Stereoscopic Light Stripe Scanning: Interference Rejection,Error Minimization and Calibration

Geoffrey Taylor and Lindsay KleemanDepartment of. Electrical. and Computer Systems Engineering

Monash University, Clayton 3800Victoria, Australia

Geoffrey.Taylor;Lindsay.Kleeman@eng.monash.edu.au

Abstract

This paper addresses the problem of rejecting interfer-ence due to secondary specular reflections, cross-talkand other mechanisms in an active light stripe scannerfor robotic applications. Conventional scanning meth-ods control the environment to ensure the brightness ofthe stripe exceeds that of all other features. However,for a robot operating in an uncontrolled environment,valid measurements are likely to be hidden amongstnoise. Robust scanning methods already exist, but suf-fer from problems including assumed scene structure,acquisition delay, lack of error recovery, and incorrectmodelling of measurement noise. We propose a ro-bust technique that overcomes these problems, usingtwo cameras and knowledge of the light plane orien-tation to disambiguate the primary reflection from spu-rious measurements. Unlike other robust techniques,our validation and reconstruction algorithms are opti-mal with respect to sensor noise. Furthermore, we pro-pose an image-based procedure to calibrate the systemusing measurements of an arbitrary non-planar target,providing robust validation independently of rangingaccuracy. Finally, our robust techniques allow the sen-sor to operate in ambient indoor light, allowing colourand range to be implicitly registered. An experimentalscanner demonstrates the effectiveness of the proposedtechniques.

1 Introduction

Light stripe ranging is an active, triangulation-basedtechnique for non-contact surface measurement that hasbeen studied for several decades [22, 1]. By project-

ing a known feature onto the measured surface, activescanners provide a more robust solution to the measure-ment problem than passive ranging techniques. A re-view of light stripe scanning and related range sensingtechniques can be found in [13, 4, 5]. Range sensing isan important component of many robotic applications,and light stripe ranging has been applied to a varietyof tasks including navigation [19, 2], obstacle detection[12], object recognition for grasping [3, 21], and visualservoing [7].

The drawback of conventional single-camera lightstripe ranging techniques is that favourable lightingconditions and surface reflectance properties are re-quired, which allow the stripe to be identified as thebrightest feature in the captured image. However, therange sensor presented in this paper is intended for useon a humanoid robot operating in an uncontrolled do-mestic environment [24, 25]. Under these conditions,various noise mechanisms interfere with the sensor todefeat conventional stripe detection techniques: smoothsurfaces cause secondary reflections, edges and texturesmay have a stripe-like appearance, and cross-talk canarise when multiple robots scan the same environment.The motivation for this work was to develop a robustlight stripe sensor suitable for operation in these noisyconditions.

A number of techniques for improving the robust-ness of light stripe scanners have been proposed in otherwork, using both stereo and single-camera configura-tions. Mageeet al. [16] develop a scanner for industrialinspection using stereo measurements of a single stripe.Spurious reflections are eliminated by combining stereofields via a minimum intensity operation. This tech-nique depends heavily on user intervention anda pri-ori knowledge of the scanned target. Truccoet al. [27]

1

also use stereo cameras to measure a laser stripe, andtreat the system as two independent single-camera sen-sors. Robustness is achieved by imposing a numberof consistency checks to validate the range data, themost significant of which requires independent single-camera reconstructions to agree within a threshold dis-tance. Another constraint requires valid scanlines tocontain only a single stripe candidate, but a method forerror recovery in the case of multiple candidates is notproposed. Thus, secondary reflections cause both thetrue and noisy measurements to be rejected.

Nakanoet al. [18] develop a similar method to rejectfalse data by requiring consensus between independentscanners, but using two laser stripes and only a singlecamera. In addition to robust ranging, this configurationprovides direct measurement of the surface normal. Thedisadvantage of this approach is that each image onlyrecovers a single range point at the intersection of thetwo stripes, resulting in a significant acquisition delayfor the complete image.

Other robust scanning techniques have been pro-posed using single-camera, single-stripe configurations.Nygards and Wernersson [20] identify specular reflec-tions by moving the scanner relative to the scene and an-alyzing the motion of reconstructed range data. In [12],periodic intensity modulation distinguishes the stripefrom random noise. Both of these methods requiredata to be associated between multiple image, which isprone to error. Furthermore, intensity modulation doesnot disambiguate secondary reflections, which vary inunison with the true stripe. Alternatively, Clarket al.[6]use linearly polarized light to reject secondary reflec-tions from metallic surfaces, based on the observationthat polarized light changes phase with each specularreflection. However, the complicated acquisition pro-cess requires multiple measurements through differentpolarizing filters.

Unlike the above robust techniques, the method pro-posed in this paper uniformly rejects interference due tosecondary reflections, cross-talk, background featuresand other noise mechanisms. The proposed algorithmsolves the association problem to allow the true stripe tobe disambiguated from a set of noisy candidates. Thus,our method offers a significant improvement over pre-vious techniques for error detection, by providing bothnoise rejection andrecoveryof valid measurements.The depth data reconstructed by our stereo scanner isoptimal with respect to sensor noise (unlike the stereotechniques in [18, 27]), and fuses stereo measurementswith the light plane parameters. Thus, our sensor pro-

cameraright

leftcamera

positionencoder

laser diode

Figure 1: Experimental stereoscopic light stripe scanner

vides greater precision than a single-camera configu-ration, as demonstrated experimentally. Furthermore,we develop an image-based calibration procedure usinga scan of a non-planar but otherwise arbitrary surface.Our calibration procedure provides robust validation in-dependently of ranging accuracy. Finally, the ability ofour sensor to operate in ambient indoor light allows sur-face colour and range to be captured in the same cam-eras. Since the intended application is to support objectmodelling and tracking [24], this implicit registrationof colour and range is highly desirable. The system de-scribed in this work was first proposed in [26], and isextended here by providing a more rigorous treatmentwith respect to measurement noise.

The following Section briefly describes the hardwareconfiguration of our stereo stripe scanner. Section 3develops the underlying framework for optimal noiserejection and reconstruction. Image-based calibrationof the system is described in Section 4. Implementa-tion details are discussed in Section 5, and Section 6presents experimental results to compare the perfor-mance of our system with other stripe scanning tech-niques.

2 Overview

2.1 Basic Operation

Figure 1 shows the components of the experimentalstereoscopic light stripe scanner, which is mounted on apan/tilt active head. A vertical light plane is generatedby a laser diode module with a cylindrical lens, and is

2

light planeaxis ofrotation

lightplane

left cameraframe

L

viewing direction

right image

left imageplane

plane

b

f

b

Rright cameraframe

Ccameraframe

θz

θy

Plight planeframe

Z0

X0θx

CR

CL

y

y

y

x

x

x

z

Figure 2: Light stripe camera system model.

scanned across a scene by rotating the laser about a ver-tical axis. The angle of rotation is measured by an opti-cal encoder connected to the output shaft via a toothedbelt. PAL colour cameras capture stereo images of thestripe at 384×288 pixel (half-PAL) resolution.

