MEASUREMENT
DIGITAL IMAGE PROCES ING AND
OF A CONVERGENT PAIR
i Mori and Mikio Hirokane
Dept .. of Civil Eng
Faculty f
Okayama Uni v
Comission
ABSTRUCT
As
an
stereoscopic measurement
images were
results were
3000 x 2000 pix Is
nsm
Introduct
Technology related to di
comes into wide
are
with a
digital image proces ing
the authers investigated
measurement
a pair
process
system current
resolving power
2000 x 3000
investigation the accu cy te
out
The results are as
ws
could be
viewing an image
of display unit with the aid
accuracy of the camera were re
2 .. Camera
Image Processing
iti nand
im
e acqu
of universit es in Japan
and
general
Considering
ibi ities of s ereoscopic
an image
wi
high
in
thi
s
ixel
u
ra were also
ts f
c
c easurement
pair represented on a screen
of a st re s ope
(2) the
tern
high
PICamera Such
pI ne of a
array with
re
2350A ..
huge
ta can
camera with a line sensor
2,000
xels as shown in
This scanning mechanism
it may lea
to non- niform a
sensor
The efo e po iti
1
investigated Fr m th te
the
t
s
in a fault namely
m
ment of the
the pi
s was
Ie
i
is
errors
ions
use of
mage f a
MB buffer
a image are
a operation boa
full scene or t re
cial or
memory"
1
a
Fig
method
of
bi-linear and
method were
igital mage
Coordinate of a
easi
enlarged
in the
cursor ..
of
i
cubic
appli
enlargme
center
found
im ge
f
a
3
F
for
c viewing
.. 3
in the
ft and
half
he s reen respectively .. A mirror stereoscope was
f the
pla
image pair
Fig .. 3 shows the
practicing this
cope
I
a full scene
m
y small
ld be represented because the
xel number,
f the screen wa too small
one of t e
camera. This fact result in
Section
the purpose of
paral ax-free image pa r
d be epre en ed We
tal image process
images or other
have
method presented here
on
mage pa ir,
ce that image pair
pair is
relative
1 ent
mera Cal
s on the walls
d
within the
( is)
si
e image
Camera calibrat on was carried
the well
which
LI
5
mage
Table 3
Interior orientation elements
se
in the first stage
Location
principal point:
~D' 20
Dif
of principal distance
C
al distorsion of the lens : At and AZ
Decentering distorsion of the lens : B( and B2
Scale differense in 1'L direct~on : I\..
y
s to x-axis~
~
cans ed by s canni ng *)
() 1
by scannin<,r *)
in thi s
report
special
moving mechanism descri
above. In order to correct
the image deformation ef
,
.
tively and sufficiently,the
I I,
geometrical properties of
the special mechanism were
10
20m (.}A-.l,;.,IB-----~C::r--;s... X
considered, and 8 interior o
exposure stations
orientation elements were
z
selected at first .. These
Fig.4 Plan of the test field
elements consist of 11 parameters as shown in Table3e
The distorsions .£15 and 4''2. of an image at a location J,
~
caused by the parameters are given by the following
equations, under the assumption that each parameter is very
small ..
t i
...L._ _.....I
! . - '_ _
Images of the test field were obtained at 3 different
exposure stations A,B and C shown in Fig .. 4.. Preliminary
calibration tests were carried out for determining the
parameters by use of these images. From these tests, it was
found that the effect of 5 parameters A..., Q1' Q3' B1 and B2
was so small that these parameters could be disregarded.
New calibration computations were performed after
disregarding the 5 parameters. Table 4 is the result. It is
evident that each parameter is stable in magnitude through all
over images and standard error ~ of an observation
image
coordinates is
ss than 3.7 pme Therefore, the average values
of Table 4 were used as the standard calibration values of the
interior orientation elements
They are also described in
Table 4 ..
5 .. Error
Obj ect Space Coordinates Computed from Several
Single Images
Table 4
Interior orientation elements obtained by
3 different images
Image
5
10
mm)
A
10 3 ( m)
10 6 (rad)
1240 ±27
-1225
24:l:13
-10u8
-4±26
3
6
4 0
- 41 .. 2
10 9 (mm 4 )
1 3 ..
(fbn)
Average
-1215±24
10 6 (mm- 2 )
0
C
1:t13
-1
(mm)
'10
B
.. 5
7
3 1
46260
1
46220±7
-4562
32
- 4 6 5 9 ::t.11 7
-4570
-51 .. 216.3
43 .. 0:t2 .. 3
- 4 5 .. 1
33 .. 9
3.7
9 .. 6
1 6 ..
2.7
46 .. 235
7
23 7
-
Table 5 Mean va
re
depth
The images deerrors of targets
scribed in Section
(0/00)
4 were also
No ..
of points
estimating an
Model Base
accuracy of coor5*)
10
Total
te determinaA-B
015-0 .. 27
0 .. 209
0.231
0 .. 224
in the object
B-C
0 .. 56'V'1 .. 00
0 .. 068 0 .. 1 93 0" 1 51
space
Exterior
A-C
0 .. 71-1 25
0 .. 088
0" 1 35 0 .. 120
orientation paraA-B-C 0 .. 15"",,1 .. 25
0 .. 085 o 1 31
O. 1 1 6
meters
each
*) res
1 error at control
indivisual image
were
ly
ined by
a resection method
of a single image..
