jject's surface
is not accept-
N
Cameras: The
often used in
iews. It works
aces, because
formation. On
he results are
c)
only used in
ed lines.
c)
only used in
rojector:
grid.
s: Here, each
| which comes
nformation re-
re be used to
| by each cam-
pattern is pro-
ojector pixels,
ion of camera
and projector, can be used to find a coordinate on the
object using triangulation. Regular patterns may also be
useful for image matching, but in most application these
patterns are projected by a calibrated device, so that
triangulation can be made with one camera.
intersection
point
stripe matrix
projector camera
triangulation base
Figure 9 : Camera-projector pair.
Here the lateral continuity in remission and height is also
important, because the image processing uses neigh-
boring pixels to find the center of the spot, the center
line(s) or the absolute phase of the sine grid [Tak82] (for
further explanation see 2.3).
To derive the local parameters of light remission and
finally to calculate the 3-D information at one pixel posi-
tion, all single pattern/single image measurement princi-
ples use the intensity distribution in small image areas.
This lateral image processing assumes lateral continuity
of remission and topology on the object surface. In addi-
tion, it reduces the lateral resolution of 3-D information
(for example: a 512 x 512 matrix camera cannot produce
512 independent 3-D coordinates !). This is not accept-
able in most industrial applications with non-diffuse and
non-smooth surfaces.
2.3 Sequential Light Processing
As mentioned before, one major problem of optical 3-D
measurement is the fact that the local remission of pro-
jector light from the object surface is a priori unknown. If
the camera is linear and the A/D converter clips hard
(255, for example), the digitized value g can be described
as
g 7 min (ur p, 255),
Where u is an unknown offset value from camera elec-
tronics or environmental light and r the remission factor
of the surface (Figure 10). Thus the projector intensity p
and therefrom the projector coordinate © cannot be
estimated from a single grey value.
The critical assumption of continuous surfaces can be
suspended, if we accept, that sensor and object have to
be kept in a fixed relative position, while the projector
produces sequential patterns and the camera digitizes
image sequences (Figure 11). This sequential concept is
applicable in almost every industrial reverse engineering
task (it would become a problem in robotics).
+ ideal
S
> transfer
3 function
>
> 9
5 tw
t = remission
D factor r
20 1
projector intensity p
Figure 10 : Different intensity transfer functions.
The common idea of all subsequent discussed principles
is the implicit or explicit estimation of the parameters u, r
and p from at least three grey values under different
projector light patterns. The simplest principle (which is
only good for explanation) is shown in Figure 11: project
black, white and a ramp and solve the linear equation
system g,=u+pr, g, = u+1r, g, = u+0r which
results in p = (g - g,)/(g, - g,). This is the simplest 3-D
sensor, where each pixel has independent range values,
but it’s range resolution is rather bad.
code position,
phase step, t
mage frame
time
y^ 14
>
code index, unwrapped phase,
space, projector coordinate
Figure 11: Temporal light encoding principle (left)
and the simplest pattern for grey calibration (right).
2.3.1 Phase Shifting with a Single-Frequency Pattern: À
great variety of interferometrical phase-shifting tech-
niques has been developed since the 70's [Bru74],
[Cre88]. Phase-calculating and phase-unwrapping algo-
rithms can also be used in triangulation-based sensors
where periodic patterns are projected [Zum87].
The advantage of a set of phase shifted fringes compared
to a single fringe pattern is the following: from three grey
values that are measured at the same pixel position, a
local phase can be evaluated, that is independent from
the lateral distribution of grey values. This local phase
value, which is always in the range (0, 2x) can be seen as
an absolute phase ¢ modulo 27, where ¢ corresponds to
the projector coordinate C. If the object surface is con-
339
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