Captured image are processed to extract all possiblelocations of the light stripe on each scanline. Scan-lines typically contain multiple candidates, with thetrue stripe (primary reflection) hidden amongst spuri-ous measurements. The true stripe is identified on eachscanline by searching for the pair of stereo measure-ments most likely corresponding to the projection of a3D point on the light plane, given the current encodermeasurement. The validation process is detailed in Sec-tion 3. Finally, the validated measurements are used toreconstruct the 3D profile of the illuminated surface.

As the stripe is scanned across the scene, the laserprofiles are assembled into an array of 3D points, whichis referred to as arange map. A colour image is cap-tured and registered with the range map at the comple-tion of a scan. Captured frames are processed at PALframe-rate (25 Hz) on the 2.2 GHz dual Xeon host PC.Motor control and optical encoder measurements areimplemented on a PIC microcontroller, which commu-nicates with the host PC via an RS-232 serial link.

2.2 Coordinate Frames and Notation

The following sections adopt the convention of repre-senting 3D points in upper-case, such asX, and 3Dpoints on the image plane using lower-case, such asx,with all vectors inhomogeneouscoordinates. Coordi-nate frames are specified in super-script, such asAX,

and the homogeneous transformation matrixBHA trans-forms points from frameA to frameB asBX = BHA

AX.Figure 2 shows the relevant coordinate frames for theexperimental scanner:L andR denote the left and rightcamera frames,P is rigidly attached to the light planeandW is the world frame.

The cameras are modelled by the 3×4 projection ma-tricesLP andRP, which project points from the worldframe onto the image planes according to the homoge-neous transformationL,Rx = L,RPWX. The cameras arearranged in a rectilinear stereo configuration (parallelaxes and coplanar image planes), with optical centres atCL,R = (∓b,0,0)> (taking the negative sign forL andpositive forR) in the world frame. In practice, the cam-eras can verge about they-axis (violating the conditionsof rectilinear stereo) but rectilinear measurements arerecovered by applyingprojective rectificationto cap-tured frames (see [10]). Thus, without loss of gener-ality, the analytical models consider only the rectilineararrangement shown in Figure 2.

2.3 System Model

A theoretical model of the experimental scanner is nowdeveloped to identify points on the light plane. Sincethe light plane is fixed inP, points PX on the planemay be represented by the plane equationPΩ>PX = 0,wherePΩ represents the parameters of the light plane.Now, P is defined such that the light plane is approxi-mately vertical and parallel to thez-axis, which allowsPΩ to be expressed as

PΩ = (1, B0, 0, D0)> (1)

whereB0 is related to the small angle between the planeand they-axis (B0 1 for an approximately verticalplane), andD0 is the distance of the plane from the ori-gin. During a scan, frameP rotates about itsy-axis withangleθy, whereθy , 0 when the light plane is parallelto the optical axes of the cameras. The rotation axis in-tersects thexz-plane of the world frame at(X0,0,Z0)>,and the orientation of the rotation axis relative to they-axis of the world frame is defined by the small fixedanglesθx andθz. The scan angle (θy in Figure 2) is lin-early related to the measured optical encoder valueeviatwo additional parametersmandk:

θy = me+k (2)

Now let WHP represent the homogeneous coordi-nate transformation fromP to W. If Rx(θx), Ry(θy)

3

and Rz(θz) represent the homogeneous transforma-tions for rotations about thex, y and z-axes, andT(X0,0,Z0) represents the transformation for transla-tion by (X0,0,Z0)>, WHP can be expressed as

WHP = T(X0,0,Z0) ·Rz(θz) ·Rx(θx) ·Ry(θy) (3)

It is straightforward to show that ifWHP is the coordi-nate transformation fromP to W, the plane parameterstransform fromP to W as

WΩ = (WHP)−> ·PΩ (4)

Finally, combining equations (3) and (4) and makingthe simplifying assumptionsB0,θx,θz 1 to elimi-nate insignificant terms, the laser plane parameters canbe expressed in the world frame by the approximatemodel:

WΩ≈

cosθy

θx sinθy +θzcosθy +B0

−sinθy

−X0cosθy +Z0sinθy +D0

(5)

whereci = cosθi andsi = sinθi , for i = x,y,z. Now, us-ing equations (2) and (5), points in the world frame canbe identified as coincident with the light plane (giventhe system parameters and current encoder measure-ment) using the plane equation:

WΩ>(B0,D0,X0,Z0,θx,θy,θz)WX = 0 (6)

3 Robust Stripe Scanning

3.1 Problem Statement

As discussed earlier, the problems associated with lightstripe scanners result from ambiguity in identifying theprimary reflection. The following sections describe anoptimal strategy to resolve this ambiguity and robustlyidentify the stripe in the presence of secondary reflec-tions, cross-talk and other sources of noise by exploit-ing redundancy.

Figure 3 shows a simplified plan view of the scan-ner to demonstrate the issues involved in robust stripedetection. The surface atX causes a primary reflectionthat is measured (using a noisy process) atLx andRx onthe stereo image planes. However, a secondary specularreflection causes another stripe to appear atX′, which ismeasured on the right image plane atRx′ but obscuredfrom the left camera (in practice, such noisy measure-ments are produced by a variety of mechanisms other

secondaryreflection

primaryreflection

planeright image

planeleft image

CRCLgeneratorlight plane

X′R

X′

X

XL

XR

Lx Rx′ RxRx

Figure 3: Validation/reconstruction problem.

than secondary reflections). The 3D reconstruction foreach measurement, labelledXL, XR and X′

R in Figure3, is recovered as the intersection of the light plane anda ray back-projected through the image plane measure-ments. These points will be referred to as thesingle-camera reconstructions. As a result of noise on theCCD (exaggerated in this example), the back-projectedrays do not intersect the physical reflections atX andX′.

The robust scanning problem may now be stated asfollows: given the laser plane position and the mea-surementsLx, Rx andRx′, one of the left/right candidatepairs, (Lx,Rx) or (Lx,Rx′), must be chosen as represent-ing stereo measurements of the primary reflection. Al-ternatively, all candidates may be rejected. This task isreferred to as thevalidation problem, and a successfulsolution in this example should identify (Lx,Rx) as thevalid measurements. The measurements should then becombined to estimate the position of the ideal projectionRx (arbitrarily chosen to be on the right image plane) ofthe actual pointX.

Formulation of optimal validation/reconstruction al-gorithms should take account of measurement noise,which is not correctly modelled in previous relatedwork. In [27] and [18], laser stripe measurements arevalidated by applying afixed threshold to the differ-ence between corresponding single-camera reconstruc-tions (XL, XR andX′

R in Figure 3). Such a comparisonrequires a uniform reconstruction error over all depths,

4

generatorlight plane

image plane

C

δx δx

x1 x2

∆X1

∆X2

Figure 4: Variation of single-camera reconstruction er-ror with depth.

which Figure 4 illustrates is clearly not the case. Twoindependent measurements atx1 andx2 generally ex-hibit a constant error variance on the image plane, as in-dicated by the intervalδx. However, projectingδx ontothe laser plane reveals that the reconstruction error in-creases with depth, since∆X1 < ∆X2. Thus, the valida-tion threshold on depth difference should increase withdepth to account for measurement noise, otherwise val-idation is more lenient for closer reconstructions. Sim-ilarly, taking eitherXL, XR or the arithmetic average12(XL + XR) as the final reconstruction is generally sub-optimal for noisy measurements.

