STEREO VISION-BASED DETECTION OF MOVING OBJECTS

UNDER STRONG CAMERA MOTION

Hernan Badino, Uwe Franke, Clemens Rabe, Stefan GehrigDaimlerChrysler AG

71059 Sindelfingen, Germany

{hernan.badino, uwe.franke, clemens.rabe, stefan.gehrig}@daimlerchrysler.com

Keywords: Stereo Vision, Kalman Filter, Tracking, Ego-Motion Estimation

Abstract: The visual perception of independent 3D motion from a moving observer is one of the most challengingtasks in computer vision. This paper presents a powerful fusion of depth and motion information for imagesequences. For a large number of points, 3D position and 3D motion is simultaneously estimated by means ofKalman Filters. The necessary ego-motion is computed based on the points that are identified as static points.The result is a real-time system that is able to detect independently moving objects even if the own motion isfar from planar. The input provided by this system is suited to be used by high-level perception systems inorder to carry out cognitive processes such as autonomous navigation or collision avoidance.

1 INTRODUCTION

The visual perception of independent 3D motion froma moving observer is one of the most challengingtasks in computer vision. Independent 3D motionis defined as the rigid or articulated change in po-sition over time of an object with respect to an en-vironment which is considered static. The percep-tion of visual motion in animals and humans servesa wide variety of crucial roles: ”way-finding (opticflow), perception of shape from motion, depth segre-gation, judgments of coincidence (time to collision,time to filling a tea cup), judgments of motion direc-tion and speed, and perception of animate, biologi-cal activity” (Sekuler et al., 2004). In this paper wepresent a passive approach for the simultaneous esti-mation of position and velocity of single points, pro-viding low-level information to more complex visualperception systems, such as autonomous navigationor collision avoidance. Treating such a process as alow-level task should not be surprising since, from thebiological point of view, motion detection is a directexperience uniquely specified by the visual system.1

1Neurons in the middle temporal visual area integratemotion signals over large regions of visual space and re-spond to motion in their preferred direction, e.g. these neu-rons register motion information per se. More advancedperception activities are distributed over many areas of thebrain, each extracting somewhat different information from

The further segmentation and integration of the infor-mation provided by our approach is here referred toas high-level vision, which must introduce some addi-tional knowledge and intelligence to carry out a cog-nitive process (”a bicyclist is approaching from theleft and we are going to collide with him within thenext two seconds”).

In order to estimate the velocity of a world point,we must be able to observe its change of position overtime. The point position is easily obtained with multi-ocular platforms2, which allow the instantaneous ex-traction of 3D position through triangulation. Thetime component is obtained by finding correspon-dences in consecutive frames. The correspondencesare found between image points, i.e. optical flowor normal flow, or at the level of objects, which re-quires the previous segmentation of stereo points andthe further tracking of objects. This last approachis commonly solved by an orthographical projectionof the 3D points into an evidence-grid-like structuregiving a bird-view of the scene, and grouping theprojections according to their vicinity (Martin andMoravec, 1996). This method has its difficulties insegmenting distant objects and in separating distinctobjects which are close together. The second op-

the retinal image (Sekuler et al., 2004).2For the state-of-the-art on monocular methods see for

example (Kang et al., 2005), (Vidal, 2005) and (Woelk,2004)

1st International Conference on Computer Vision Theory and Applications (VISAPP)

Setúbal, Portugal. 25 - 28 February, 2006

tion, i.e. normal flow, has some advantages with re-spect to optical flow in the sense that it reduces thecorrespondence problem (see for example (Argyrosand Orphanoudakis, 1997) and (Morency and Darrell,2002)). Nevertheless, normal flow is less informativecompared to optical flow since it reflects only the mo-tion in the direction of the image gradient and, there-fore, does not provide an accurate estimation of pointmotion.

Methods based on optical flow have been widelyproposed. One of the first attempts to fuse stereoand optical flow information was studied by Wax-man and Duncan in (Waxman and Duncan, 1986),exploiting the relationship between 3D motion andimage velocities with stereo constraints. Kellmanand Kaiser (Kellman and Kaiser, 1995), Heinrich(Heinrich, 2002) and Mills (Mills, 1997) also makeuse of such constraints to detect independent mo-tion. Demirdjian and Horaud (Demirdjian and Ho-raud, 2000) propose a method for the estimation ofthe ego-motion and the segmentation of moving ob-jects. Demirdjian and Darrel (Demirdjian and Darrel,2001) estimate rigid motion transformation mappingtwo reconstructions of a rigid scene in the disparityspace (which they called d-motion). Dang et al (Danget al., 2002) fuse optical flow and stereo disparity us-ing Kalman Filters for object tracking, where the de-tection and segmentation of the object must have al-ready been carried out. Kalman Filters were also usedby Zhang and Faugeras (Zhang and Faugeras, 1991)for multiple motion estimation. Algorithms for thedetection of moving objects using dense stereo andoptical flow were proposed by Talukder and Matthies(Talukder and Matthies, 2004) and by Agrawal et al(Agrawal et al., 2005).

