Page - 17 - in Proceedings of the OAGM&ARW Joint Workshop - Vision, Automation and Robotics

TC,2C,1 TC,m−1C,1 TC,mC,1 TC,m−1C,2 TC,mC,m−1 C2 Cm−1 Cm C1 v2 vm−1 vm v′2 v′m−1 v′m Fig. 1: Illustrated VO problem of a stereo system (relative transformations TC,m−1C,2, TC,mC,m−1 / absolute transformations TC,2C,1, TC,m−1C,1, TC,mC,1) Furthermore, the usage of additional sensors like GPS, laser scanner or IMU can improve the pose estimation. For example, in [1], [23], [17] or in [27] the integration of an IMU reduces the error in orientation. In [17] Konolige et al. achieve with their implemented real-time VO a maximum relative position error of just 0.1% over a 9km long track. Another good result is shown by Tardif et al. [27] over a 5.6km long track. This dataset was acquired by a tractor driving next to an orange grove and on a street for the return to the garage. III. VISUAL ODOMETRY As discussed in Section II, Visual Odometry incrementally estimates the pose. Figure 1 shows this for a typical case using a stereo-camera system. The calculation of a relative homogeneous transformation TC,mC,m−1∈SE(3) of an image pair {m−1,m} with camera centers / camera coordinate systems Cm−1 and Cm is done via features in the images. As shown in the figure, the coordinate system of the left camera is the reference point of a transformation TC,mC,m−1, which transforms from Cm−1 to Cm. The rigid body transformation is given by TC,mC,m−1= [ RC,mC,m−1 C,mtC,mC,m−1 0 1 ] (1) where RC,mC,m−1∈SO(3) is the orthogonal rotation matrix and C,mtC,mC,m−1∈R3 the translation vector, represented in the coordinate system Cm. The concatenation of all rela- tive transformations results in the absolute transformation TC,mC,1=TC,mC,m−1TC,m−1C,1 from C1 to Cm. Therefore, themain taskofaVOis tocalculate the relative transformations TC,mC,m−1 and finally to concatenate them to get the full camera trajectory TC,m:C,1={TC,2C,1,...,TC,mC,1} between the camera centers C1 and Cm. The structure of our VO approach is similar to the one of Nister et al. [22] and it starts with the feature detection and descriptionbut it uses themoredistinct featuresA-KAZE [2] instead of Harris [15]. The next step is to match features between a stereo pair and one consecutive image, either left or right. Then, the triangulated stereo correspondences and the matched 2D features are used for the pose estimation. At the end, key frames are selected and windowed bundle adjustment [28] is applied to further optimize the previous calculated poses [27]. A. Feature Detection andDescription Feature detection is one of the most important steps in a feature-based Visual Odometry system. Regarding to Fraundorfer [13], important properties of features are detec- tion repeatability, localization accuracy, robustness against noise as well as computation efficiency. In [8], Cordes et al. compare many different detection algorithms and the detector A-KAZE [2] proofs to be the best candidate in terms of localization accuracy and suitable number of detected features. This detector is implemented in OpenCV [5] and is an extension of the algorithm KAZE [3] to detect blobs. In general, these features are image patterns with different intensity, color and texture compared to its adjacent pixels and they are more distinctive than corners [13]. This is especially important in natural environment with ambiguous structures like branches or leaves. In our case, A-KAZE detects blobs in a nonlinear scale space with four octaves and the same amount of sub-levels. In addition to the detection algorithm, A-KAZE also provides one for the description of a feature, which is implemented in OpenCV as well. It converts the area around a feature into a binary descriptor which has a length of 486bit. Every comparison between two areas results in three bit. The description algorithm of A-KAZE is called M-LDB (Modified-Local Difference Binary) and is rotation and scale invariant.According to Alcantarilla et al., A-KAZE allows efficient and successful feature matching, which are mandatory properties of a good descriptor. B. FeatureMatching The task of this step is to find feature correspondences among images. The easiest way to achieve matching between two images is to compare all feature descriptors of the first image with every other descriptor of the second one. This search is quadratic in the number of features. Fortunately, the usage of epipolar or motion constraints simplifies this task and reduces the computation time drastically. This is necessary to facilitate an online VO system, which could be used on a vehicle like a tractor during its operation in a field or forest. Our stereo VO relies on rectified images, which are remapped image pairs with horizontal and aligned epipolar lines to each other (see [13]). Thus, epipolar matching just allows a match between features which lie on the same horizontal epipolar line or rather image row. Descriptors of two consecutive left or right images can be matched via a motion constraint. As proposed in [10], we assume a constant velocity model between two frames. Using the known motion, we can project the 3D point of a already matched stereo correspondence into the other image. Aconstantwindowof2·35×2·35pixelaround theprojected position defines the allowed area of possible features and therefore reduces the computing time. 17