The following sections present optimal solutions tothe validation/reconstruction problem, based on an er-ror model with the following features (the assumptionsof the error model are corroborated with experimentalresults in Section 6.2):

1. Light stripe measurement errors are independentand Gaussian distributed with uniform varianceover the entire image plane.

2. The dominant error in the laser plane position isthe angular error about the axis of rotation due tothe shaft encoder (e in equation (2)), which cou-ples all the image plane measurements in a givenframe.

3. All other parameters described in Section 2.3

(apart from the visual measurements and shaft en-coder position) are assumed to be known with suf-ficient accuracy that any uncertainty can be ig-nored for the purpose of validation and reconstruc-tion.

3.2 General Solution

We now present a general analytical solution to the vali-dation/reconstruction problem. LetLx andRx representnoisy candidatemeasurements of the stripe on corre-sponding epipolar lines, and letΩ = (A,B,C,D)> rep-resent the parameters of the light plane. Thecostof as-sociating the measurements with the primary reflectionof the stripe can be formulated as an error distance onthe image plane (similar to the reconstruction methodproposed in [11]). LetX represent the minimum meansquared error 3D reconstruction, which is constrained tocoincide with the laser plane, but not necessarily at theintersection of the back-projected rays from the noisyimage plane measurements. Errors in the light planeparametersΩ are considered in the next section, but fornow the light plane parameters are assumed to be knownexactly. The optimal reconstructionX corresponds tothe ideal projections,Lx and Rx, on the left and rightimage planes according toL,Rx = L,RPX. Now, the sumof squared errors between the ideal and measured pointscan be used to determine whether the candidate mea-surement pair (xL,xR) corresponds to a pointX on thelight plane:

E = d2(Lx,LPX)+d2(Rx,RPX) (7)

whered(x1,x2) is the Euclidean distance betweenx1

andx2. For a given candidate pair, the optimal recon-structionX with respect to image plane error is foundby a constrained minimization ofE with respect to thecondition thatX is on the laser plane:

Ω>X = 0 (8)

When multiple ambiguous correspondences exist, equa-tion (7) is optimized with respect to the constraint in (8)for all possible candidate pairs, and the pair with mini-mum error is chosen as the most likely correspondence.Finally, the result is validated by imposing a thresholdon the maximum allowed squared image plane errorE.

Performing the constrained optimization of equations(7)-(8) is analytically cumbersome. Fortunately, theproblem may be reduced to an unconstrained optimiza-tion by formulating the ideal left projectionLx as a func-tion of the ideal right projectionRx for points on the

5

light plane. To determine this relationship, the 3D re-construction is first expressed as a function ofRx bytaking the intersection of the laser plane and the rayback-projected fromRx. Plucker matrices provide aconcise notation for the intersection of planes and lines(see [9]). IfA andB represent the homogeneous vectorsof two points on a line, the Plucker matrix L describingthe line is

L = AB>−BA> (9)

Then, the intersectionX of a planeΩ and the line de-scribed by L is simply

X = LΩ = (AB>−BA>)Ω (10)

The Plucker matrix for the back-projected ray fromRx can now be constructed from two known points onthe ray: the camera centreCR, andRP+Rx, whereRP+ isthe pseudo-inverse of the camera projection matrixRPsuch thatRP(RP+Rx) = Rx, given by

RP+ = RP>(RPRP>)−1 (11)

Applying these to equation (9), the Plucker matrix forthe back-projection ofRx is

L = CR(RP+Rx)>− (RP+Rx)C>R (12)

The intersection of L with the laser planeΩ, can nowbe expressed using equation (10) as:

X = LΩ = [CR(RP+Rx)>− (RP+Rx)C>R ]Ω (13)

Finally, the ideal projectionLx corresponding toRx isobtained by projectingX onto the left image plane:

Lx = LPX

= LP[CR(RP+Rx)>− (RP+Rx)C>R ]Ω

= LPCR(RP+Rx)>Ω− LP(RP+Rx)(C>RΩ)

Using the identity(RP+Rx)>Ω = Ω>(RP+Rx), and not-ing that(C>

RΩ) is scalar, the common factors and col-lected to simplify the above expression to

Lx = LP(CRΩ>)(RP+Rx)− LP(C>RΩ)(RP+Rx)

=(

LP[CRΩ>− (C>RΩ)I]RP+

)Rx (14)

Equation (14) is of the formLx = HRx and simply statesthat points on the laser plane induce a homography be-tween coordinates on the left and right image planes,

which is consistent with known results [9]. Finally, theerror function becomes

E = d2(Lx,HRx)+d2(Rx,Rx) (15)

where H= LP[CRΩ>− (C>RΩ)I]RP+. The reconstruc-

tion problem can now be formulated as an uncon-strained optimization of equation (15) with respect toRx. The validation problem is solved by finding thepair of candidates on each scanline with the minimumsquared errorE, and the optimal reconstructionX is re-covered from equation (13) and the ideal projectionRx.

3.3 Special Case: Rectilinear Stereo andPin-Hole Cameras

The results of the previous section apply to generalcamera models and stereo geometry. However, the spe-cial case of rectilinear stereo and pin-hole cameras isimportant as it reduces equation (15) to a single de-gree of freedom. Furthermore, rectilinear stereo ap-plies without loss of generality (after projective rectifi-cation), and the pin-hole model is a good approximationfor CCD cameras (after correcting for radial lens distor-tion). The stereo cameras used in this work are assumedto have unit aspect ratio and no skew, and the pin-holemodels are parameterized by identical focal lengthf .For rectilinear stereo cameras with optical centres atCL,R = (∓b,0,0,1)>, the projection matricesL,RP aregiven by

L,RP=

f 0 0 ± f b0 f 0 00 0 1 0

(16)

where the positive sign is taken forL and the nega-tive for R. Now, substituting equation (16) andCL,R =(∓b,0,0,1)> into equation (14), the homography be-tween the projections of a point on the laser plane canbe expressed as:

Lx =

Ab−D 2Bb 2Cb f0 −(Ab+D) 00 0 −(Ab+D)

Rx

(17)With Rx = (Rx,R y,1)T andLx = (Lx,L y,w)T, the abovetransformation can be evaluated as Lx

Lyw

=

(Ab−D)Rx+2BbRy+2Cb f−(Ab+D)Ry−(Ab+D)

(18)

6

Expressed in inhomogeneous coordinates, the relation-ship betweenLx andRx is

Lx = − (Ab−D)Rx+2BbRy+2Cb fAb+D

(19)

Ly = Ry (20)

Since the axes ofL and R are parallel (rectilinearstereo), the notation ˆy , Ly = Ry replaces equation(20). Rectilinear stereo gives rise to epipolar linesthat are parallel to thex-axis, so the validation algo-rithm need only consider possible correspondences onmatching scanlines in the stereo images. Any mea-surement error in the stripe detection process (see Sec-tion 5.1) is assumed to be in thex-direction only, whilethe y-coordinate is fixed by the height of the scanline.Thus, they-coordinate of the optimal projections arealso fixed by the scanline, ie. ˆy = y, wherey is they-coordinate of the candidate measurementsLx andRx.