In this paper we describe an elegant approachfor the estimation and continuous refinement of theposition and velocity of world points. The six-dimensional state (i.e. 3D position and 3D velocity)as well as the six degrees of freedom (d.o.f.) of theego-motion (translation and rotation in 3D Euclidianspace) are estimated only based on the analysis of theimages provided by the cameras and the required cali-bration parameters. Steps towards this approach havebeen described in (Franke et al., 2005) where ego-motion was restricted to a planar motion and obtainedwith the inertial sensors of the vehicle. Our approachcombines binocular disparity and optical flow usingKalman Filters (KF), providing an iterative refine-ment of the 3D position and the 3D velocity of singlepoints. Ego-motion estimation is achieved by com-puting the optimal rotation and translation betweenthe tracked static points of multiple frames. Thesetwo processes are explained in detail in sections 2 and3. In section 4 the whole algorithm is summarized.In Section 5 we present experimental results with realimage sequences. In the last section we summarize

the paper.

2 ESTIMATION OF 3D POSITION

AND 3D VELOCITY

The main goal of our approach is the estimation ofposition and velocity of world points in 3D Euclid-ian space, and the recursively improvement of theseestimates over time. A continuous improvement ofthe estimations is motivated by the noisy nature ofthe measurements and, therefore, Kalman Filters arethe appropriate method to address this problem. Inthis section we describe a model which estimates therelative motion of world points relative to the ob-server, compensating the ego-motion of the cameraplatform with the observed motion of the points. If aworld point is static, its observed motion is describedas the inverse of the camera motion. Otherwise thepoint presents an independent 3D motion which weestimate. In the following subsections we assume avehicle-based coordinate system, i.e. the origin of thecoordinate system moves along with the observer.

2.1 Kalman Filter Model

Let suppose ~x′k−1 = (X, Y, Z)T represents a world

point observed by the system at time tk−1 and~v′k−1 = (X, Y , Z)T is its associated velocity vector.As the camera platform moves in its environment, so

also does ~x′ and after a time ∆tk the new position ofthe point in the vehicle coordinate system is given by:

~x′k = Rk

~x′k−1 +

~dk + ∆tkRk

~v′k−1 (1)

where Rk and~dk, are the rotation matrix and transla-

tion vector of the scene, i.e. the inverse motion of the

camera. The velocity vector ~v′k, in vehicle coordinatesystem, changes its direction according to:

~v′k = Rk~v′k−1 (2)

Combining position and velocity in the state vector

~xk = (X, Y, Z, X, Y , Z)T leads to the discrete linearsystem model equation:

~xk = Ak~xk−1 + Bk + ~ω (3)

with the state transition matrix

Ak =

[

Rk ∆tkRk

0 Rk

]

(4)

and the control matrix

Bk =

~dk

000

(5)

Figure 1: 3D motion vectors obtained when the vehicledrives on a flat street. The inertial sensors of the vehicleare used for the computation of the camera motion.

The noise term ~ω is assumed to be Gaussian whitenoise with a covariance matrix Q.

The measurement model captures the informa-tion delivered by the stereo and optical flow sys-tems. Assuming a pin-hole camera at the position(0, height, 0)T in the vehicle coordinate system withthe optical axis parallel to the Z component, the non-linear measurement equation for a point given in thecamera coordinate system is

z =

[

uvd

]

=1

Z

[

Xfu

Y fv

bfu

]

+ ~ν (6)

where (u, v) corresponds to the updated position ofthe point obtained with the optical flow, d is the dis-parity measured with stereo and (fu, fv) are the fo-cal length in pixel width and height respectively. Thenoise term ~ν is assumed to be Gaussian white noisewith a covariance matrix R.

