Page - 81 - in Proceedings - OAGM & ARW Joint Workshop 2016 on "Computer Vision and Robotics“

The idea is that the Euclidean distance between SIFT matches of an image pair taken spatially closer togetheris lowerthanwhentakenfrompositionsfartherapart.E isusedtofindtheimagestoinitialize thealgorithm and tofindsubsequent images to iteratively extend themodel. 4.3. LaserPointCorrespondenceComputation Withtheimagepairs(Ii,Ij) remainingintheworkingset(seeSec4.2.),weestablishcorrespondences for the measurements of the LRF. We then compute the 2D laser point l2D,i,i by projecting l3D,i into its respective image using the extrinsic calibration (see Sec. 3.). As we typically deal with planar structures like facades, we estimate a homography and transform l2D,i,i into image Ij to get l2D,i,j. This approach proves to be fairly robust in our experiments, however due to the highly repetitive natureofmanyfacades, falsepositives still posechallenge. 4.4. Structure fromMotion (SfM) Our structure from motion (SfM) approach consists of three successive steps: finding an initial set formodel initialization (i), iterativelyaddingone imageata time(ii) andonefinalbundleadjustment overall pairs (iii). Model Initialization As for all iterative SfM systems, finding a good set of starting images is challenging. Due to the manyavailable features incommonapproaches,onlyone imagepair isnecessary to initializecamera pose estimations. In contrast, our approach needs a larger initial set to account for its sparse nature. Each camera has 6 degrees of freedom (3 for rotation, 3 for translation), hence we need at least 6 equations to estimate its pose. In the previous step we obtained for each image pair (Ii,Ij) two 3D- 2D correspondences l3D,i⇔ l2D,i,j and l3D,j⇔ l2D,j,i, i.e. 4 equations for each given image pair. For a set of at least 4 images, the resulting equation system is solvable with 6 different image pairs resulting in 4 equations each. The initial set Iinit is chosen as the set of 4 images with the smallest sumofmutual errorsEi,j. We solve the task of finding relative rotationsRi and translations ti in 3D for each camera by min- imizing the reprojection errorC(·) of a laser measurement l3D,i and its 2D correspondences l2D,i,j· withbundleadjustment. The reprojectionerror isdefinedas: C(Iinit) =min||pi(Rj(R−1i l3D,i−ti)+tj)− l2D,i,j||22,∀i,j∈ Iinit,i 6= j, (4) withR and t the rotation and translation of each respective view andpi(·) the projection. This for- mulation first projects a laser measurement l3D,i in 3D from its respective camera coordinate system i into a common world coordinate system and subsequently reprojects it to the camera coordinate systemj. Wesolve theminimizationproblemofbundleadjustmentwithaLevenberg-Marquardt [17] least-squares solver. We denote the resulting set of rotations and translations of all camera views currently involvedasourcurrentmodelMcurr. IterativeBundleAdjustment In the next step, we extend our modelMcurr by adding a new image Ik from the pool of candidates. We find Ik by summing up the errorEcurr,k of all possible image pairs (Icurr,Ik) and take the one with the most correspondences and the lowest overall error. We also set the initial rotationRk and translation tk of the newly added camera equal to the parameters of the closest camera, i.e. the one with the lowestEi,k,i ∈Mcurr. For each image pair, i. e. 3D-2D correspondence, we get two 81