Finally, substituting equations (19)-(20) with ˆy = yinto (15), the image plane errorE can be expressed as afunction of asingleunknown,Rx:

E = (Lx+αRx+βy+ γ f )2 +(Rx−Rx)2 (21)

where the following change of variables in the planeparameters is introduced (noting thatΩ has only threedegrees of freedom due to the unconstrained scale):

α = (Ab−D)/(Ab+D) (22)

β = 2Bb/(Ab+D) (23)

γ = 2Cb/(Ab+D) (24)

For the experimental scanner, withΩ given by equation(5), α, β andγ can be written as:

α = −k1cosθy +k2sinθy +k3

cosθy +k2sinθy +k3(25)

β =(1−k1)(θx sinθy +θzcosθy +B0)

cosθy +k2sinθy +k3(26)

γ =(k1−1)sinθy

cosθy +k2sinθy +k3(27)

whereθy = me+ c and the following change of vari-ables is made in the system parameters:

k1 = −(b+X0)/(b−X0) (28)

k2 = Z0/(b−X0) (29)

k3 = D0/(b−X0) (30)

Optimization of equation (21) now proceeds usingstandard techniques, settingdE

dRx= 0 and solving for

Rx. Let Rx∗ represent the optimal projection resultingin the minimum squared error,E∗. It is straightforwardto show that the optimal projection is given by

Rx∗ = [Rx−α(Lx+βy+ γ f )]/(α2 +1) (31)

and the corresponding minimum squared errorE∗ is:

E∗ = (Lx+αRx+βy+ γ f )2/(α2 +1) (32)

For completion, substituting equation (31) andRy∗ = yinto (19) gives the corresponding optimal projection onthe left image plane as

Lx∗ = [α2Lx−αRx− (βy+ γ f )]/(α2 +1) (33)

Finally, the optimal 3D reconstructionX∗ is recoveredfrom equation (13). Evaluating (13) for rectilinear, pin-hole cameras with the change of variables in equations(22)-(24), and expressing the result in inhomogeneouscoordinates, the relationship betweenX∗ and the opti-mal projectionRx∗ is:

X∗

Y∗

Z∗

=

b[βy+γ f+(α−1)Rx∗](α+1)Rx∗+βy+γ f

−2by(α+1)Rx∗+βy+γ f

−2b f(α+1)Rx∗+βy+γ f

(34)

Finally, substitutingRx∗ from equation (33) into theabove, the optimal reconstruction from candidate mea-surementsLx andRx on the scanline at heighty is:

X∗

Y∗

Z∗

=

[(α−1)(αLx−Rx)−(α+1)(βy+γ f )]b(α+1)(αLx−Rx)+(α−1)(βy+γ f )

2by(α2+1)(α+1)(αLx−Rx)+(α−1)(βy+γ f )

2b f(α2+1)(α+1)(αLx−Rx)+(α−1)(βy+γ f )

(35)

Now, let Lxi , i = 1. . .nL, andRx j , j = 1. . .nR rep-resent candidate measurements of the stripe on corre-sponding scanlines at heighty. Furthermore, lete rep-resent the current measured encoder value for the scan-ner (see Section 3.4). The validation problem, that is,determining which pair of measurements correspond tothe primary reflection, can now be solved as follows:

1. Light plane parametersα, β andγ are calculatedfrom e and the system parameters using equations(25)-(27) and (2).

7

2. For every possible pair of measurements(Lxi ,Rx j),

the optimal reconstruction errorE∗ is calculatedfrom equation (32). Then, the pair(Lx∗i ,

Rx∗j ) withthe minimal reconstruction error are chosen as themost likely valid measurements, given by:

(Lx∗i ,Rx∗j ) = arg min

(Lxi ,Rx j )E∗(Lxi ,

Rx j ,α,β ,γ) (36)

3. A final test, E∗(Lx∗i ,Rx∗j ,α,β ,γ) < Eth, ensures

that the optimal candidates are valid, whereEth iscalculated off-line from the expected measurementerror. If this test is violated, no reconstruction isrecovered in current frame.

4. For valid measurements, the optimal reconstruc-tion X∗(Lx∗i ,

Rx∗j ) is finally calculated from equa-tion (35). The reconstructions from all scanlinesin the current frame are added to the range map.

3.4 Laser Plane Error

The above solution is optimal with respect to the errorof image plane measurements, and assumes that the pa-rameters of the laser plane are known exactly. In prac-tice, the encoder measurements are likely to suffer fromboth random and systematic error due to acquisition de-lay and quantization. Unlike the image plane error, theencoder error is constant for all stripe measurements ina given frame and thus cannot be minimized indepen-dently for candidate measurements on each scanline.

Let Lxi andRxi , i = 1. . .n represent valid correspond-ing measurements of the laser stripe on then scanlinesin a frame. The reconstruction errorE∗

i (e) for each paircan be treated as a function of the encoder count via thesystem model in equations (25)-(27). The total errorE∗

tot(e) over all scanlines for a given encoder counte iscalculated as:

E∗tot(e) =

n

∑i=1

E∗i (e) (37)

Finally, an optimal estimate of the encoder counte∗ iscalculated from the minimization

e∗ = argmine

[E∗tot(e)] (38)

SinceE∗tot(e) is a non-linear function, equation (38) is

implemented using the LM minimization from MIN-PACK [17], with the measured value ofe as the initialestimate.

As noted above, valid corresponding measurementsmust be identified before calculatingE∗

tot(e). However,since the correspondences are determined by minimiz-ing E∗ over all candidate pairs given the plane parame-ters, the correspondences are also a function of the en-coder count. Thus, the refined estimatee∗ may relateto a different set of optimal correspondences than thosefrom which it was calculated. To resolve this issue, theoptimal correspondences and encoder count are calcu-lated recursively. In the first iteration, correspondencesare calculated using the measured encoder valuee toyield the initial estimatee∗0 via equations (37)-(38). Anew set of correspondences are then extracted from theraw measurements using the refined encoder valuee∗0.If the new correspondences differ from the previous it-eration, an updated estimate of the encoder valuee∗1 iscalculated (usinge∗0 as the initial guess). The process isrepeated until a stable set of correspondences is found.

The above process is applied to each captured frame,and the optimal encoder counte∗ and valid correspond-ing measurements are substituted into equation (35) tofinally recover the optimal 3D profile of the laser.

3.5 Additional Constraints

As already described, robust stripe detection is basedon minimization of the image plane error in equation(32). However, the minimum image plane error is anecessary but insufficient condition for identifying validstereo measurements. In the practical implementation,two additional constraints are employed to improve therobustness of stripe detection.

The first constraint simply requires stripe candidatesto be moving features; a valid measurement must notappear at the same position in previous frames. This isimplemented by processing only those pixels with suf-ficiently large intensity difference between successiveframes. While this constraint successfully rejects staticstripe-like edges or textures in most scenes, it has lit-tle effect on cross-talk or reflections, since these alsoappear as moving features.

