Table Of ContentHand-guided 3D surface acquisition by combining simple light
sectioning with real-time algorithms
Oliver Arold · Svenja Ettl · Florian Willomitzer · Gerd H¨ausler
University Erlangen-Nuremberg
Institute of Optics, Information and Photonics
91058 Erlangen, Germany
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1 Abstract
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2
Precise3Dmeasurementsofrigidsurfacesaredesiredinmanyfieldsofapplicationlikequalitycontrolorsurgery.
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Often, views from all around the object have to be acquired for a full 3D description of the object surface. We
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present a sensor principle called “Flying Triangulation” which avoids an elaborate “stop-and-go” procedure. It
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combines a low-cost classical light-section sensor with an algorithmic pipeline. A hand-guided sensor captures
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a continuous movie of 3D views while being moved around the object. The views are automatically aligned
] and the acquired 3D model is displayed in real time. In contrast to most existing sensors no bandwidth is
s wasted for spatial or temporal encoding of the projected lines. Nor is an expensive color camera necessary for
c
i 3D acquisition. The achievable measurement uncertainty and lateral resolution of the generated 3D data is
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p merely limited by physics. An alternating projection of vertical and horizontal lines guarantees the existence of
o corresponding points in successive 3D views. This enables a precise registration without surface interpolation.
. For registration, a variant of the iterative closest point algorithm – adapted to the specific nature of our 3D
s
c views – is introduced. Furthermore, data reduction and smoothing without losing lateral resolution as well as
i the acquisition and mapping of a color texture is presented. The precision and applicability of the sensor is
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y demonstrated by simulation and measurement results.
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Keywords 3D metrology · optical sensor · physical limits · hand guided · low cost · real time · registration ·
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iterative closest point · line indexing · texture mapping
[
1
1 Introduction monlyrestrictedbythetrackingsystem. Inthesecond
v
case,enoughoverlapandcommoninformationbetween
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4 the separate 3D views must be guaranteed.
Opticalsensorsallowafast,contact-free3Dacquisition
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1 of surfaces and become more and more the number- Wepresentasensorprinciplewhichavoidsa“stop-
. one choice for 3D metrology: Industry applies optical
1 and-go” measurement procedure. Instead, a simple
0 sensors for rapid prototyping and quality control. In multi-linelight-sectionsensoracquiresacontinuousse-
4 themedicalfield3Dmeasurementsprovidecrucialpre-,
ries of 3D views while being hand guided around the
1
intra-, and post-operative information for the surgeon.
: object. Overlap between consecutive views is guaran-
v Intra-oral sensors enable a comfortable way of manu-
teed. No tracking is necessary for an automatic align-
i
X facturingtoothcrowns. Inthefieldofculturalheritage mentoftheviews. Akeycharacteristicoftheproposed
optical 3D sensors are a helpful tool for restoration,
r sensor compared to other hand-guided systems is that
a documentation, and duplication of sculptures.
no bandwidth is wasted for spatial or temporal encod-
Most of these applications require 3D views from ing methods. The width of each projected line is as
many different directions to cover the relevant surface narrow as possible and as wide as necessary to allow a
of the rigid object under test. This leads to an elabo- precise subpixel localization. This leads to both high
rate and time consuming repositioning of the sensor or depthandhighlateralresolutionofeachcalculated3D
the object (see Figure 1). Furthermore, the acquired point. Butinreturn3Dpointsareonlyacquiredalong
3D views have to be aligned to each other to yield a fewseparatelines. Toourknowledge,mostotherhand-
complete3Dmodel. Thisalingmentcanbedonebyex- guidedsensorsystems abandonmeasurementaccuracy
ternal tracking systems or by registration algorithms. in order to obtain more dense 3D views and hereby al-
In the first case, the movement of the sensor is com- lowtheapplicationofwell-establishedsurfaceordense-
1
point-cloud registration methods for the alignment of 2.1 Hand-guided Sensors
the views.
The focus in this section lies on sensors and tech-
niques that enable all-around measurements of static
sensor positions
objects. Methods for the acquisiton or reconstruction
of dynamic scenes aim for different kinds of applica-
tionsandthusarenotdiscussed(Koninckxetal,2003;
overlap Kawasaki et al, 2008).