4 stereoscopic pairs were
thereafter
selected to form the space models respectively, and object
coordinates of 2 kind of points, control and check points,
were computed. An example of the tests is shown below ..
Only 8 control points were used for the exterior orientation
5
in those and other 10 check points were selected
for estimating an error produced in each modelm Some of the
results are presented at Table 5, in which a relative depth
error means an
value
a ratio of standard error of
Z to Z .. Table
ws that the error is fairly small
throughout the
) and increasing a base ratio, which
results in convergent images, is effective for reducing an
error
iments of a Stereos
c Measurement
All data described in the previons sections were the results
which were obtained by measuring the targets on single images ..
Any result performed by a stereoscopic measurement is not yet
presented.. But the anthers had succeeded in stereoscopic
measurement by using a pair of rectified images, even in the
case of converged image pair A-C" The measureing method will
be explaned with the aid
another test
g..
s owns a differ t
test perform
in a room 1 2
s were pasted on a wall
in the extent of 15m width
and 1 .. 6 m height f r a
purpose of control points
The distance
the camera
to the wall was 3 9 m$ The
distances
the camera
tat ons and the
ects were
hanged f am exposu e
to
e posu e" Therefore
th
in ipal distance
f the
camera was al
so as
b
sui
g od
sing"
Measurement
coordinates
of a cen er f a target was
car ied out on ea h imag as
desc i
in Section 3 All
control
s signalized
5 Tes
s
F
c
targets
used fo
the
measurements
relat
s
Table 6
suIt of the relative
relative
orientation of selected stereo
orientation elements
pairs of image in Fig.
and the estimated
s a
rd error of an
b-e
Photo
b-c
a-b
observation of a
cente
in
-1 55 0
several models are
o 34' 4
shown in Table 6 ..
o
06' 1
Table 7 shows the
24 59/ 09"/
mean value of a
o 421 59""
relative depth error
in all 12 points
17m
2 .. 4 jA--m
s
.. From
the fact that the
errors
in Table
Table 7 Mean Value of relative
7 are simillar in
error of control
value to those shown
i
the
te t
in Table 5 and very
error is reasonably
small
it
is
re ognized that the
satis ctory results
are obtained
both
0.094
0 .. 1 4
0 .. 0 4
met
s the single
image orientation and
o 165 0 287 0 .. 241
the double imag
orientation But in
Table 7
it is not
I
evident that the error decreases
increases as usually indicated
as
se
ratio
BIz
6-
orientation, each original image was
rectified digitally by use of the relative orientation
elements from model to model so as to perceive a good
stereoscopic impression .. The bi-linear interpolation was
employed for the
tal image rectification.
A brief test concerning measuring accuracy was
out
with the aid of the rectified images. Location of the 12
nts indicated
the
s were again measured on
the rectified images by the same method described in
Section 3
And the locations of the control points were
computed from these data. The error of the computed control
points is also shown in Table 7 as to enable to compare with
the residual error at the absolute orientation.
It is evident and natural that latter computed error in
Table 7 is larger than the former residual error without
exception. In spite of such fact, the latter error indicated
is still rea
small This indicates that a considerably
precise photogrammetry will
able to be performed by use of
system pre
here.
oscop c
was rectifi d and
ing
of the dis
For
it may be effective in an usual
t
i w the rectifi
image
th ough
But in the case of view
of the screen in
hould not be magnified throu
I nses
ze on the screen appears too coarse to
perceive a corn
s
impression. The pixel size
of the s r
6 mm nd the maximum pixel size to enable
to feel a
r
opic perception was estimated as 1 .. 0 mm or
so without
ficat on from the
I
experience.
In order
a tereoscopical
presize measurement,
it s ne
ry to nlarge images on the screen becaus the
minimum m a uring un t 0 c
inates is pixel size(pitch) ..
Only on method to re liz it is to enlarge images and to view
them on th contrary, at a reduction ratio through lenses.
For realizing this method, however, t
fact that each half
the screen contains
256 pixels in width causes a
bottleneck as
lows. The
xel number of the screen was too
small to perceive a good stereoscopic impression from the
image pair
more than 3 or 4 times. Consider
these
experiences,
the
ratio
original image was
8
Test condition of stereoscopic
measurements
limitted within 2 and as to the viewing magnification, on the
other hand, the reduction ratio of 1 NO .. 7 was adopted in this
test. Table B indicates the notation and condition of the
test .. Fig .. 6 shows the examples of the image pair on the full
screen ..
There was another bottleneck in the system, which was caused
by the fact that only one cursor was provided in the display
unit. The cursor should be used for a measuring mark in this
system. Therefore, a yellow square mark was selected as a
cursor and anthor identical mark was produced in the image and
represented on the screen. If the 2 marks were placed on the
conjugate image points in question, a stereo model on which
the mark was placed was percei ved by the aid of a stereoscope ..