The second constraint is based on the fact that validmeasurements only occur within a sub-region of the im-age plane, depending on the angle of the light plane.From equation (34), the inhomogeneousz-coordinate ofa optimal reconstructionX can be expressed as a func-tion of the image plane projectionRx = (Rx,y)> as

Z =−2b f

(α +1)Rx+βy+ γ f(39)

8

Rearranging the above, the projectedx-coordinate of apoint on the light plane may be expressed as a functionof depthZ and the heighty of the scanline:

Rx =−βy+ γ fα +1

− 2b f

Z(α +1)(40)

The extreme boundaries for valid measurements cannow be found by taking the limit of equation (40) forpoints on the light plane near and far from the camera.Taking the limit for distant reflections gives:

limZ→∞

Rx =−βy+ γ fα +1

(41)

Taking the limit Z → 0 for close reflections gives theother boundary atRx → −∞. Now, if w is the widthof the captured image, valid measurements on the rightimage plane at heighty must be constrained to thex-coordinate ranges

−w2

< Rx < −βv+ γ fα +1

(42)

Following a similar development, it is straightforwardto show that the limits of valid measurements on theleft image plane are:

−βv+ γ fα +1

< Lx < +w2

(43)

Stripe extraction is only applied to pixels within theboundaries defined in (43)-(42); pixels outside theseranges are immediately classified as invalid. In additionto improving robustness, sub-region processing also re-duces computational expense by halving the quantityof raw image data and decreasing the number of stripecandidates tested for correspondence.

4 Active Calibration

In this section, determination of the unknown parame-ters in the model of the light stripe scanner are consid-ered. Let the unknown parameters be represented by thevector

p = (k1,k2,k3,θx,θz,B0,m,c)

wherek1, k2 andk3 were introduced in equations (28)-(30). Since most of the parameters relate to mechani-cal properties, the straightforward approach to calibra-tion is manual measurement. However, such an ap-proach would be both difficult and increasingly inac-curate as parameters vary through mechanical wear. To

overcome this problem, a strategy is now proposed tooptimally estimatep using only image-based measure-ments of a non-planar but otherwise arbitrary surfacewith favourable reflectance properties (the requirementof non-planarity is discussed below). This allows cali-bration to be performed cheaply and during normal op-eration.

The calibration procedure begins by scanning thestripe across the target and recording the encoder andimage plane measurements for each captured frame.Since the system parameters are initially unknown, thevalidation problem is approximated by recording onlythe brightest pair of features per scanline. LetLxi j andRxi j , i = 1. . .n j , j = 1. . . t represent the centroids ofthe brightest corresponding features onn j scanlines oft captured frames, and letej represent the measured en-coder value for each frame. As described earlier, im-age plane measurements have independent errors, whilethe encoder error couples all measurements in a givenframe. Thus, optimal system parameters are determinedfrom iterative minimization of the stripe measurementand encoder errors, based on the algorithm first de-scribed in Section 3.4. First, the total image plane errorE∗

tot is summed over all frames:

E∗tot =

t

∑j=1

n j

∑i=1

E∗(Lxi j ,Rxi j ,ej ,p) (44)

whereE∗ is defined in equation (32). The requirementof a non-planar calibration target can now be justified.For a planar target, the stripe appears as a straight lineand the image plane measurements obey a linear rela-tionship of the formxi j = a jyi j + b j . Then, the totalerrorE∗

tot reduces to the form

E∗tot =

t

∑j=1

n j

∑i=1

(A jyi j +B j)2 (45)

Clearly, the sign ofA j and B j cannot be determinedfrom equation (45), since the total error remains un-changed after substituting−A j and−B j . The geomet-rical interpretation of this result is illustrated in Figure5, which shows the 2D analogue of a planar target scan.For any set of encoder valuesej and collinear pointsX j measured overt captured frames, there exist twosymmetrically opposed laser plane generators capableof producing identical results. This ambiguity can beovercome by constraining the calibration target to benon-planar. It may also be possible for certain non-planar targets to produce ambiguous results, but the cur-

9

scanningdirection

scanningdirection

X1

light plane

light planegenerator

generator

XtX j

scanned plane

e1 et

e1 et

ej

ej

Figure 5: Possible positions of the light plane from thescan of a planar calibration target. The position of thelight plane generator is ambiguous.

rent implementation assumes that such an object willrarely be encountered.

An initial estimatep∗0 of the parameter vector is givenby the minimization

p∗0 = argminp

[E∗tot(p)] (46)

using the measured encoder valuesej and stereo cor-respondencesLxi j and Rxi j . Again, equation (46) isimplemented numerically using LM minimization inMINPACK. The stripe measurementsLxi j andRxi j arelikely to contain gross errors resulting from the initialcoarse validation constraint (in the absence of knownsystem parameters). Thus, the next calibration step re-fines the measurements by applying out-lier rejection.Using ej and the initial estimatep∗0, the image planeerrorE∗(Lxi j ,

Rxi j ,ej ,p∗0) in equation (32) is calculatedfor each stereo pair. The measurements are then sortedin order of increasing error, and the top 20% are dis-carded.

The system parameters and encoder values are thensequentially refined in an iterative process. The initialestimatep∗0 is only optimal with respect to image planeerror, assuming exact encoder valuesej . To accountfor encoder error, the encoder value is refined for eachframe using the method described in Section 3.4 withthe initial estimatep∗0 of the system model. The result-ing encoder estimatese∗j,0 are optimal with respect top∗0. A refined system modelp∗1 is then obtained fromequation (46) using the latest encoder estimatese∗j,0 and

in-lier image plane measurements. At thekth iteration,the model is considered to have converged when thefractional change in total errorE∗

tot is less then a thresh-old δ :

E∗tot,k−1−E∗

tot,k

E∗tot,k−1

< δ (47)

The final parameter vectorp∗k is stored as the near-optimal system model for processing regular scans us-ing the methods described in Section 3. A final checkfor global optimality is performed by comparing theminimum total errorE∗

tot,k to a fixed threshold, basedon an estimate of the image plane error. The rare caseof non-convergence (less than 10% of trials) is typicallydue to excessive out-liers introduced by the sub-optimalmaximum intensity validation constraint applied to theinitial measurements. Non-convergence is resolved byrepeating the calibration process with a new set of data.

The calibration technique presented here is practi-cal, fast and accurate, requiring only a single scan ofany suitable non-planar scene. Furthermore, the methoddoes not rely on measurement or estimation of any met-ric quantities, and so does not require accurate knowl-edge of camera parametersb and f . Thus, image-basedcalibration allows the validation and correspondenceproblems to be solved robustly and independently of re-construction accuracy.

5 Implementation

This section describes the signal processing used to im-plement stereoscopic light stripe scanning on the exper-imental system introduced in Section 2. The output ofthe scanner is a 384× 288 element range map, witheach element recording the 3D position of the surfaceas viewed from the right camera. During normal oper-ation, the laser is scanned across a scene and the shaftencoder and stereo images are recorded at regular 40 msintervals (25 Hz PAL frame-rate). The laser is mechan-ically geared to scan at about one pixels of horizontalmotion per captured frame, so a complete scan requiresapproximately 384 processed frames (15 seconds).