The “Artec 3D Scanner” is a hand-guided sensor
without need for external tracking (Suhovey, 2010). It
isbasedonlightsectioningandusesaspatiallyencoded
line pattern to increase the number of distinguishable
lines. A continuous stream of 15 views per second is
acquired. Due to the relatively high data density stan-
dard full-field registration methods can be applied to
automatically align the captured views in real time.
Colored texture can be captured and mapped onto the
object
data. Sincethelinesarespatiallyencodedboththelat-
Fig.1: Anall-aroundmeasurementrequiresanacquisition eral and longitudinal resolution are reduced and small
of views from many different directions details are not resolved.
Rusinkiewicz also describes a hand-guided sensor
In our case, a robust and precise real-time registra-
system based on light sectioning with an encoded line
tionoftheacquiredseriesofsparse3Dviewsisenabled
pattern (2002). In this case the pattern is temporally
byanalternatingprojectionoforthogonallinepatterns
encoded and projected onto the object by DLP tech-
and by applying a specifically developed algorithmic
nology. From each single camera image 3D data is cal-
pipeline. There is no need for surface interpolation
culated, but four consecutive images are necessary in
across the acquired line profiles. Furthermore, an on-
order to find the correct line indices. This leads to
time visualization of the current measurement result
a restriction of both sensor movement and object to-
provides the operator with information about not yet
pography: The sensor has to be moved slowly and the
acquired object areas.
object must not comprise high steps. A variant of the
The physical setup and optimization of the under- iterative closest point algorithm is applied to align the
lying light-section sensor and the basic measurement views in real time.
principle are described in Ettl et al (2012) and sum- Afurtherhand-guidedsensorbasedonlightsection-
marized in Section 3.1. The main focus of the present ing is described by Matabosch et al (2007; 2008). A
paper is a description of the algorithmic architecture, continuous stream of 15 views per second is acquired
which is the most crucial part of the suggested sensor and registered in real time. Each view contains 3D
principle. This comprises 3D data generation, line in- data along 19 separate lines. The correct indexing of
dexing, registration, visualization, data reduction, and theuncodedlinesrequiresthevisibilityofalllinesinat
texture mapping. Eventually, the sensor performance least one row of the camera image. This considerably
is evaluated by simulations and measurements. restricts both the object surface and the movement of
the sensor. Furthermore, the accuracy of the applied
registrationislimitedduetotheneedforsurfaceinter-
polation between the acquired lines.
2 Related Work
The “kolibri CORDLESS” is a hand-held sensor
system based on fringe projection (Ku¨hmstedt et al,
This section gives an overview of other hand-guided 2007). Foramorerobustanderror-tolerantphaseeval-
sensor systems and registration algorithms. The key uation a stereo approach is applied. Since a series of
characteristics are described and compared. Further- camera images is necessary to calculate 3D data both
more, the weaknesses that are overcome by the ap- sensor and object are not allowed to move during the
proaches in this paper are identified. acquisitionofone3Dview. Thismakesthesystemmo-
2
tionsensitive,butinreturneachviewprovidesfull-field resultmainlydependsontheprecisionandlocalcurva-
3D data. Instead of a continuous stream, views from ture of the acquired 3D data (Laboureux and H¨ausler,
distinct positions and directions are acquired. Due to 2001).
the employment of a fast projection unit with at least In our case, none of these methods can be applied
60fps,thesensorcanbehandheldwhileacquiringone directly, since we only acquire 3D information along
single view. To enable an automatic registration the few separated line profiles. For this reason a variant of
operator has to ensure sufficient overlap between the theICPspecificallyadaptedtothenatureofoursparse
acquired views. 3D views is presented in Section 5.
As described above, we aim for a sensor that ren-
ders none of these drawbacks: no waste of bandwidth
3 Flying Triangulation
by line encoding – and thus no sacrifice of lateral res-
olution, no restriction of sensor movement for correct
lineindexing, no“stop-and-go”procedure, andnosur- In this section, the measurement principle, the sensor
face interpolation to enable registration. setup, and the physical optimization of Flying Trian-
gulation is described.
