In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B
With the given rotation matrices the normal vector for the coil
front v cn and the normal vector for the triangular shaped area
spanned by the laser v Ln can be calculated in the fixed-place
coordinate system, shown in Eqns 9 and 10.
(°\ ( sin (^) \
VLn= R a ■ Rp ■ E- f ■ o = sin(a) cos(/3) (9)
\lJ \cos{a) cos{(3) J
e <
Due to Eqn. 13 the gradient of the laser line k yx in the photograph
is dependent on the linear trend of the coil windings represented
by 9 and the laser rotation around the symmetry axis represented
by /3. Both angles affect the gradient k yx in the same way and
so an estimation using the Eqns 15 and 16 will fail because they
can not be determined seperately by a single measurement. The
solution to this problem is to make a reference measurement for
the skewness of the laser line related to /3 by using a plane with a
defined angle 9 instead of the coil front. A vertical plane as ref
erence (0 = 0°) allows to extract /3 from Eqn. 13, (see Eqn. 17).
(10)
/3 = — arctan (k yx {9 = 0°) sin(a)) (17)
0 = arctan (k yx tan(a) + (18)
Then the direction of the intersection vector u between the coil
front and the laser can be determined by the cartesian product of
the according normal vectors v cn and v Ln, shown in Eqn. 11.
Now the intersection of the coil front and the triangular shaped
area spanned by the laser, results in the visible laser line on the
coil with the coordinates (xl, Vl, zl). The intersection vector
u is a scaled version (by a factor u) of the laser line with the
same orientation, see Eqn. 12. Further the intersection vector u is
independent of 7 so the orientation of the laser line is independent
of an up or down tilting of the laser.
U = V L n X V C n
(H)
( XL \
yL = V U
(12)
\ZL
To eliminate the influence of the laser alignment and the linear
trend of the coil front the remaining angles ¡3 and 9 must be calcu
lated. Therefore the orientation of the laser line will be separably
examined in the y,ax-plane and in the y,z-plane. Due to the setup
the orientation of the laser line k yx in the y,x-plane is present in
the observable image scene in Fig. 9 and can be measured by a
trend estimation of the extracted laser line, the associated relation
of the laser coordinates yz, and xl is shown in Eqn. 13.
, _ Vl _ cos(o:) cos(/3) sin(6>) - sin(/3) cos(fl)
yX XL sin(a:) cos(/3) cos($)
The second laser line orientation k yz in the y ,2-plane is predeter
mined by the laser light section technique given by Eqn. 2 and the
associated relation of the laser coordinates yL and zl is shown in
Eqn. 14.
c yz — — = tan(</?)
zl
cos(a) cos(/3) sin($) — sin(/3) cos(9)
sin(a) cos(/3) sin($)
(14)
With Eqns 13 and 14 for the orientation of the laser line it is
possible to determine the remaining angles /3 and 9, shown in
Eqns 15 and 16.
Due the fact that the triangulation angle ip, and so a (= <p — 7r/2.)
is not constant with respect to /3, a slight error occurs. Despite the
fact that <p is influenced by /3, the approximation approach works
excellent to determine the laser alignment and the linear trend of
the coil front for values of /3 less than ±15°. For example a laser
rotation by /3 = —7.5° results in an error of 9 of less than 0.01°.
4 LASER LINE EXTRACTION ALGORITHM
Before the coil profil can be determined, the laser line must first
be extracted out of the image. Figure 10 shows a steel coil and a
laser line projected on it. Due to a rotation of the camera of 90°
(to obtain the profil length at a higher resolution corresponding to
the camera chip with 1392 x 1040 pixel) the laser line is horizon
tal in the acquired images. The laser line is clearly visible due to
the use of optical filter mentioned in Sec. 1.
200 400 600 800 1000 1200
Width in pixel
Figure 10: Post-processed image (for better contrast of the laser
line) of a steel coil with a laser line.
First of all the algorithm detects if a laser line is present in the im
age by simply accumulating intensities along rows and searching
for a clearly visible maxima. Also a first elimination of pack
aged coils and a rough estimation of the laser position is done.
For coils with packaging material a laser line extraction is mean
ingless and therefore an early elimination is preferable. After
the rough estimation of the laser position, the orignal image is
cropped to a vertical region around the laser. Then a median fil
ter with a rectangular mask (with 15x10 pixel) is applied at the
cropped image to reduce noise and to smooth the laser line, the
result is shown in Fig. 11.
/3 = - arctan (v (15)
0 = -arctan(j-7jyj (16)
The detection of the maxima positions is an easy way to extract
the whole laser line out of the cropped image. But due to the fact
that the horizontal position of the coils in the images can vary in
dependence on the coil size, the considered image area extends