an examples of the sensor’s performance. Chapter 3 de-
scribes the fundamental quantities characterizing the local
behavior of a surface and gives the mathematical formulas
to compute these quantities. In chapter 4 the actual clas-
sification and segmentation process is presented detailing
our approach to curvature approximation from range data.
The proposed approach is demonstrated on a test scenario
acquired with our sensor.
2 DENSE RANGE ACQUISITION
For dense surface measurement several alternative mea-
surement techniques are available. If the object’s surface
shows sufficient radiometric detail, image matching tech-
niques can be employed to recover surface geometry. How-
ever in most industrial cases surfaces are not very cooper-
ative with respect to texture detail. One method thus is to
use an artificial static texture pattern projected onto the ob-
ject by a slide projector. Instead of using a static 2D texture
pattern, one can just use a single spot, most often generated
by a laser beam, which is moved across the surface. Alter-
natively one-dimensional structures, most often a line, can
be projected. To speed up the process several lines can be
projected in parallel, leading to the method of coded light
projection.
All the methods mentioned above are triangulation based
methods. Completely different approaches use the time-
of-flight or interferometer principle to determine distance.
These approaches have just recently become popular in
close range applications now that several commercial laser
scanners are available on the market. While each of the
methods has its unique advantages and disadvantages, tri-
angulation has the best potential for accurate measurement
at very close distances. Because of the speed of mea-
surement a stripe projection system is the most frequent
choice for industrial applications in the measurement of
small parts and was thus chosen for our project. Since ev-
ery sensor system has its unique features and also unique
problems, we will detail below the sensor system we use.
2.1 Sensor Hardware
We use a LCD type projector for our experiments. The
line pattern is generated by switching lines on a two di-
mensional LCD backlit from behind. This type of pro-
jector has the advantage that there are no moving parts.
On the other hand, due to the LCD with polarizing filters,
brightness is inferior to projectors using metal coated glass
plates. While normal LCD stripe projectors use two glass
plates with conducting stripes aligned precisely, a cross-
pattern projector has one of the glass plates turned by 90
degrees. Since all stripes can be switched individually, ar-
bitrary vertical and horizontal stripe patterns can be gener-
ated (albeit no arbitrary 2D patterns can be generated, since
the 2D pattern always results from a XOR of the two line
patterns). In the context of a photogrammetric evaluation,
this means that the projector can be modeled as an inverse
camera delivering 2D 'image' coordinates. On the down
side, twice as many stripe patterns have to be projected per
sequence in order to obtain x and y coordinates.
Figure 1: The sensor hardware used for the experiments
consists of a LCD stripe projector and a digital camera.
The projector we use features a LCD with 640 x 640 lines,
line spacing of 0.09 mm (LCD size 57.6? mm, and a halo-
gen light source of 400W). Patterns can be switched in
14 milliseconds making it feasible to acquire images in
video realtime, although we do not use this option since
it requires hardware support. Commands and pattern se-
quences can be sent to the projector via a RS-232 interface.
The camera we use is a digital CCD camera with a resolu-
tion of 1300 x 1030 pixels and approximately 0.0067 mm
pixel size. Projector and camera are mounted on a stable
aluminum profile with a fixed relative orientation.
2.2 Sensor Calibration
Sensor calibration is a fundamental prerequisite for any vi-
sion system that relies on quantitative measurements of the
Observed scene. Although it is very common to calibrate
optical 3-D systems, like stripe projectors, by means of di-
rect calibration techniques (e.g. polynomial models) we
found it favorable to use model based calibration (Brenner
et al., 1999), where parameters of a geometric model of the
sensor, so called intrinsic and extrinsic parameters, are de-
termined. The fact, that model parameters hold true for all
the measurement volume of the sensor increases flexibil-
ity and omits problems with measurements lying outside
the volume originally covered by calibration. In addition,
residuals and the obtained covariance matrix give a clear
diagnosis for the determination of the calibration param-
eters and object point coordinates. The model parameters
describe how points in 3-D space are projected onto the im-
age plane, considering imperfect cameras and lenses. For
a camera this means to find appropriate values for the fo-
cal length, principal point position and lens distortion. If
a sensor consists of multiple components their relative po-
sition and orientation must also be determined. The stripe
projection systems are either modeled as inverse cameras
or used as an aid to establish point correspondences be-
tween at least two cameras e.g. the cameras of the stereo
head.
Despite the existence of techniques in photogrammetry to
simultaneously estimate these parameters during measure-
ment tasks, we are using a specially designed test object to
effectively compute the desired quantities from a few cali-
bration measurements. Since any short-term geometrically
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