Even if such improvement had been performed, the new measuring
mark could not still be moved on the screen. Owing to such
limitation on mechanism, the stereoscopic measurement was
carried out from point to point.
6-S Test Measurements
Some results obtained from the test illustrated in Fig.S are
described below ..
Graduation marks of a staff which was placed in the xy-plane
were measured and the distance between graduations were
(a) TV, original scale
(b) upper part of a large
cylinder, x3
Fig.6 Stereogram of Model b-e on the screen
Table 9
Distance measurement between gradnations of a
staff which is placed in the xy-plane (by the
method T1-1 .. S)
(mm)
Distance in a staff 1S0
SOO
600
BOO
200
300
Distance
799 .. S
300 .. 1 499.4
a-b
measured
S9B.9 BOO .. 1
b-c
200 .. 3
in the model of b-e 14B .. 4
B0 1 .. 1
301 .. 9
computed. The distances obtained from the test are in good
agreement with those of staff as showm in Table 9 .. The image
scale of the staff was 1 : 85 .. Consequently, an error 1 mm in
the object space corresponds to an error 0.012 mm on the
image ..
The 2nd example is a measurement of front edges of a
television frame .. Corners and several points on the edges of
the frame were measured stereoscopically in 3 models. An
average of edge lines and the deviation from the average were
computed from the measured coordinates.. Fig.7 shows the
deviation of the measured edges in 2 models. The acuracy is
not good enough throughout the test. But, through a detail
(a)
( c)
Z,
at test T1-1 .. 5
L.-.
Z,
at test T2-0.7
________ _
'-----------y
I
I
I
I
I
Z
(b)
o model a-b
xand y,
• model b-e
deviation
o 10 20 30mm
at test T1-1.5
I
L _________ .
I
I
I
I
Fig.7 Deviation from the average edge lines
300
350
400
450
500
-11----------~I~--------~I----------+I----------~I-------e X(mm)
~
.~- ___ .....
--:::~~"~~:~~,:;~.,A
-~ .. - ....~-~---
Model
test
------------ ......... --~~ ...... -...
/'
... ----... a -b Tl -1 .5
. . . . . "at(;
.dr-----.A b-c
Tl -1 .5
. - - - a-b T2-0. 7
~ b-c
T2-0.7
,.,&-.. _-..
310
380
390
400
410
Z(mm)
Fig.8 Horizontal section measured stereoscopically
inspection
7 (a) and b) it seams that the deviation in
model b-e is small
regular It sugge ts that the accuracy
in model
which is
from the
conve
images, is best. Comparing Fig 7 (c) with (a), it is eviend
that the accuracy of Test T -0 7 i
better than that of Test
T1 -1 ,,5 ..
As the 3rd example, a measurement of an upper part of a
large cylindrical
shown in Fig.5 were carri
out. Fig.8
shows the measured horizontal cross section in the 2 models
with the 2 differ nt meth
s of viewing The error pr uc
from the method T2 0 7 s distinctly smaller than hat from
the method T1 1 5 in this case,
00
7
Conclusions
On
a general-purpose
peripherals were used,
any
s
s
in this
Nevertheless
works necessary to stereoscopic photogrammetry have been
ac
i
The mea sur
accuracy in di tal process
is
fairly good in this test and also it is evid nt that a high
accuracy will be achieved
improving a display unit The
most
ffi
t task to be overcome will be to
a cursor
currently used into a mechanism which is as convenient as a
stereo-plotter
The u~
of rectified images is advantageous for stereo
technique is important for
maching
The stereo mach~
automation of
me
not dealt with in
)
is also excluded.
this
Real time
1
BIBLIOGRAPHY
1) J"Albertz and G.. Koenig
A Digtal stereo
togrametric
System, Int. Archives of P & RS Vol.25/2, pp 1-7(1984}.
2) B"Kunji :
ments in Digital Processing
Photogrammetric Images, ibed., pp.298-303(1984) ..
3) K.. W.Wong : Close-Range Mapping with a
id State Camera
Photogramm. Eng. and Remote Sensing Vol 52 pp,,67-74(1986)
4) S.Hattori, C.. Mori and O.Uchida : A Coarse-to-Fine Correlation Algorithm Considering Occulusions
s of P &
RS, Vol .. 26, 3/2, pp.317-328.
5) H.. Schewe : Automatishe
metrische Karossrie-verme
sung, Bildmessung und Luftbildwesen, 56
, pp .. 16-23(1988) ..
6) K"W.Wong : Real Time Machine Vision
tern, The Canadian
Surveyor, Vol .. 41, pp .. 173-180(1987)
7) AaW.Gruen and
Real Time
the
tal Photogrammetric Stat
(DIPS)
pp .. 181-199(1987}.
8) H.Haggren : Real Time Photogram
as Used for
Vision Applications, ibid, pp 201-208(1987) ..
1