been performed with a Stereocom
parator OMI - TA3/P, available at the Institute of Topography (Politecnico di Milano), which allows to get plate coordinates both
with monocular and stereoscopic observation .
Text
Most of the instruments used in photogrammetry are based on bino
cular observation of stereoscopic photograms, but there are also
other instruments, as the monocomparators, based on monocular ob
servation .
The process of vision is much complicated and it is still being
studied; in order to deepen it, the so- called evoked potential
method is also used; this method consists in registering,by el~
ctrodes fixed on the skin of the head with a tape , the potenti
als which are evoked from the eye perceptions. These potentials
are very weak, of about 5 microvolts or less, so it is very dif
ficult to register them . However, it is known that the brain fu
ses the images of the same object received from the two eyes as
it fuses the colours (anaglyphic method).
In the same way the brain fuses two completely different images
which it receives from the two eyes; actually if you look f.i .
026.
the tangent of the angle 8 formed by the straight line and the X
axis .
Analogously it is made for the other terns of points thus obtai
ning , given n Straight lines , n X 3 Values Of m , and thence Of S.
Among all the calculated values of 8 , the max and min values are
individuated and in this interval 10 values of 8 are considered ,
differing in the constant increase .
Here is now the iteration : for each value of e , the most probable
position for each straight line based on the least squares prin
ciple i s determined , that is the value for which the sum of the
square residuals of the points collimated as regards the strai ght
line is minimum .
3
A I . v~ is in fact calculated and memorized , and the elements a
1 ~
&
re also kept def i ning the position of the straight l i ne .
Analogous l y it is made for all the straight lines and at last if
n
3
n are the straight lines Ik I . v ~k is calculated and memorized .
1
1 1.-
~
All these calcul at i ons are repeated for the 1 0 considered values
of e , still taking into account the above sum .
The chosen value of 8 still based on the least squares cr i terion ,
is that corresponding to the double sum minimum value ; for such
a value the program has already calculated the optimum straight
line pos i tion . The width between the white strips as the i nter va l between the straight lines themselves and thence the mean
and the m. s . e . may be obta i ned .
In order to simplify and improve calculations at each iteration
the axes X and Y are r otated so as the considered direction be
para l lel to the axis X (Fig .1 ) . Coordinates of collimated points
are of course changed and for each value of 8 cons i dered , it will
result for every considered tern
X'
Y'
---
sen j e j+ X cos jel
Y cos 181 - X sen 1e1
Y
if
e
is positive
X ' -- - Y senlel
+X cosl e l
if e is negative
Y' -Y cosl8j
+X sen181
When the coordinates are changed , -the residuals v . become 6 y and
3
1.therefore to obtain the condition I i
=
min , the straight l i nes
1
must be moved para l lelly with axis X.
vi
Results
In the different rows of Table 1 are reported :
1)
-
the number of the zebra cross i ng taken into consideration ;
2) - the number of the examined strips in the zebra crossing ;
1) -
the width of the wh i te (and b l ack) strip obtained with the
stereoscopic observation ;
4) - the width of the white (and b l ack) strip obtained with the
monocular observation ;
_?) - the difference between the width obtained with the stereosco
pic observation and the monocular one ;
.§_) 7) 8) - the m. s . e . respectively of the values in rows 3 , 4 , 5;
027.
at the same time with one eye a cage and with the other eye a
lion , of proper dimension , you ' l l see the l ion in the cage .
It would be interesting to investigate if this fusing has some
effect also on the measurements and if the monocular and the ste
reoscopic observations g i ve the same resu l ts . In fact that is the
aim of this study .
Subject of the exper i ments and methodology
As subject of study were taken the white strip images on a zebra
crossing wh i ch are very common in urban aerial photograrns and ea
sily distinguishab l e .
Among the photograms which were at our disposal , we have chosen
a photograrn taken in Milan at a height of 1 200 rn ; the photograrn
sca l e is 1: 8 000 . It includes the images of about f i fty zebra
crossings . The stereoscopic observation needed of course the pr~
ceding and the success i ve photograrn .