5.1 Light Stripe Measurement

Laser stripe extraction is performed using intensity dataonly, which is calculated by taking the average of thecolour channels. As noted in Section 3.5, the motionof the stripe distinguishes it from the static background,which is eliminated by subtracting the intensity values

10

intensityprofile

pixel position

δe

δh

xl

xr

δw

Figure 6: Thresholds for robust extraction of multi-modal pulses.

in consecutive frames and applying a minimum differ-ence threshold. The resultingdifference imageis mor-phologically eroded and dilated to reduce noise andimprove the likelihood of stripe detection. In Section3.5 it was also shown that valid measurements occurin a predictable sub-region of the image. This is cal-culated from equations (43)-(42) and the measured en-coder value, and pixels outside this region are set to zeroin the difference image. Further processing is only ap-plied to pixels with non-zero difference.

The intensity profile on each scanline is then exam-ined to locate candidate stripe measurements. If thestripe appeared as a simple unimodal pulse, the localmaxima would be sufficient to detect candidates. How-ever, mechanisms including sensor noise, surface tex-ture and saturation of the CCD interfere and perturb theintensity profile. These issues are overcome by extract-ing pulses using a more sophisticated strategy of inten-sity edge extraction and matching. On each scanline,left and right edges are identified as an increase or de-crease in the intensity profile according to the thresh-olds defined in Figure 6. Processing pixels from left toright, the location of a left edgexl is detected when theintensity difference between successive pixels exceedsa thresholdδe, and the closest local intensity maximato the right ofxl exceeds the intensity atxl by a largerthresholdδh. Right edgesxr are extracted by process-ing the scanline in reverse. Finally, the edges are ex-amined to identify left/right pairs without interveningedges. Whenxl andxr are closer than a threshold dis-tanceδw, the pair are assumed to delimit a candidatepulse. The pulse centroid is calculated to sub-pixel ac-curacy as the mean pixel position weighted by the in-

tensity profile within these bounds.The result of the above process is a set of candidate

stripe locations on each scanline of the stereo images.Along with the measured encoder value, these candi-dates are analyzed using the techniques described inSection 3 to refine the laser plane angle, identify validcorresponding measurements and reconstruct an opti-mal 3D profile. The reconstruction on each scanlineis stored in the range map at the location of the corre-sponding measurement in the right image.

5.2 Range Data Postprocessing

Post-processing is appliedafter each complete scan tofurther refine the measured data. Despite robust scan-ning, the raw range map may still contain outliers asthe stripe validation conditions are occasionally satis-fied by spurious noise. Fortunately, the sparseness ofthe outliers make them easy to detect and remove usinga simple thresholding operation: the minimum distancebetween each 3D point and its eight neighbours is cal-culated, and when this exceeds a threshold (10 mm inthe current implementation), the associated point is re-moved from the range map.

Holes (pixels for which range data could not be re-covered) may occur in the range map due to specu-lar reflections, poor surface reflectivity, random noiseand outlier removal. A further post-processing step fillsthese gaps with interpolated depth data. Each emptypixel is checked to determine whether it is bracketed byvalid data within a vertical or horizontal distance of twopixels. To avoid interpolating across depth discontinu-ities, the distance between the bracketing points must beless than a fixed threshold (30 mm in the current imple-mentation). Empty pixels satisfying these constraintsare assigned a depth linearly interpolated between thevalid bracketing points. The effect of both outlier rejec-tion and interpolation on a raw scan is demonstrated inFigure 7.

Finally, a colour image is registered with the rangemap. Since robust scanning allows the sensor to oper-ate in normal light, the cameras used for stripe detectionalso capture colour information. However, depth andcolour cannot be sampled simultaneously for any givenpixel, since the laser masks the colour of the surface.Instead, a complete range map is captured before regis-tering a colour image from the right camera (assumingthe cameras have not moved). Each pixel in this finalimage yields the colour of the point measured in thecorresponding element of the range map.

11

(a) Before post-processing

(b) After post-processing

Figure 7: Removal of impulse noise and holes (elimi-nated features are circled on the left).

6 Experimental Results

6.1 Robustness

To evaluate the performance of the proposed robust ac-tive sensing method, the scanner is implemented alongwith two other common techniques on the same exper-imental platform. The first method is a simple single-camera scanner without any optimal or robust proper-ties. A single-camera reconstruction is calculated fromequation (13), using image plane measurements fromthe right camera only. Since no validation is possi-ble in this configuration, the stripe is simply detectedas the brightest feature on each scanline. The sec-ond alternative implementation will be referred to as adouble-camerascanner. This approach is based on therobust techniques proposed in [18, 27], which exploitthe requirement of consensus between two independent

single-camera reconstructions. The single-camera re-constructionsXL and XR are calculated independentlyfrom measurements on the left and right image planes,and discarded when|XL− XR| exceeds a fixed distancethreshold. For valid measurements, the final reconstruc-tion is calculated as12(XL + XR).

The performance of the three methods in the presenceof a phantom stripe (secondary reflection) was assessedusing the test scene shown in Figure 8. A mirror at therear of the scene creates a reflection of the objects andscanning laser, simulating the effect of cross-talk andsecondary reflections. To facilitate a fair comparison,the three methods operated simultaneously on the sameraw measurements captured during a single scan of thescene.

Figure 9(a) shows the colour/range data captured bythe single-camera scanner. As a result of erroneous as-sociations between the phantom stripe and laser plane,numerous phantom surfaces appear in the scan withoutany physical counterpart. Figure 9(b) shows the outputof the double-camera scanner, which successfully re-moves the spurious surfaces. However, portions of realsurfaces have also been rejected, since the algorithm isunable to disambiguate the phantom stripe from the pri-mary reflection when both appear in the scene. Finally,Figure 9(c) shows the result using the techniques pre-sented in this paper (see also Extension 1). The por-tions of the scene missing from Figure 9(b) are suc-cessfully detected using the proposed robust scanner,while the phantom stripe has been completely rejected.Also noteworthy is the implicitly accurate registrationof colour and range.

The single-camera result highlights the need for ro-bust methods when using light stripe scanners on a do-mestic robot. While the double-camera scanner suc-cessfully rejects reflections and cross-talk, the high re-jection rate for genuine measurements may cause prob-lems for segmentation or other subsequent processing.In contrast, segmentation and object classification havebeen successfully applied to the colour/range data fromthe proposed robust scanner to facilitate high-level do-mestic tasks [25]. Extensions 2 and 3 provide addi-tional colour/range maps of typical domestic objects todemonstrate the robustness of our sensor in this appli-cation.

6.2 Error Analysis

The results in this section experimentally validate of thesystem and noise models used to derive the theoreti-

12

Figure 8: Robust scanning experiment.

cal results. In particular, the encoder angle estimationand calibration techniques described in Sections 3.4 and4 are shown to be sufficiently accurate that any uncer-tainty in the system parameters and encoder values canbe ignored for the purposes of optimal validation andreconstruction.