This fusion of binocular disparity and optical flowoffers a powerful tool for the iterative estimation ofthe position and velocity of world points. An exam-ple is shown in figure 1. The arrows correspond tothe estimated direction. The warmth of the color en-codes the 3D Euclidian velocity. Notice that the bi-cyclist and the vehicle at the background are close to-gether. Nevertheless a clear segmentation of both ispossible thanks to the additional information of ve-locity. The rotation matrix and the translation vectorof equations 1 to 5 are normally obtained from the in-ertial sensors of the vehicle which usually consist ofa speedometer and a yaw-rate sensor (Franke et al.,2005). For indoor applications the information deliv-ered by these inertial sensors is usually sufficient inorder to robustly estimate the position and velocity ofworld points. However, for many other applications(e.g. vehicle assistance systems) the motion of thecamera platform is not purely planar. Figure 2 showsan example when the cameras are mounted in a vehi-cle. It is obvious that the error in the velocity vectorsis produced by the roll rotation. A better approach ispossible if all six d.o.f. are considered computing the

Figure 2: 3D motion vectors obtained when the vehicledrives on an uneven street. Only yaw-rate and velocity areconsidered in the ego-motion compensation.

ego-motion only from the images.

3 ROBUST EGO-MOTION

ESTIMATION

Computing ego-motion from an image sequencemeans obtaining the change of position and orienta-tion of the observer with respect to a static scene,i.e. the motion is relative to an environment whichis considered static. In most approaches this factis exploited and ego-motion is computed as the in-verse of the scene motion (Demirdjian and Horaud,2000), (Mallet et al., 2000), (Matthies and Shafer,1987), (Olson et al., 2003), (van der M. et al., 2002),(Badino, 2004). In the latter a robust approach for theaccurate estimation of the six d.o.f. of motion (threecomponents for translation and three for rotation) intraffic situations is presented. In this approach, stereois computed at different times and clouds of 3D pointsare obtained. The optical flow establishes the point-to-point correspondence. The motion of the camerais computed with a least-squares approach finding theoptimal rotation and translation between the clouds.In order to avoid outliers, a smoothness motion con-straint is applied rejecting all correspondences whichare inconsistent with the current motion. This lasttwo steps are also applied between non-consecutiveframes. In the next sub-sections we briefly review themain steps of this approach.

3.1 Obtaining the Absolute

Orientation Between Two

Frames

Let X = {~xi} be the set of 3D points of the pre-vious frame and P = {~pi} the set of 3D points ob-served at the current frame, where ~xi ↔ ~pi, i.e. ~pi isthe transformed version at time tk of the point ~xi at

time tk−1. In order to obtain the motion of the cam-era between the current and the previous frame weminimize a function which is expressed as the sum ofthe weighted residual errors between the rotated andtranslated data set X with the data set P , i.e.:

n∑

i=1

wi‖~pi − Rk~xi − ~dk‖2 (7)

where n is the amount of points in the sets, Rk is

a rotation matrix, ~dk is a translation vector, and wi

are individual weights representing the expected er-ror in the measurement of the points. To solve thisleast-squares problem we use the method presentedby Horn (Horn, 1987), which provides a closed formsolution using unit quaternions. In this method the op-timal rotation quaternion is obtained as the eigenvec-tor corresponding to the largest positive eigenvalue ofa 4 × 4 matrix. The quaternion is then converted tothe rotation matrix. The translation is computed asthe difference of the centroid of data set P and the ro-tated centroid of data set X . The computation of therelative orientation is not constrained to this specificmethod. Lorusso et al (Lorusso et al., 1995) shortlydescribe and compare this and another three methodsfor solving this problem in closed form.

3.2 Motion Representation with

Matrices

In order to simplify the notation of the following sub-sections, we represent the motion in homogeneous co-ordinates. The computed motion of the camera be-tween two consecutive frames, i.e. from frame k − 1to frame k, is represented by the matrix M ′

k where:

M ′

k =

[

Rk~dk

0 1

]

(8)

The rotation matrix Rk and translation vector~dk from

equations 1 to 5 are obtained by just inverting M ′

k,i.e.:

M′−1

k =

[

Rk~dk

0 1

]

=

[

R−1

k −R−1

k~dk

0 1

]

(9)

The total motion of the camera since initialization canbe obtained as the products of the individual motionmatrices:

Mk =

k∏

i=1

M ′

i (10)

A sub-chain of movements from time tn to time tm

is:

Mn,m = M−1n Mm =

m∏

i=n+1

M ′

i (11)

Figure 3 shows an example of motion integration withmatrices. As we will show later in section 3.4 equa-tion 11 will support the integration of the motion be-tween two non-consecutive frames (multi-step esti-mation).

0

1

2

3

�

��

�

��

�

��

4

�

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∏=

− ==�

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∏=

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Figure 3: The integration of single-step estimations can beobtained by just multiplying the individual motion matrices.Every circle denotes the state (position and orientation) ofthe camera between time t0 and time t4. Vectors indicatemotion in 3D-space.