We have investigated whether the two different methods give the
same value for the wi dth of white str i p i mages measured on the
same photograrn . The measures have been performed with an accura
cy of about.±. 2 )..liD ; with a Stereocornparator OHI - TA3 / P .
In order to obtain the width of each white strip image , the 4
coins de l imiting i t were firstly coll i mated ; this method was how
ever soon abandoned owi ng to its i nsuffic i ently accurated results .
It must be noticed however how often the area surrounding the co
in i s qui te badly defined .
Therefore it was thought i t suitable to deduce the strip i mage
wi dth as the i nterval between the l i miting straight l i nes : assu
rned s u ch l i nes as paral l el , theoretically the coordinates of 2points of a straight line delimiting a strip and the coordinates
aEonly 1 point for a l l the other straight lines are sufficient .
Ai ming at gather i ng plentiful and thence more rel i able results ,
3 points were co ll imated for each separating line : 1 on the cen
tre , 2 at the extremities of the strip , recording the coordinates .
A program was then studied for the computer to obta i n for each
zebra crossing , the wi dth of each strip , wh i ch approaches 1 00~rn .
In the repeated measurements however differencies nearing
re obtained i n the values of the width calculated for the
str i p . On the other han d , taking i nto account the mean of
wi dths obtained , such d i fferencies did not exceed 2~rn . It
then deemed it useful to der i ve for each zebra crossi n g a
more reliable than the s i ng l e value , on which compar isons
made .
6)..lrn we
same
the
was
mean
were
Measur ements were carri ed out as above said by tvm different ob
servi ng methods , name l y :
a) - monocul ar v i ewi ng
stereoscopi c b i nocular viewing .
b) -
The program for the computer i s i terat i ve : given the coordinates
of three po i nts 1, 2 , 3 of the separati ng l i ne , the directions
of t he strai ght l ines y = mx + b defined by the couples of po ints 1- 2 , 1- 3 , 2 - 3 are calculated . In total 3 directions for
the tern of points belon g i ng to the first separating line ; m is
028.
TABLE
2
3
'+-
O'l
0
IJl
L
Q)
..0
-c
If)
co
L
..0
Q)
0
N
U
L
If)
If)
c.
E ·::J ~
c
If)
c.
·-L
+"'
strip
width
stereo
vision
If)
/urn
15
strip
width
monocu
lar vi-
6
6 l
3-4
4-3
um
sion /urn
1
white
black
114
28
100
42
+ 14
-
14
3
w
b
111
30
1 01
40
+ 10
3
13
w
b
1 11
34
102
44
+ 9
4
14
w
b
102
40
93
49
+ 9
5
9
w
b
11 3
32
106
39
+ 7
6
9
w
b
105
38
7
6
w
b
95
47
8
8
w
b
105
.
36
0
0
-
-
-
10
10
9
c
Q) 0
L ·Q) If)
+"'
If)
2
0
1\J
lO
5
4
>
·-
7
8
0
0
c
0 0
c0 ·If)
6 l
9
Q)
O'l
co
10
If)
If)
X
Q)
E §_
E ·:;
·-
11
12
y
L
co
.c
If)
mm.
mm.
