OUTLINE Nowadays, stereo vision techniques are broadening to a wide range of applications. They provide a 3D representation of the real world scene captured by a couple of cameras, from which a large amount of information can be inferred. Characterizing object's trajectory, whether they are vehicles or people, finds a useful application in event detection, traffic monitoring and video-surveillance. Furthermore, the estimation of positioning and aligning parameters of a target object is widely employed in machine vision as well as in industrial automotive applications.
The estimation of a vehicle's trajectory can be performed using systems integral with the vehicle (odometry) or systems placed outside the vehicle. In visual odometry, the motion of the camera is characterized stemming from the analysis of the changing scene or of some target objects. Accordingly, it reveals useful information regarding positioning and dynamics of the integral moving vehicle. These systems are mainly employed in automatic guidance and robot navigation, gathering information from different sensors (e.g. rotary encoders) and inertial navigation systems in relative positioning approaches. To perform trajectory estimation, the installation of such sensors has to be done for each vehicle to be analyzed. Besides being invasive, such systems are even subject to error drift, so that to achieve a high accuracy they require complex algorithms and to keep continuously aligned with a global reference system, like that provided by GPS devices. On the other side, the reconstruction of the 3D vehicle trajectory can be carried out by analyzing stereo flow acquired from outside, where the acquisition system is placed in a fixed position and the moving vehicle is tracked frame by frame. These systems usually need to obtain an accurate averaged trajectory, to know just where vehicles are moving to. In these cases, they manage to achieve measurements with an accuracy not better than a few degrees.

METHOD We devised a stereo-based, markerless and non-invasive approach, capable to appreciate deviations in motion direction of even tenths of degrees. Usually, in order to manage measuring the vehicle alignment with a high accuracy, it needs to be performed when the vehicle is still, on the testing platform. Our approach joints photogrammetry and videogrammetry principles by gathering all the data coming from the vehicle while approaching the test apparatus, by analyzing the tangent to its trajectory tracked and recovered using 3D stereo [MV1][MV2]. To measure the longitudinal deviation of the vehicle trajectory using stereo tracking in real time, using a low power architecture, it is suitable to track a region of the vehicle that is integral with the vehicle itself. To this purpose, we have chosen a natural target always present in the vehicles, i.e. the license plate, a textured region always offering a high number of features to be tracked.
The first step before using a stereo system concerns stereo calibration to recover the intrinsic and extrinsic parameters of the stereo rig. Exploiting these parameters is possible to generate the correspondent rectified pair of images. After that, the feature-based sparse stereo matching algorithm we have developed can be summarized as follows:

• features are tracked separately for each image, using the Lukas-Kanade feature tracker, within the 2D region defined by the four vertices of the licence plate detected automatically (highlighted in Fig. 2)
• for each feature in the left image, the correspondent features is searched in the right image, within the z-region defined by the 3D coordinates of the four vertices, according to the epipolar constraint
• among the candidates defined at the previous point, the features in the right image retaining the minimum Euclidean distance from the license plate plane are chosen

Fig. 2 shows the features tracked in the left and the right rectified stereo image couple, where same colour means same "intensity". For the sake of clarity, just some of the features are numbered. For instance, features 1 and 2 match, while 3 and 4 do not.

Fig. 2: From left to right: the stereo couple; the features detected by our algorithm in the left and right image of the stereo couple. For instance, features 1 and 2 match, while 3 and 4 do not.

Since this algorithm works at 25 frame per second (fps), the vehicle's trajectory can be approximated by its instant tangets, using RANSAC to filer each of the three vectors components. These vectors can be thus projected onto the floor reference plane and the vehicle’s trajectory can be built incrementally, until the vehicle stops.

RESULTS The accuracy of our algorithm has been first assessed using a license plate mounted on a mechanical support free of moving with controlled velocity along a rigid linear guide (Fig. 3, first stereo pair, from left to right). The guide is placed at the ground level and the deviation angle with respect to a line used as a reference (0° angle) to the sistem can be varied and measured with an accuracy of 0.02°. This yields a perfectly linear trajectory with its tangents coinciding with the trajectory itself.

(a)	(b)	(c)	(d)

Fig. 3: From left to right: left (a) and right (b) rectified pair of images of the license plate moving along a known trajectory; left (c) and right (d) pair of images of the vehicle moving toward the stereo rig, with the "sand track" deposited on the floor.

In order to establish a ground truth even in real conditions, a track of the car trajectory has been obtained by fixing to the vehicle a rigid case releasing sand to draw a colored track (the sand track) deposited on the floor (the second stereo pair of Fig. 3). The sand track is processed with an accuracy of 0.05° and acts as a ground truth line.
In Fig. 4, left, the angular error versus the ground-truth deviation angle for 14 test sequences is shown.


The measures have been achieved by averaging the values in the last three meters, since we are mostly interested to the last value, when the vehicle stops. In this plot, 10 sequences have been collected using the mechanical guide validation method, whereas 4 more sequences have been achieved through the sand track method. Most of the trials (9 out of 14) using fixed ground truth have been accomplished for small variations of 5° in absolute value. This is because in this application we are interested to study small angles with the highest accuracy, supposing that while approaching the test system the vehicle is already somehow aligned ([-15°,+15°]). As it can be seen, the system proves to be very accurate. In fact, the absolute angular error is less than 0.1°, comparable with the accuracy of the calibration procedure of the stereo rig. Fig. 4, right, shows that the percentage errors, keep under 10%, independently of the deviation angle (the near-zero measures circled in the left image have been left out of consideration), thus proving that our method is reliable in all the range of interest. More details are reported in [MV3].

Acknowledgements
This research has been partly funded by SIMPESFAIP SPA (CORGHI Group).

Measurements of geometric properties of a vehicle beam's light profile (also, see here)

REFERENCES
[MV1] A. Bevilacqua, A. Gherardi, L. Carozza, An industrial vision-based technology system for the automatic test of vehicle beams, IEEE International Symposium on Industrial Electronics (ISIE 2009), Seoul, Korea, July 5-8, 2009, pp.2178-2183
[MV2] A. Bevilacqua, A. Gherardi, L. Carozza, An automatic system for the real time characterization of vehicle headlamp beams exploiting image analysis, to appear on IEEE Transactions on Instrumentation and Measurement, 2010
[MV3] A. Bevilacqua, A. Gherardi, L. Carozza, Accuracy Estimation of Vehicle Trajectory using Real Time Stereo Vision, IEEE International Symposium on Industrial Electronics (ISIE 2009), Seoul, Korea, July 5-8, 2009, pp.2230-2235