2.2 Registration
3.1 Measurement Principle
The alignment of two 3D views is commonly split into
two steps. First, a coarse registration finds an initial The basic principle is depicted in Figure 2 (a). Two
transformation between the views. Then, a fine regis- linepatterns, whichareorientedperpendiculartoeach
trationimprovestheresultbyaniterativeprocedure. A other, are alternately projected onto the surface and
general overview over common registration techniques observed by a camera with at least 30 frames per sec-
isgivenbySeegerandLaboureux(2000)andSalvietal ond. Fromeachcameraimageasparse3Dviewconsist-
(2007). ing of line profiles is generated. The views are aligned
Mostcoarseregistrationtechniquesarebasedonthe in real time and the visualization of the current result
detectionofcommonfeaturesintheoverlappingregion serves as feedback to the operator.
of the views. Therefore, 3D neighborhood information
is necessary. Sch¨on and H¨ausler (2006) search for so-
3.2 Sensor Setup
called salient points in both views and map them onto
each other. A method especially developed for tech- Thesingle-shotsensorisbasedonthewell-knownlight
nical surfaces with planar parts is presented by Maier sectioning illustrated in Figure 2 (b): Lines are pro-
and H¨ausler (2006). Johnson and Hebert (1997) and jected onto the surface of the object and observed
Kaminski et al (2007) present approaches suitable for by a camera under a triangulation angle θ. From
free-form surfaces. For Faugeras and Hebert (1986) the displacement ∆u of the lines in the camera im-
and Stein and Medioni (1992) lines, surface parts or age the depth ∆z is calculated. This calculation is
objects serve as features and are used for an initial done by using the calibration technique described in
mapping. Gelfand calculates descriptor values based Section 4.2. No spatially or temporally encoded pat-
on local geometry to identify common features in par- tern is employed. As a result, each acquired 3D point
tially overlapping views (2005). provides high precision and high lateral resolution, as
For the fine registration of two point clouds most shown below.
often methods based on the iterative closest point al- Since there is a considerable spacing between the
gorithm (ICP) are used. The ICP was first introduced line profiles, no dense surface information is obtained
by Besl and Chen (1992; 1992). Further improvements in one single 3D view. Therefore, a trick is applied,
weregivenbyZhang(1994). Acomprehensiveoverview which makes an accurate registration of subsequent
is given by Rusinkiewicz and Levoy (2001). The key sparse views possible: Instead of one single projection
idea of the ICP algorithm is to find corresponding unit, two projection units are integrated in the setup
points in two overlapping views. In each iteration the (see Figure 3). One projects a vertical and the other
points closest to each other are assumed to correspond a horizontal line pattern. A detailed description of the
and the best mapping transformation in terms of least registration algorithm, specifically developed for this
squares is calculated. The accuracy of the registration purpose, is discussed in Section 5.
3
Fig. 2: (a) Flying Triangulation principle. A multi-line single-shot sensor generates a series of sparse 3D views. The views
are aligned to each other in real time to yield a complete and dense 3D surface model with high lateral resolution. (b) The
single-shot sensor is based on triangulation. A line pattern is projected onto the object and observed by a camera under a
triangulation angle θ. From the displacement ∆u of the line in the camera image the depth ∆z can be calculated
Fig. 3: (a) Basic hardware setup. Two illumination units (V and H) alternately project vertical and horizontal lines into
the measurement volume. One observation camera (OC) acquires a continuous series of images for the 3D data generation.