GDR
X
87
97
- 48
3, 15
X X X
89
100
- 49
1' 22
2, 1
X X X
77
87
- 46
1' 21
1' 39
1' 8
X
76
85
+ 42 9
1' 45
1' 45
2,7
X X X
73
75
- 45
um
/urn
/um
1
1' 12
1' 30
1' 72
2,60
1' 78
1' 63
9
9
9
9
-
7
97
46
+
8
8
1 ' 31
1' 71
2, 1
X X
95
65
+ 44 9
90
+
5
3
4,75
1' 25
2, 1
X X X
93
-59
9
+ 89
4
4
1' 55
1 '51
2,2
X X X
95
-53
- 45
so
101
40
+
-
9
2
9
5
10
10
11
4
11
3
bis
0
w
12
16
13
13
14
13
15
11
16
5
17
10
3
w
b
w
b
w
b
w
b
w
b
b
w
b
w
b
w
b
w
b
5
6
7
8
9
10
11
12
111
31
104
39
+ 7
- 8
1' 86
1' 5 1
2, 4
X
90
- 49
- 45 9
108
34
103
39
+ 5
- 5
1' 58
1' 60
2, 2
X
69
- 48
- 45
114
28
105
40
+ 9
- 12
1' 07
2 , 11
2, 4
X X
54
- 67
- 46
97
30
88
39
+ 9
- 9
2 , 12
2 , 07
2, 9
X X
54
- 67
- 46
104
39
98
45
+ 6
- 6
1' 20
1' 28
1' 7
X X X
56
- 60
+ 89 9
10 1
42
96
47
+ 5
5
-
1' 44
1' 66
2, 2
X X X
53
- 53
+ 43 9
107
36
103
39
+ 4
3
1' 27
1' 54
2, 0
X X X
40
- 53
- 44
99
44
99
44
0
0
1' 39
1' 17
1' 8
X
38
- 60
- 89
97
46
91
49
+
6
3
2 , 09
1' 90
2, 8
X X
41
- 67
+ 43 9
104
40
10 1
43
+
3
3
1' 23
1' 09
1' 6
X X
73
- 87
+ 44 9
0
w
4
-
-
9
9
9
9
9
2
0
19
11
20
5
21
6
22
8
23
6
24
8
25
10
26
8
27
13
w
~
28
13
3
102
39
5
4
6
99
43
+ 3
99
45
96
49
+ 3
103
39
100
42
+ 3
92
49
87
56
+ 5
88
52
82
58
+ 6
11 0
32
103
38
99
42
102
38
+ 4
b
101
43
100
42
+ 1
+ 1
w
107
96
+ 11
b
36
47
-11
w
109
33
98
45
+ 11
w
b
w
b
w
b
w
b
w
b
w
b
w
b
w
b
- 4
- 4
-
-
-
3
7
6
+ 7
- 6
-
3
-12
7
8
1' 18
1' 18
1' 7
1' 72
2,06
1' 51
9
10
11
X X X
11 0
- 20
2,7
X X X
110
2
+ 41 9
1' 77
2,3
X X X
112
2
- 89
1' 45
1' 24
1' 9
X X
109
8
+ 89 9
1' 10
1' 60
1' 9
X
109
11
+ 89 9
1' 45
2,09
2,5
X
103
104
- 44
1' 23
1' 20
1' 7
X X
105
103
+ 42
9
1' 39
1' 50
2,0
X X
81
76
+ 44
9
1' 70
1' 39
2,2
X X X
20
60
-
1' 30
1' 36
1' 9
X X
18
58
- 45
12
- 39
45
9
9
9
9
9
3
2
0
w
29
9
31
13
32
7
33
8
34
7
36
4
37
7
38
8
39
9
40
13
w
b
w
b
w
b
w
b
w
b
4
5
6
7
8
9
10
11
12
97
45
91
52
+ 6
- 7
1 '45
1' 36
2,0
X X
20
- 55
+ 43 9
106
36
101
42
+ 5
- 6
1' 68
1' 46
2,2
X
14
- 30
- 57
96
44
91
47
+ 5
- 3
2,15
1' 88
2,9
X
15
- 34
+ 51 9
100
41
99
41
+ 1
0
1' 79
2, 13
2,8
X X X
15
- 37
- 59
107
38
101
43
+ 6
- 5
1' 65
1' 91
2,5
X X X
31
- 17
- 46
95
45
92
so
+ 3
- 5
1' 51
1' 16
1' 9
X X
31
19
+ 42 9
95
45
97
43
- 2
+ 2
2,55
2, 11
3, 3
X X
38
17
+ 42 9
104
42
96
47
+ 8
- 5
1' 48
1' 45
2,07
X X
- 6
-
1
- 58
1 OS
48
94
49
+ 11
- 9
1' 71
1' so
2,3
X
- 4
-
5
- 58
107
36
100
43
+ 7
- 7
2, 11
2,27
3, 1
X
3
9
9
9
N
w
b
w
b
w
b
w
b
w
b
- 43
9
9
- 46 9
2
41
6
42
7
43
7
44
11
45
6
46
16
47
10
48
7
49
9
so
13
0
w
w
.