3.3 Smoothness Motion Constraint

Optical flow and/or stereo can deliver false informa-tion about 3D position or image point correspondencebetween image frames. Some of the points might alsocorrespond to an independently moving object. A ro-bust method should still be able to give accurate re-sults facing such situations. If the frame rate is highenough in order to obtain a smooth motion betweenconsecutive frames, then the current motion is similarto the immediate previous motion. Therefore, beforeincluding the pair of points ~pi and ~xi into their corre-sponding data sets P and X , we evaluate if the vec-tor ~vi = −−→pixi indicates a coherent movement. Let usdefine ~m = [ xmax ymax zmax 1 ] as the max-imal accepted error of the position of a 3D point withrespect to a predicted position. Based on our previ-ous ego-motion estimation step we evaluate the mo-tion coherence of the vector ~vi as:

~ci = M ′

k−1~xi − ~pi (12)

i.e. the error of our prediction. If the absolute valueof any component of ci is larger than ~m the pair ofpoints are discarded and not included in the data setsfor the posterior computation of relative orientation.Otherwise we weight the pair of points as the ratio ofchange with respect to the last motion:

wi = 1 −‖~ci‖

2

‖~m′‖2(13)

which is later used in equation 7. Equations 12 and13 define the smoothness motion constraint (SMC).

3.4 Multi-Frame Estimation

Single step estimation, i.e. the estimation of the mo-tion parameters from the current and previous frame

is the standard case in most approaches. If we areable to track points over m frames, then we can alsocompute the motion between the current and the mprevious frames and integrate this motion into thesingle step estimation (see figure 4). The estimationof motion between frame m and the current frame k(m < k−1) follows exactly the same procedure as ex-plained above. Only when applying the SMC, a smallchange takes place, since the prediction of the posi-tion for k − m frames is not the same as for a singlestep. In other words, the matrix M ′

k−1of equation 12

is not valid any more. If the single step estimation for

the current frame was already computed as Mk equa-tion 12 becomes:

~ci = M−1

k−mMk−1Mk~xi − ~pi. (14)

Equation 14 represents the estimated motion betweentimes tk−m and tk−1 (from equation 11), updatedwith the current simple step estimation of time tk.This allows the SMC to be even more precise, sincethe uncertainty in the movement is now based on anupdated prediction. On the contrary in the single stepestimation, the uncertainty is based on a position de-fined by the last motion.

Once the camera motion matrix Mm,k betweentimes tk−m and tk is obtained, it is integrated withthe single step estimation. This is performed by aninterpolation. The interpolation of motion matricesmakes sense if they are estimations of the same mo-tion. This is not the case since the single step motionmatrix is referred to as the motion between the lasttwo frames and the multi-step motion matrix as themotion between m frames in the past to the current

one. Thus, the matrices to be interpolated are Mk and

M−1

m,k−1Mm,k (see figure 4). The corresponding ro-

tation matrices are converted to quaternions in orderto apply a spherical linear interpolation. The interpo-lated quaternion is converted to the final rotation ma-trix Rk. Translation vectors are linearly interpolated,

obtaining the new translation vector ~tk. The factorsof the interpolation are given by the weighted sum ofthe quadratic deviations obtained when computing therelative motion of equation 7.

The multi-frame approach performs better thanksto the integration of more measurements. It also re-duces the integration of the errors produced by thesingle-step estimation between the considered timepoints. In fact, our experience has shown that withoutthe multi-frame approach the estimation degeneratesquickly and, normally, after a few hundred frames theego-position diverges dramatically from the true solu-tion. Thus, the multi-frame approach provides addi-tional stability to the estimation process.

0

1

2

3

4�

��

�

�� �

��

�

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4

4���

��

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− �

��

Figure 4: multi-frame approach. Circles represent the posi-tion and orientation of the camera. Vectors indicate motionin 3D-space. M4 (single step estimation) and M

−1

1,3 M1,4

(multi-step estimation) are interpolated in order to obtainthe final estimation M

′

4.

4 THE ALGORITHM

This section summarizes the main tasks of our ap-proach. 1. Left and Right Image Acquisition.

2. Measurement.a. Compute optical flow (tracking).b. Compute stereo disparity.

3. Ego-Motion Computation.a. Apply SMC Single Step.b. Compute Single Step (SS) estimation.c. Apply SMC Multi-Step.d. Compute Multi-Step (MS) estimation.e. Interpolate SS and MS results.

4. Kalman Filter.a. Compute A and B matrices with ego-motion

estimation (Step 3).b. Update models.

5. Go to Step 1.

5 EXPERIMENTAL RESULTS

Our current implementation tracks 1200 points. Itruns at 12 − 16 Hz on a 3.2 GHz PC. We use aspeed-optimized version of the KLT algorithm (Shiand Tomasi, 1994) and compute stereo using a coarseto fine correlation method as described in (Franke,2000). In order to show the robustness of the method,we demonstrate the performance on three real worldsequences.

