For points, corresponding energy is :
© RG uM RV
En = hr AA Et
p=] R( $-T. R(P, — T).
(13)
Finally, expression to minimize will be :
x n1 p | y
E — sen Ei + rg a (14)
1 2
c, and c» express expected standard deviation on estimation of
segments and points. They balance relative importance between
points and segments during compensation.
4 SYSTEM RESOLUTION
It is quite clear that equations (8), (9) and (10) are non-linear
with respect to R and T. This entails linearization , which is done
with a formal calculator, and iterative estimation. At each itera-
tion stage, global energy E in equation 14 is minimized through
Gauss-Newton algorithm.
Equation (5) is applied to each 2D segment end. So, one matching
gives two constraints. To solve the system for R and T, e.g. seven
unknowns( we use quaternion representation for rotation), with-
out points, four segments minimum are necessary. Of course, in
most cases, four segments are not enough : they could be copla-
nar or/and parallel.
4.1 Approximate solution
Classically, resolution by linearization requires to find an ini-
tial estimate close to function global minimum. Approximate
solution is achieved by space resection on three or more well-
distributed matched points.
Visualizing clouds under an image topology The perception
of objects structures and limits from point cloud is difficult and
not very appropriate in a 3D viewer, even if the operator is well
trained. A way of representing the 3D points acquired from one
laser scanner station is an image topology. Indeed, scans are an-
gular resolution constant. This representation has major advan-
tages, c.g. ability of visualization of huge clouds, but the one
among all is the casiness of interpretation.
Image topology is recovered from scan angular resolution : from
points in Cartesian coordinates, we need to go to spherical co-
ordinates to produce a range image. We estimate scan angular
resolution looking for couples of consecutive points.
Then, we can plot points into this image, where each pixel cor-
responds to a 3D point. As for each scanned point, we have got
on top of coordinates, retro-diffusion information (coming from
the laser beam signal) and radiometry (coming from the low res-
olution camera), we can create clearer images (see Figure 3) and
select points into these images. From geometry, we can also com-
pute images more understandable, such as normal image, shaded
range image or distance to principal plane. Small 3D details are
perfectly highlighted in the range image by shading the surface.
The retro-diffusion image also provides complementary very de-
tailed information. We can then switch over different layers to
choose point position.
Accuracy of points plotted into these images obviously depend on
scan resolution. As system converges well from initial estimate
rather far from final solution (Kumar and Hanson, 1994), the
problem of finding approximate solution is not so crucial. Nev-
ertheless, initial solution remains important for matching reasons.
1132
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
Figure 3: Laser data in image topology : retro-diffusion image.
4.2 Points matching
We carry out points matches by correlation between retro-
diffusion image and intensity image. Since we have got approx-
imate solution, we can project laser points into image and com-
pute a new image holding radiometry RGB mean value. We call
it intensity image. À pixel from intensity image points at 3D co-
ordinates. The same pixel in retro-diffusion image points at the
same 3D coordinates.
Feature points extraction in intensity image is then achieved using
Harris detector (Harris and Stephens, 1988). Generally, far too
much corners are extracted. Since for some scenes most of the
"strongest" corners are located in the same area, this scheme is
refined further to ensure that in every part of the image a sufficient
number of features is found. To achieve this, image is divided into
a regular grid. For each area, the corner with the maximum value
is selected. The number of areas can be tuned to yield the desired
number of features.
Assuming that homologous point should lie near from its
counterpart in intensity image, because of the fine approximate
solution calculated, we look at it in retro-diffusion image in
a window centered on the Harris' point. Correlation value is
calculated for each window's pixel. The maximum correlation
score position is considered as the matched point. To get a better
estimate of this position, interpolation in the correlation window
would bring matched point's subpixelar position.
Figure 4: Gradient on digital and retro-diffusion image (right).
Intei
Sinc
bec:
is de
15x
edge
only
rj
—
ag
S
C
e
as
At
sh
wi