First, the calibration procedure described in Section4 was performed using the corner formed by two boxesas the calibration target, and the valid image planemeasurements and encoder values for each frame wererecorded. Using the estimated system parameters, theoptimal projectionsL,Rx∗ and residuals(L,Rx− L,Rx∗)were calculated from equations (31) and (33) for allmeasurements. Figure 10 shows the histogram of resid-uals for measurements on the right image plane, anda Gaussian distribution with the same parameters forcomparison. The residuals are approximately Gaussiandistributed as expected, and assuming the light stripemeasurement errors are similarly distributed, the errormodel proposed in Section 3.1 is found to be valid. Thevariance of the image plane measurements are shown inthe first two rows of Table 1.

The variance of the system parameters and encodervalues were determined using statistical bootstrapping.In this process, the residuals were randomly and uni-formly sampled (with replacement) from the initialdata, and added to the optimal projectionsL,Rx∗ to gen-erate a new set of pseudo-measurements. The systemparameters were then estimated for each new set ofpseudo-measurements using the calibration process de-scribed in Section 4. A total of 5000 re-sampling ex-periments were performed, and the resulting variance inthe estimated system parameters are shown in the third

(a) Single-camera

(b) Double-camera

(c) Robust scanner

Figure 9: Comparison of range scanner results in thepresence of secondary reflections.

13

0

2000

4000

6000

8000

10000

12000

14000

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

His

togr

am c

ount

Residual error (pixels)

Figure 10: Distribution of residual reconstruction errorson the image plane.

Table 1: System parameter errors and contribution toreconstruction error.

pi pi var(pi) var(Rx∗)i

xL 59.2 8×10−3 2×10−3

xR -47.4 7×10−3 2×10−3

y 6.0 0.0 0.0e 451.5 5×10−5 2×10−5

k1 -1.1033 2×10−8 1×10−5

k2 0.1696 4×10−8 2×10−8

k3 0.0717 1×10−8 2×10−5

θx -0.0287 3×10−10 2×10−12

θz 0.0094 5×10−8 2×10−6

B0 -0.0004 5×10−8 2×10−6

m 0.001105 7×10−16 3×10−5

c -0.4849 1×10−10 4×10−5

column of Table 1.Finally, the optimality of the reconstruction is as-

sessed by calculating the contribution from each pa-rameter to the variance of the optimal projectionRx∗

in equation (31). Representing the components of theparameter vector asp = pi, and assuming the param-eters have independent noise, the contribution of param-eterpi (with all other parameters fixed) to the varianceof Rx∗, represented as var(Rx∗)i , is calculated as

var(Rx∗)i =

(∂ Rx∗

∂ pi

∣∣∣∣p

)2

·var(pi) (48)

The independence of the parameters is readily verified

from the covariance matrix ofp.Choosing a test point near the centre of the image

plane, the contribution of each parameter to the totalvariance was calculated from equation (48) and the re-sults are shown in the far right column of Table 1. Im-portantly, the errors due toRx andLx are two orders ofmagnitude greater than the contribution from the sys-tem parameters and encoder value. For comparison, thevariance inRx∗ measured from the bootstrapping pro-cess was 0.0035 pixels2, which agrees well with thesum of contributions fromLx andRx. Finally, it shouldbe noted that the variance ofRx∗ is about half the vari-ance ofRx, indicating that the optimal reconstructionhas a higher precision than a single-camera reconstruc-tion.

These results demonstrate the reliability of theimage-based techniques presented in Sections 3.4 and4 for estimating the encoder value and calibrating thesystem parameters in the presence of noisy measure-ments. Furthermore, the main assumptions in derivingequations (31) and (32) are now justified: any uncer-tainty in the system parameters and encoder value canbe reasonably ignored for the purpose of validation andreconstruction.

7 Discussion

In addition to providing a mechanism for validation, theerror distanceE∗ in equation (32) could be used to mea-sure the random error of range points. As discussed inSection 3.1, the error variance of a 3D reconstructionincreases with depth as the reconstruction problem be-comes ill-conditioned. This systematic uncertainty canbe calculated directly from the reconstruction in equa-tion (35). In contrast,E∗ measures the random uncer-tainty due to sensor noise. A suitable function of thesesystematic and random components could be formu-lated to provide a unique confidence interval for each3D point, which would be useful in subsequent process-ing. For example, parametric surface fitting could beoptimized with respect to measurement error by weight-ing each point with the confidence value.

One of the main limitations of light stripe scanning(compared to methods such as passive stereo) is the ac-quisition rate. In the current implementation, the PALframe-rate of 25 Hz results in a 15 second measurementcycle to capture a complete half-PAL resolution rangemap of 384 stripe profiles. Clearly, such a long acqui-sition time renders the sensor unsuitable for dynamic

14

scenes. However, a more subtle issue is that the robotmust remain stationary during a scan to ensure accurateregistration of the measured profiles. Obviously, the ac-quisition rate could be improved using high-speed cam-eras and dedicated image processing hardware; high-speed CMOS cameras are now capable of frame-ratesexceeding 1000 Hz. Assuming the image processingcould be accelerated to match this speed, the sensorcould be capable of acquiring 2-3 range maps per sec-ond. An example of a high-speed monocular light stripesensor using a “smart” retina is described in [8].

To minimize complexity and cost, the experimentalprototype uses a red laser diode to generate the lightplane. Consequently, the scanner only senses surfaceswhich contain a high component of red. Black, blueand green surfaces reflect insufficient red laser lightand are effectively invisible to the sensor. Since thelight plane is not required to be coherent or monochro-matic, the laser diode could be replaced by a white lightsource such as a collimated incandescent bulb. How-ever, laser diodes have particular design advantages in-cluding physical compactness, low power consumptionand heat generation, and are thus more desirable thanother light sources. To solve the colour deficiency prob-lem while retaining these advantages, the light planecould be generated using a triplet of red, green and bluelaser diodes. Currently, the main obstacle to this ap-proach is the high cost of green and blue laser diodes.

As with colour, surfaces with high specular and lowLambertian reflection may appear invisible, since insuf-ficient light is reflected back to the sensor. This lim-itation is common to all active light sensors and canalso defeat passive stereopsis, since the surface appearsdifferently to each viewpoint. To illustrate this effect,Figure 11 shows the raw image and resulting scan of ahighly polished object. The only visible regions appear-ing in the range map are the high curvature edges thatprovide a specular reflection directly back to the sensor.The best that can be achieved is to ensure that secondaryreflections do not interfere with range data acquisition,as demonstrated in this result.

8 Summary and Conclusions

We have presented the theoretical framework and im-plementation of a robust light stripe scanner for a do-mestic robot, capable of measuring arbitrary scenes inambient indoor light. The scanner uses the light planeorientation and stereo camera measurements to robustly

Figure 11: Scan of a highly polished object. The lightstripe (with specular reflections) is shown on the left,and the resulting range map is shown on the right.

identify the light stripe in the presence of secondary re-flections, cross-talk and other sources of interference.The validation and reconstruction framework is basedon minimization of error distances measured on the im-age plane. Unlike previous stereo scanners, this formu-lation is optimal with respect to measurement error. Animage-based procedure for calibrating the light planeparameters from the scan of an arbitrary non-planar tar-get is also demonstrated.

Results from the experimental scanner demonstratethat our robust method is more effective at recoveringrange data in the presence of reflections and cross-talkthan comparable light stripe methods. Experimental re-sults also confirm the assumptions of our noise model,and show that image-based calibration produces reli-able results in the presence of noisy image plane mea-surements. Finally, the optimal reconstructions fromour proposed scanner are shown to be more precise thanthe reconstructions from a single-camera scanner.