A texture camera (TC) captures colored texture images. (b) Sketch of the triggering signals for the illumination units and
cameras
3.3 Physical Optimization cause of measurement uncertainty for a light-section
sensor is speckle noise:
In order to achieve the highest possible precision the
setup of the sensor is physically optimized. The key
C λ
aspects and parameters that have to be taken into ac- δz = , (1)
2π sinu sinθ
count are summarized. A more detailed discussion is obs
given in (Ettl et al, 2012). where C is the speckle contrast, λ the wave length,
sinu the observation aperture, and θ the triangu-
obs
According to Dorsch et al (1994) the fundamental lation angle. Unfortunately, most of the parameters
4
cannot be chosen independently. Thus, trade-offs have ment uncertainty in the z-direction, the ability to lat-
to be made to minimize the measurement uncertainty erally resolve small shape details in 3D space is an im-
within the entire desired measurement volume. portant feature of 3D sensors. This will briefly be dis-
A high observation aperture sinu reduces the cussed:
obs
specklenoise,butalsodecreasesthedepthoffocusand Perpendicular to the lines, only lateral details big-
therebyleadstoahigheroutoffocusmeasurementun- gerthanthewidthw oftheprojectedlinesontheob-
0
certainty. jectsurfacecanbereliablymeasuredandresolved. For
Since the sensor should be able to measure deep gaps example: to measure two grooves oriented in the line
without being restricted by shadowing effects, the tri- direction, these grooves must have a distance (pitch)
angulation angle is limited. Experiments have shown not smaller than 2w (we assume properly band lim-
0
that for most applications a triangulation angle of ited grooves). So, for the lateral resolution in a direc-
about 7◦ is a good compromise. tionperpendiculartothelines,thewidthw shouldbe
0
For a motion-robust acquisition the exposure time as small as possible.
texp for a single 3D view should be below 30ms. Thus, However, the pixelated camera image of the pro-
light source and apertures have to be chosen to pro- jected line, with a width w(cid:48), must allow a precise sub-
0
vide sufficient light. Again, one has to bear in mind pixel localization of the line signal. This is guaranteed
that larger apertures reduce the depth of focus. if the camera imaging satisfies the sampling theorem.
The remaining option to minimize speckle noise is A proven and tested approach is that the full-width-
the reduction of the speckle contrast C. For this pur- half-maximumdimensionofthelinesignalatthecam-
pose, the following strategies are applied. First, no era chip covers at least 3 pixels. This corresponds to a
lasers are employed. Instead, white-light LEDs and minimumtotallinewidthw(cid:48) ≈4p,wherepisthepixel
0
lithographicpatterns are usedfor the projection ofthe pitch. This optimal line width will allow for the best
lines. The low temporal coherence of the white light possible resolution.
helps to reduce the temporal speckle contrast in the In practice, due to the limited depth of focus, the
presence of volume scattering. This way, the signal-to- linewidthattheobjectvariesalongthez-axis. Forthe
noise ratio can be improved by almost a factor of 10 face sensor, the line width ranges from about 800µm
compared to laser illumination. If necessary, system- to1200µmand, fortheintra-oralsensor, itvariesfrom
atic height errors due to strong volume scattering can about 80µm to 180µm. This corresponds to a line
bereducedbysprayingthesurfacewithtitaniumdiox- width w(cid:48) at the camera chip of 4p-6p, respectively 4p-
0
ide. The thickness of the sprayed layer is about 20µm. 9p.
Since its surface roughness is still larger than the co- Theseconsiderationsarevalidbothforthehorizon-
herence length of the white-light source, the speckle tal and vertical lines.
contrast is still low. Furthermore, for a reduction of Westillhavetoestimatethelateralresolutionalong
the spatial coherence the setup comprises an illumi- the line direction. Principally, this is not much differ-
nation aperture larger than the observation aperture ent. A properly designed camera should satisfy the
(H¨ausler, 2003). Again, the choice is limited by the sampling theorem in any direction. So the camera im-
desired depth of focus. ageoftheprojectedlines(and,hence,thedetailsofthe
Considering all these aspects, we implemented a 3D object structure) is smoothed along the line direc-
sensor for objects like faces or sculptures with a mea- tion in the same way as across the line direction.
surementuncertaintyoflessthan120µminsideamea- It remains to be mentioned: If the line width at
surementvolumeofabout150mm×200mm×100mm. the camera chip is bigger than the minimal allowed
Figure4displaysthesensorandtheachievedmeasure- line width 4p, the lateral resolution along the line di-
ment uncertainty along the depth of the measurement rection is different from the resolution across the line
volume. direction: The latter is given by the line width itself
For the measurement of (sprayed) teeth we imple- (as explained above), while the resolution along the
mented an intra-oral sensor with a measurement un- line direction is given by the point spread function of
certainty of less than 30µm within a measurement the camera lens. So it may happen that the resolution
volume of 20mm × 15mm × 15mm. forgroovesperpendiculartothelinedirectionisbetter
than the resolution across the line direction.
