cations in
ition and
this paper
al bundle
ield more
industrial
Noodham
based on
he object
ct surface
d to each
(1)
ve p; and
"pi, qi)
'e surface
ric Stereo
s should
ironment,
incident
normal),
eeds the
to be
source.
different
degree or
jy should
/ diffuse
nitations,
e in real-
round the
incident
e to be
t. Using
Jjustment
lved. The
tests at the laboratory environment have been done on
some objects types such as ; metal, plastic, wood, etc.
2. THE SYSTEM SPECIFICATIONS
The system which utilizes Photometrically Extended
Bundle Adjustment technique, consists of CCD camera
pairs for stereoscopic view, frame grabber in a PC,
laser six-point pattern generator (as it is shown in
Figure 1), rotating platform (to manipulate the object
for inspection from different views) and the light source
(filament lamp). Before recognition tasks, the CCD
cameras have to be equally calibrated. This should
contain ; principal distance determination, perspective
and lens distortion corrections and camera grey-scale
calibration. Some other minor corrections to frame
grabber jitter effects, CCD detectors location errors,
etc. may be neglected. During the recognition task,
each camera acquires the images in real-time
simultaneously even if the object is in motion.
Object surface —— ih
2°. D
ig 1 N
7 N
\
/ o \
E blam
J 5 oum
\ 6 !
\ /
M © o T
Sind 3 ut
Figure 1. Six-dots laser pattern
The stereoscopic data acquired by photogrammetric
system, unlikely to photometric stereo, contains only
the image coordinates of six-dot laser pattern (Figure
1). Matching of the corresponding points of pattern in
stereo images is very easy and suitable to real-time
applications due to shorter time requirement than full-
frame image processing. In next step, the image data
set contributes to Bundle Adjustment solution (simply
the solution of collinearity equations by iterations) and
the real XY Z cartesian coordinates of six-dots are
found with the camera orientation parameters. The
formulation of the link between image coordinates and
real cartesian coordinates is as below ;
EX LEX rr, 7 Yr -2Z.)
[206i X ria (Yi7 Yrs (Zi- 2.)
“=
Ta KiKa) +20 Y. tion (Zi -Z.)
[13 (X; - X.) c r4 (Y; 7 Y.) 33 (Zi - Z,)
(Moffit and Mikhail, 1980). The rj elements belong
to the Rotation matrix and contribute to the o, q, x
tilts of each image plane. Each element may be written
as follows :
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
Ig 7 COS COSK
Il27 -COS Q sink (3)
r3= sine
I21= Sin W Sin Q cos K t cosw sink
rm = -Sinw + sing sink + COSW COSK
3 = -SINW COS
I317 -COSW Sing cosK + sinw sink
[327 COSW sing sink + sinw cosk
[33 = COSW COS
In Equation 2, f : camera lens principal distance
(same for both cameras), Xs, Ys, Zs : perspective
center coordinates (camera locations), ri: the elements
of image rotation matrix, X,Y,Z : cartesian coordinates
of a single point on the object surface. For both
cameras, the collinearity equations are solved in
Bundle Adjustment algorithm. With the solution, the
local surface orientation parameters can be easily and
accurately determined since at least XYZ
coordinates of three surface points are already known.
In this case the average slopes of X and Y directions of
this local surface patch surrounded by the three
perpendicularly distributed points (such as points 5-4-
2) may be found as; p = dz / dx (along X direction) ;
q = dz / dy (along Y direction). This surface patch later
Will be illuminated by a circular pattern (with about 10
mm diameter) for surface quality inspection, which is
totally based on the analysis of surface reflectance
characteristics related to randomly selected pixels on
the corresponding image segment. The formulation of
reflectance map which corresponds to surface intensity
values for the ideal surface is as below ;
;- SC +AP, + 410.)
(4)
NIT Dd.
here, “g” is the surface reflectance factor, the vector
[ps, Gs, -1] points the direction of the light source. The
surface characteristics formulated above does not suit
to the practical applications nor does not give the
correct results at non-ideal conditions. To overcome
this, a data set acquired by the Photometrically
Extended Bundle Adjustment technique which contains
the surface patch orientation parameters (pi, qi ) and
the randomly selected pixel values of the surface
reflectance within the patch ( 1), gives us the planar
curves shown in Figure 2.
In the figure, each curve belongs to different type of
object surface. At the beginning of recognition task,
each object surface must be introduced once to the
system for object model curve achievement. To
realize this procedure, the object takes place on the
rotating plate and surface reflectance values are then
remotely acquired by a CCD camera (from 1-2 meter
distance) and recorded, with the corresponding
angles of the surface rotation. The data of graph,
likely to Figure 2, is to be stored in the data base.