w
b
w
b
w
b
w
b
w
b
w
b
w
b
w
b
w
b
w
b
3
4
5
98
41
102
39
+ 2
97
45
95
47
+ 2
92
46
88
52
+ 4
95
48
93
49
+ 2
102
41
99
43
+ 3
103
40
102
41
+ 1
98
45
96
46
+ 2
102
38
97
45
+ 5
93
51
87
58
+ 6
105
39
0
- 1
105
38
- 4
- 2
- 6
-
1
- 2
-
-
1
1
- 7
- 7
6
7
8
2,44
2, 31
1' 56
9
10
11
12
3, 4
X X
65
- 46
- 46
2, 19
2,7
X
3
- 45
+ 43 9
1' 51
1' 43
2, 1
X
- 19
100
+ 22 9
1' 09
1' 64
2,0
X X X
- 43
88
- 67
1' 85
1' 87
2,6
X X X
- 44
91
- 66
1' 28
1' 55
2,0
X X
- 43
60
- 56
1' 98
2,07
2,9
X X X
- 77
60
- 34
2,29
2,39
3, 3
X X
- 87
- 77
+ 88 9
1' 48
0,99
}' 8
X X
- 83
- 77
-
1' 23
0,77
1' 4
X X X
- 54
-101
+ 46 9
9
9
9
9
9
29
2
0
51
8
52
7
53
8
w
b
w
b
w
b
3
4
129
33
108
38
+
11
5
1' 82
1' 53
2,4
107
38
103
42
+
4
4
1' 66
1 ' 17
112
31
11 0
34
+
2
3
1' 26
1' 40
5
-
-
6
yl
7
8
9
10
11
12
X X X
- 52
- 101
- 47
2,0
X X X
- 52
-
99
+ 439
1' 9
X X X
- 54
-
98
- 48 9
y
I
w
V1
V2
V3
~
,- -
~----~L---~--~--L---------------~>
-J
~------------------------------------->
X
X
FIG.1
9
the image sharpness: three asterisks correspond to the hi
ghest degree of sharpness;
1 0)
the x coordinate of the centre of the zebra crossing as re
gards the axes of the photogram; the X direction is
the flight one;
11) - they coordinate ;
~)
~)
the angle 8 between the X axis and the direction of the
strips of the zebra crossing .
Table 1 shows that the width of white strips obtained with stere
oscopic observation is greater than the one obtained with monocular observation . The greatest difference is 14 ~m, but the we
ighted mean of the obtained values is 4 . 9 + 0 . 5 ~m and this isthe most meaningful result obtained .
Moreover, it does not seem to exist a remarkable correlation bee
ween the values of the resulting differences and the examined va
riables X, Y, 8.
At this point we have got to present some hypotheses on the po
i nt of the major strip width obtained with the stereoscopic ob
servation in comparison to the monocular one . The major width
can be attributed :
a) - to the instruments;
b) - to the operator because of his faulty sight ;
~) - to the operator as an ordinary consequence of the stereosco
pic observation.
Of course the various hypotheses might coexist .
In order to ascertain the validity of the hypothesis a), the sa
me operator needs to repeat the measurements with many instru-ments of high precision; as for the hypotheses b) and c) we
can ' t help repeating the same measures on the same instruments
with different operators .
BIBLIOGRAPHY
- Rapport du Groupe de Travail IV/2 - Commission IV : Congres In
ternational de Photogrammetrie , Losanna 8- 20 Luglio ,1 968
- Gregory Richard L . : Occhio e cervello - Il Saggiatore ,
~ilano, 1966
- Mach Ernst : L ' analisi delle sensazioni , ed il rapporto tra fi
sico e psichico - Feltrinelli , Milano , 1975
- Ross J . : Le risorse della percezione binoculare - Illusione
e realta - Le Scienze S . p . A. editore
035.