It should be noted that besides a small measure- To conclude: For the best possible lateral resolu-
5
Fig. 4: (a) Picture of the sensor during a measurement. (b) Measurement uncertainty in µm depending on depth in mm
within the measurement volume
tion,thewidthofeachprojectedlineshouldbeassmall mainlydependsonthelocalizationoftheselines. Since
as possible. At the same time, the width of the line theobservedimagesarepixelated,aninterpolationhas
signalsatthecamerachipmustnotbesmallerthanal- to be used to calculate subpixel-precise localizations.
lowedbythesamplingtheorem,inordertoachievethe We apply the well-known three point Gaussian inter-
minimal measurement uncertainty in the z-direction. polation. This is a reasonable choice given the inten-
Table 1 summarizes the most important specifica- sity profile of a line being similar to a Gaussian curve.
tions of the face sensor stemming from physical opti- Figure 5 illustrates the interpolation and localization
mization. More details about the intra-oral sensor can process. Additionally, in order to reduce the influence
be found in Ettl et al (2012). ofnoise,theintensityprofilesofthelinesaresmoothed
byanarrowGaussianfilterbeforethecalculation. The
Table 1: Physical specifications of the face sensor.
localization is performed for each row (in case of ver-
tical lines) or each column (in case of horizontal lines)
Light source White-light LED
of the camera image. With the proposed method and
Measurement volume 150×200×100mm3
realnoiseastatisticallocalizationuncertaintyofabout
Triangulation angle 7◦
one seventh of a pixel has been achieved which cor-
Vertical Lines 12
responds to the achieved measurement uncertainty of
Horizontal Lines 9
δz ≈ 120µm (face sensor) and δz ≈ 30µm (intra-oral
Measurement uncertainty < 120µm
sensor).
Pixel resolution ≈ 200µm
Line width 800µm-1200µm
I
maximum position
4 3D Data Generation
In this section the calibration and the challenges of chosen points
for interpolation
calculating correct and precise 3D data from each in-
dividual camera image are described.
px
4.1 Line Localization
Fig. 5: A Gaussian bell curve is fitted to the intensity
As mentioned in Section 3.2, for light sectioning 3D
profile in order to localize the line with subpixel precision
data is calculated from the positions of the lines in the
camera images. Thus, the measurement uncertainty
6
4.2 Calibration 4.4 xy-Calibration
The calibration of the sensor system enables the cal- The lateral calibration allows the calculation of the
culation of 3D data from the line position obtained lateral coordinates of the acquired 3D points. In the
by the localization process described above. Most es- proposedapproachthecoefficientsofthefollowingtwo
tablishedcalibrationmethodsforcamera-projectorsys- polynomial transformations are determined:
temsperformamodel-basedintrinsiccalibrationofthe
camerabutlackacorrespondingintrinsiccalibrationof x=X(u,v,z)=a0+···+a17u3+a18v3+a19z3, (3)
the projector. The distortion of the projected pattern
caused by the imaging system of the projector is ne- y =Y(u,v,z)=b +···+b u3+b v3+b z3, (4)
0 17 18 19
glected. For the light-sectioning sensor proposed in
this paper a model-free calibration is applied which where (x, y) is the desired lateral position in the 3D
incorporates the intrinsics of the imaging systems of spaceand(u,v)thesubpixel-precisepositionoftheline
camera and projector. The methhod can be split into in the camera image. For this purpose, camera images
two parts: a z-calibration for the calculation of depth ofaplanarsurfacewithbrightdotsareacquiredatthe
values and an xy-calibration to obtain the right met- samez-positionswhichwereusedforthez-calibration.
ric along the x- and y-axis. The z-calibration has to Figure6(b)demonstratesthisapproach. Sincethepo-
be calculated for both the vertical and horizontal line sitions of the dots are known in 3D space and can be
projection. localizedinthecameraimageswithhighprecision,one
can again set up an over-determined linear system of
equationstocalculatethedesiredcoefficientsbymeans
of least squares.