Uneven Street. In this sequence, the vehicle driveson a slightly uneven street. A bicyclist appears sud-denly from a back street at the right. The sequence has200 stereo image pairs and was taken at 16 Hz. Thebaseline of the stereo system is 0.35 meters and theimages have a VGA resolution. The car starts from astanding position and accelerates up to a velocity of30 km/h.

Figure 5(a) shows the improved results for the es-timation already illustrated in figure 2. Thanks to theego-motion estimation, the artefacts disappear and thebicyclist is clearly visible now. Figure 5(b) shows the

ego-motion estimation results for every frame of thesequence. The minimum in the roll rotation at frame120 correspond to the same frame number as above.Notice that the lateral translation decreases togetherwith the velocity despite the small yaw rotation. Thisindicates that the optical axis of the camera is notaligned with the driving direction of the vehicle, i.e.the camera is fixed mounted on the vehicle but view-ing slightly to the right.

This last observation reveals another advantage ofcomputing the ego-motion directly from the images:there is no need of an external calibration of the cam-era platform w.r.t. the vehicle. Figure 6(a) shows thevelocity vectors for frame 146, using only inertial sen-sors when the yaw rotation of the camera w.r.t. thevehicle was wrongly estimated by 5 degrees. Figure6(b) shows the results for the same camera configura-tion using only ego-motion estimation.

Crossing Traffic with Background Occlusion.Figure 7 shows the estimation results with an oncom-ing bus. In this sequence, both the ego-vehicle and thebus are driving in a curve. In the worst case, the bustakes up more than 35% of the image area. The com-putation of ego-motion is still possible here thanks tothe smoothness motion constraint, which selects onlystatic points (blue points in the image) for the ego-motion computation.

Indoor Environment. Figure 8 shows an exampleof the results in an indoor environment. The sequenceshows a person walking behind a desktop while thecamera is translated and rotated by hand. The colorencoding is the same as in the two previous examplesbut red now means 1.75 m/s. The different colorsof the arrows on the moving person correspond to thedifferent velocities of the different body parts (arms,body and legs).

6 SUMMARY

We have presented a method for the efficient es-timation of position and velocity of tracked imagepoints, and for the iterative improvements of theseestimates over time. The scene structure is obtainedwith a binocular platform. Optical flow delivers thechange of this structure in consecutive frames. By ob-serving the dynamics of the individual 3D points, anestimation of their velocity is possible. This way weobtain a six dimensional state for every world pointwhich is given in a vehicle coordinate system. As thecamera moves, the state of every point needs to beupdated according to the motion of the observer and,therefore, the ego-motion of the cameras needs to beknown. Instead of obtaining motion information fromthe error-prone inertial sensors of the vehicle, the sixd.o.f. of ego-motion are obtained as the optimal rota-

(a) 3D motion vectors. The arrows correspond to the esti-mated 3D position of the points in 0.5 seconds back projectedinto the image. The color encodes the velocity as shown inimage (c)

-0.023

-0.008

0.007

-0.017

-0.002

0.013

-0.050

0.130

0.310

0.490

-0.600

-0.300

0.000

0.300

0.600

-0.120

-0.020

0.080

-0.700

-0.200

0.300

5 20 35 50 65 80 95 110 125 140 155 170 185 200

5 20 35 50 65 80 95 110 125 140 155 170 185 200

M e

t e

r s

D e

g r

e e

s

(b) Ego-motion estimation. The plots show the observed mo-tion between consecutive frames. From top to bottom: X, Y ,Z translations; pitch, yaw, roll rotations.

2 . 2 5 m / s

0 m / s

4 . 5 m / s

2 . 2 5 m / s

0 m / s

4 . 5 m / s

(c)

Figure 5: a bicyclist approaches from the right while thevehicle drives on an uneven street.

tion and translation between the current and previousset of static 3D points of the environment. All thisinformation is fused using Kalman Filters, obtaining

(a) 3D motion vectors using inertial sensors.

(b) 3D motion vectors estimating the six d.o.f. of motion.

Figure 6: results when the camera orientation was wrongestimated. The images shows the state of the scene 1.5 sec-onds later as in figure 5.

an iterative improvement over time of the 3D pointposition and velocity.

This algorithm turned out to be powerful for thedetection of moving obstacles in traffic scenes. How-ever, it is not limited to this application but may bealso useful for other applications such as autonomousnavigation, simultaneous localization and mapping ortarget detection for military purposes.

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