The ability to solve the stripe association problemmay provide interesting future research in the develop-ment of a multi-stripe scanner. Multi-stripe scannershave the potential to solve a number of issues asso-ciated with single-stripe scanners: illuminating a tar-get with two stripes could double the acquisition rate,and projecting the stripes from different positions re-veals points that would otherwise be hidden in shadow.Single-camera multi-stripe systems rely on colour [23],sequences of illumination [15] or epipolar constraints[14] to disambiguate the stripes. However, the methodproposed in this paper could allow the stripes to beuniquely identified using the same principles that pro-vide validation for a single stripe.

Finally, the over-arching goal in this development is

15

to allow a robot to model and manipulate arbitrary ob-jects in a domestic environment. Our other results inthis area [25] already demonstrate that the scanner pro-vides sufficiently robust measurements to achieve thisgoal.

Acknowledgment

This project was funded by theStrategic Monash Uni-versity Research Fund for the Humanoid Robotics: Per-ception, Intelligence and Controlproject at IRRC.

Appendix: Index to Multi-MediaExtensions

The mult-imedia extensions to this article can befound online by following the hyperlinks fromwww.ijrr.org. These results may also be found atwww.irrc.monash.edu.au/laserscans.

Extension Media type Description1 Data VRML 97 model (half

scanner resolution) ofmirror scene, (requiresVRML plug-in).

2 Data VRML 97 model (halfscanner resolution) oftypical domestic objects.

3 Data VRML 97 model (halfscanner resolution) oftypical domestic objects.

References

[1] G. J. Agin and T. O. Binford. Computer descrip-tion of curved objects. InProc. 3rd Int. Joint Conf.on Artifical Intelligence, pages 629–640, 1973.

[2] M. J. Aldon and L. Le Bris. Mobile robot localiza-tion using a light stripe sensor. InProc. of the In-telligent Vehicles ’94 Symposium, pages 255–259,1994.

[3] H. M. M. Alshawish and C. R. Allen. 3d objectrecognition using coded light projection for robot

assembly applications. InProc. 21st Interna-tional Conference on Industrial Electronics, Con-trol and Instrumentation, volume 2, pages 1420–1247, 1995.

[4] C. M. Bastuscheck. Techniques for real-time gen-eration of range images. InProc. IEEE Comp.Soc. Conf. on Computer Vision and Pattern Recog-nition, pages 262–268, 1989.

[5] P. J. Besl. Active, optical range image sen-sors.Machine Vision Applications, 1(2):127–152,1988.

[6] J. Clark, E. Trucco, and H-F. Cheung. Improv-ing laser triangulation sensors using polarization.In Proc. 5th Int. Conf. on Computer Vision, pages981–986, 1995.

[7] D. Khadraoui et al. Visual servoing inrobotics scheme using a camera/laser-stripe sen-sor. IEEE Transactions on Robotics and Automa-tion, 12(5):743–750, 1996.

[8] A. Gruss, L. R. Carley, and T. Kanade. Integratedsensor and range-finding analog signal processor.IEEE Journal of Solid-State Circuits, 26(3):184–191, Mar 1991.

[9] R. Hartley and A. Zisserman.Multiple View Ge-ometry in Computer Vision. Cambridge UniversityPress, 2000.

[10] R. I. Hartley. Theory and practice of projectiverectification. Int. Journal of Computer Vision,35(2):115–127, 1999.

[11] R. I. Hartley and P. Sturm. Triangulation.Computer Vision and Image Understanding,68(2):146–157, 1997.

[12] J. Haverinen and J. Roning. An obstacle detec-tion system using a light stripe identification basedmethod. InProc. IEEE International Joint Sympo-sium on Intelligence and Systems, pages 232–236,1998.

[13] M. Hebert. Active and passive range sensing forrobotics. In Proc. IEEE International Confer-ence on Robotics and Automation, pages 102–110,2000.

16

[14] G. Hu and G. Stockman. 3-D surface solutionusing structured light and constraint propagation.IEEE Trans. Pattern Analysis and Machine Intel-ligence, 11(4):390–402, apr 1989.

[15] D. Q. Huynh, R. A. Owens, and P. E. Hartmann.Calibrating a structured light stripe system: Anovel approach. International Journal of Com-puter Vision, 33(1):73–86, 1999.

[16] M. Magee, R. Weniger, and E. A. Franke. Loca-tion of features of known height in the presenceof reflective and refractive noise using a stereo-scopic light-striping approach.Optical Engineer-ing, 33(4):1092–1098, April 1994.

[17] J. J. More, B. S. Garbow, and K. E. Hillstrom.Users’ guide for MINPACK-1. Technical ReportANL-80-74, Applied Math. Div., Argonne Na-tional Laboratory, 1980.

[18] Kouichi Nakano, Yasuo Watanabe, and SukeyasuKanno. Extraction and recognition of 3-dimensional information by projecting a pair ofslit-ray beams. InProceedings of the 9th Interna-tional Conference on Pattern Recognition, pages736–738, 1988.

[19] J. Nygards, T. Hogstrom, and A. Wernersson.Docking to pallets with feedback from a sheet-of-light range camera. InProc. 2000 IEEE/RSJ In-ternational Conference on Intelligent Robots andSystems, pages 1853–1859, 2000.

[20] J. Nygards andA. Wernersson. Specular objects inrange cameras: Reducing ambiguities by motion.In Proc. of the IEEE Int. Conf. on Multisensor Fu-sion and Integration for Intelligent Systems, pages320–328, 1994.

[21] K. Rao, G. Medioni, H. Liu, and G. A. Bekey.Shape description and grasping for robot hand-eyecoordination. IEEE Control Systems Magazine,pages 22–29, February 1989.

[22] Y. Shirai and M. Suwa. Recognition of polyhe-drons with a range finder. InProc. 2nd Int. JointConf. on Artifical Intelligence, pages 80–87, 1971.

[23] J. Tajima and M. Iwakawa. 3-d data acquisitionby rainbow range finder. InProc. 10th Int. Conf.on Pattern Recognition, volume 1, pages 309–313,1990.

[24] G. Taylor and L. Kleeman. Flexible self-calibratedvisual servoing for a humanoid robot. InProc.2001 Australian Conference on Robotics and Au-tomation, pages 79–84, 2001.

[25] G. Taylor and L. Kleeman. Grasping unknown ob-jects with a humanoid robot. InProc. 2002 Aus-traliasian Conference on Robotics and Automa-tion, pages 191–196, 2002.

[26] G. Taylor, L. Kleeman, andA. Wernersson. Ro-bust colour and range sensing for robotics appli-cations using a stereoscopic light stripe scanner.In Proc. 2002 IEEE/RSJ International Conferenceon Intelligent Robots and Systems, pages 178–183, 2002.

[27] E. Trucco and R. B. Fisher. Acquisition of con-sistent range data using local calibration. InProc.of the 1994 IEEE Int. Conf. on Robotics and Au-tomation, volume 4, pages 3410–3415, 1994.

17