4.3 z-Calibration
The z-calibration procedure is explained for the verti-
4.5 Inverse Lateral Calibration
cal line pattern only, since the horizontal calculation is
basically the same.
Additionally, the color camera for the acquisition of
Goal of the proposed z-calibration is the determi- texture information has to be calibrated. The pro-
nation of polynomial transformations Zn with cedure is basically the same as the described xy-
v
calibration, only this time the inverse transformations
have to be determined:
z =Zn(u)=an+bnu+cnu2+dnu3, (2)
v v v v v
wherezisthedesireddepthvalue,nisthelinenumber, u=U(x,y,z)=a +···+a x3+a y3+a z3, (5)
0 17 18 19
v the row of the camera image and u is the subpixel-
precise position of the line signal in the camera image
v =V(x,y,z)=b +···+b x3+b y3+b z3, (6)
(see Section 4.1). For every line n and every row v the 0 17 18 19
set of polynomial coefficients (a,b,c, and d) is deter-
where (x, y, z) is the position of a point in 3D space
mined. This is necessary in order to eliminate errors
and (u, v) the desired projection of the 3D point onto
due to optical distortion. For the calculation of the
thepixelplaneofthecolorcamera. Moredetailsabout
transformation Zn the line pattern is projected onto
v the texture acquisition are given in Section 6.2.
a sprayed planar mirror that stands perpendicular to
thez-axis. Atseveralknownz-positionswithintheen-
tire measurement volume a camera image is acquired. 4.6 Line Indexing
Figure 6 (a) illustrates this procedure. Since the val-
ues for z, n, u and v are known or can be determined, During a measurement process the calibration data is
an overdetermined linear system of equations for each used to calculate a 3D view from each camera image.
transformation Zn can be set up and solved by means Itisimportantthateverysinglepartofalinehastobe
u
of least squares. Finally, Equation 2 can be used to labeled with the right line index n to yield correct 3D
calculatethedepthvaluesforarbitrarylineswithinthe data. The more lines are projected, the more difficult
measurement volume. this will become (see Figure 7).
7
Fig. 6: (a) z-Calibration: A sprayed planar mirror is moved along the entire measurement depth. At known z-positions
between zstart and zend camera images with the projected line patterns are acquired. (b) xy-Calibration: A plane with a
spotpatternismovedalongtheentiremeasurementdepth. Atknownz-positionbetweenzstart andzend cameraimagesof
the spot pattern are acquired
projector camera
camera image
measurement
1 2 3
volume
1 2 3
areas of uniqueness
Fig. 8: Inside the measurement volume every line is ob-
served in a unique area on the camera image
Fig. 7: Indexing: (a) Every line or part of a line has to Sinceitishardlypossibletoguaranteethattheob-
be labeled with the right number to generate correct 3D ject under test stays inside the measurement volume –
data. (b) This becomes more difficult, the more lines are especially during a hand-guided measurement – a fur-
projected
ther method is performed to detect and discard out-
liers. Due to the restricted depth of focus of the il-
lumination and observation, the width of an observed
line signal depends on its z-position. Specifically, out-
side the arranged measurement volume, the lines be-
As we have already emphasized, no spatial or tem- come considerably wider. A robust estimation for the
poralencodingmethodsareused,sincewedonotwant line width can be easily obtained using the Gaussian
to decrease the qualitiy of the acquired 3D points by interpolation described in Section 4.1. Unfortunately,
wasting bandwidth. Instead the basic idea for the in- the broadening effect is happening continuously which
dexing process is as follows: The sensor setup and the makesithardtoidentifyoutliersbytheirabsoluteline
number of lines are chosen in a way that for objects width. Thus, a trick is applied. In the z-calibration
inside the measurement volume every line is observed not only transformations for the depth values but also
in a unique area on the camera image. That way, find- transformations for the width of the lines are stored.
ing the right index for a line gets trivial. This works During a measurement, the observed width of a line is
onlyaslongasthelineisobservedwithinthemeasure- normalized using the corresponding calibrated value.
ment volume, otherwise lines can leave their unique If a line is labeled with a wrong index, a false normal-
area. Figure 8 illustrates this indexing approach. ization factor is used and the normalized width differs
8
more distinctly from the width of a correctly indexed registrationdeterminesforeachviewithetransforma-
line. As depicted in Figure 9, outliers become even tion S that maps the particular view to the so-called
i
more distinguishable, if the illumination and observa- world coordinate system. The world coordinate system
tion are focused in front of the measurement volume. correspondstothesensorcoordinatesystemofthefirst
This way, a discrete step in the normalized width ap- acquiredviewofthespecificmeasurement. Inthiscase
pearswhenalineisobservedoutsidethemeasurement the transformation S of the first view is simply the
1
volume. Of course such an asymmetric focusing re- identity matrix. Figure 10 (a) illustrates the registra-
duces the signal-to-noise ratio and leads to a slightly tion task. For real-time application each view i is reg-
higher measurement uncertainty at the deeper part of isteredtoitspredecessori−1. Thisyieldsthetransfor-
the measurement volume. mation T . The absolute transformation S is then
i−1,i i
given by:
in front of MV inside MV behind MV
line width varies S =T ·T ·T ·...·T . (7)
i 1,2 2,3 3,4 i−1,i
with depth
Afterthemeasurementaglobaloptimizationisused
normalization toregistertheviewswithoutusingsuchapreferredor-
factor der.
normalized
5.2 Modular Architecture
line width
<1 =1 >1
In order to enable real-time capability, modern multi-
Fig. 9: The width of an observed line in a camera image coresystemsareexploitedbyseparatingthealgorithms
depends on the depth of the measured object part. The and workload in different modules which run in paral-
normalized width remains constant as long as the line is
lel. Figure 10 (b) gives an overview of the underlying
observed inside the measurement volume (MV). If a line is
algorithmic architecture of the modules. The number
observedbehindorinfrontoftheMV,itsnormalizedwidth
of parallel working modules can be easily adapted to
becomes significantly larger or smaller
the available computing power.
5 Registration and Visualization
5.3 Alternating Line Patterns
This section describes the algorithms for a robust As shown in Section 3 the sensor acquires 3D points
real-time registration and visualization of the acquired with high lateral and longitudinal resolution, but only
views. Moreover, an iterative global optimization for along the projected multi-line pattern. Between the
improving the registration result off-line is presented. lines no data is obtained. Since, the sampling theorem
The key ideas and concepts are summarized and indi- iscommonlynotsatisfiedforasingleview(becausethe
cated in a symbolic representation. Due to the limited lines are too far apart), there is no possibility to cal-
space, details are avoided. culate reliable surface information in between. If the
sensorismovedaroundtheobjectandineachview3D
dataisonlyacquiredalongthesamelinepattern,there
5.1 Problem Assignment
isingeneralnoorveryfewcommoninformationintwo
First of all some general information and definitions consecutiveviews(seeFigure11a). Forthisreasonwe
are given for a better understanding of the concepts apply a trick: By alternate projection of vertical and
and algorithms. The calibration of the sensor estab- horizontal lines and thereby an alternating acquisition
lishes the so-called sensor coordinate system, in which of 3D views with vertical respectively horizontal line
the acquired views are described. During the measure- profilestheexistenceofcorrespondingpointsinconsec-
ment procedure the sensor and the connected sensor utive views is guaranteed. Figure 11 (b) demonstrates
coordinate system are moved. This means the coor- this concept. The common 3D points can now be used
dinate systems of different views do not match. The toenablearobustandpreciseregistrationoftheviews.
9
Fig. 10: (a)ThegoaloftheregistrationistofindtheabsolutesensorpositionandorientationS foreveryacquiredviewi.
i
Therefore,eachviewisalignedtothepreviousone(s). (b)Foranefficientreal-timeperformanceonamulti-coresystemthe
algorithms are separated in different modules which can run in parallel
Fig. 11: (a) 3D data is only acquired along the projected lines. Thus, no surface information between the lines is available
forregistration. (b)Thereareingeneralnoorveryfewcommonpoints,ifonlyviewswithverticallineprofilesareacquired.
The alternating acquisition of vertical and horizontal line profiles ensures the existence of several corresponding 3D points
10
