SLAM (Simultaneously Localization and Mapping)

1. SLAM (Simultaneously Localization and Mapping) Presenter : Jeongkyun Lee

2. Contents • What is SLAM • SfM-based SLAM • Filter-based SLAM • Comparison • Other SLAMs • Research topics

3. What is SLAM • Simultaneously Localization and Mapping Unknown Environment Given only images Unknown Pose

4. What is SLAM • How to localize & map • Structure-from-Motion based • Filtering based Pay attention to : Initialization Measures ( Matching features ) Localization & Mapping

5. Fundamentals • Geometry Projection matrix Rotation matrix 3D homogeneous vector 2D image point Translation vector Calibration matrix Normalized point Fundamental matrix where Essential matrix * http://www.umiacs.umd.edu/~ramani/cmsc828d/lecture27.pdf * Multiple View Geometry in Computer Vision, R. Hartley and A. Zisserman, Cambridge, University Press, 2000

6. SfM-based SLAM Fundamentals • 5-point algorithm1) Rotation matrix : 3 DoF(Rodrigues’ formula) Translation vector : 3 DoF Thus, is 5 DoF. ( 3 + 3 – 1, 1 DoF for scaling factor ) Given 5 pairs of points on the image planes, We can obtain . • PnP problem (Perspective-n-Point problem) Given n 3D-to-2D point correspondences We can obtain . • Grunert’s algorithm2) (P3P) • EPnP3) • Robust PnP4) • ... Known Environment Unknown pose Corresponding image points 1) D. Nister, An Efficient Solution to the Five-Point Relative Pose Problem, IEEE Conference on Computer Vision and Pattern Recognition, Volume 2, pp. 195-202, 2003. 2) R. M. Haralick, C. N. Lee, K. Ottenberg and M. Nolle, Review and Analysis of Solutions of the Three Point Perspective Pose Estimation Problem, International Journal of Computer Vision, 1994. 3) F. Moreno-Noguer, V. Lepetitand P. Fua, Accurate Non-Iterative O(n) Solution to the PnP Problem, IEEE International Conference on Computer Vision, Rio de Janeiro, Brazil, October 2007. 4) S. Li,C. Xu,M. Xie, A Robust O(n) Solution to the Perspective-n-Point Problem, IEEE Transactions on Pattern Analysis and Machine Intelligence (2012) Volume 34, Issue 7, pp. 1444-1450

7. SfM-based SLAM • Visual Odometry1) • Feature Detection : Harris corners • Feature Matching : Normalized Corss Correlation (NCC) Only matches between detected features within a fixed distance. • Procedure Given 3 frames 5-point algorithm3),4) & RANSAC3) Triangulation P3P P3P … … Given 1 frames 5P 5P P3P algorithm & RANSAC3) Re-triangulation using first & last observations 1) D. Nister, O. Naroditsky, J. Bergen, Visual odometry, Computer Vision and Pattern Recognition,July 2004. 2) D. Nister, Preemptive RANSAC for Live Structure and Motion Estimation, IEEE International Conference on Computer Vision, 2003. 3) D. Nister, An Efficient Solution to the Five-Point Relative Pose Problem, IEEE Conference on Computer Vision and Pattern Recognition, Volume 2, pp. 195-202, 2003. 4) D. Nister, An Efficient Solution to the Five-Point Relative Pose Problem, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004.

8. SfM-based SLAM • Real Time Localization and 3D Reconstruction1) • LBA2) (Levenberg-Marquardt algorithm (LM)) Minimize where Visual odometry + Local bundle adjustment (LBA) : Extrinsic parameters : Projection matrix : The square of Euclidean distance : Estimated projection of point through the camera : Observation 1) E. Mouragnon, M.Lhuillier, M.Dhome, F.Dekeyser, P. Sayd, Real Time Localization and 3D Reconstruction, Computer Vision and Pattern Recognition,2006. 2) B. Triggs, P. F. McLauchlan, R. I. Hartley & A. W. Fitzibbon, Bundle adjustment – A modern synthesis, in Vision Algorithms: Theory and Practice, LNCS, pp. 298-375, Springer Verlag, 2000.

9. SfM-based SLAM • Real Time Localization and 3D Reconstruction n : number of optimized camera poses N : number of cameras used for reprojection criterion minimization

10. SfM-based SLAM • Real Time Localization and 3D Reconstruction • Key frame selection • Number of matched points • Uncertainty of camera pose ( Obtained from the hessian inverse ) • Complexity : • Experiments 512 x 384 pixes, 75 fps, 94 key frames from a series of 445.

11. Filter-based SLAM • MonoSLAM1) • EKF-based To easily explain…. Filter initialization Prediction Map management ( Generate & delete features ) Prediction Measurements Acquisition Measurements acquisition Data association Update Update 1) A. J. Davison, I. D. Reid, N. D. Molton, O. Stasse, MonoSLAM: Real-Time Single Camera SLAM, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 29, no. 6, June 2007.

12. Filter-based SLAM • MonoSLAM Prediction Measurements Acquisition Update Prediction State Dynamic System Model (Constant Velocity Model) : 3D position vector : orientation quaternion : linear velocity vector : angular velocity vector : landmark position vector

13. Filter-based SLAM • MonoSLAM Prediction Measurements Acquisition Update Active search1),2) Prediction of measurements Find measurements For Matching the patch by NCC at Max NCC value at > threshold Measurement : a covariance matrix for the 2D position of ith landmark 1) A. J. Davison, Active Search for Real-Time Vision, International Conference Computer Vision, 2005. 2) M. Chli, A. J. Davison, Active Matching for Visual Tracking, Robotics and Autonomous Systems, 57(12):1173-1187, 2009.

14. Filter-based SLAM • MonoSLAM Prediction Measurements Acquisition Update Update : a Kalman gain at time t 1) A. J. Davison, Active Search for Real-Time Vision, International Conference Computer Vision, 2005. 2) M. Chli, A. J. Davison, Active Matching for Visual Tracking, Robotics and Autonomous Systems, 57(12):1173-1187, 2009.

15. Filter-based SLAM • MonoSLAM • Initialization of features • Delayed : SfM • Undelayed : Inverse depth parameterization1) • Data association • 1-point RANSAC2) • Joint Compatibility Branch and Bound3) (JCBB) • Experiment • 1.6GHz Pentium M processor 1) J. Civera, A. J. Davison, J. M. M. Montieal, Inverse Depth Parametrization for Monocular SLAM, IEEE Transactions on Robotics 24(5):932-945, 2008. 2) J. Civera, O. G. Grasa, A. J. Davison, J. M. M. Montiel, 1-Point RANSAC for EKF Filtering. Application to Real-Time Structure from Motion and Visual Odometry , Journal of Field Robotics, 2010 3) J. Neira, J. D. Tardos, Data association in stochastic mapping using the joint compatibility test, IEEE Transactions on Robotics and Automation, 17(6):890-897, Dec 2001.

16. Comparison

17. Other SLAMs • PTAM (Parallel Tracking and Mapping)1) • Separate Tracking / Mapping • Redundancy : use only key frames. • Accuracy : available to optimization. Tracking Mapping Pose estimate & Map point projection Searching a small number (50) of the coarsest-scale features by pyramid Pose update Searching a large number (1000) of the re-projected features Final pose estimation 1) G. Klein, D. Murray, Parallel Tracking and Mapping for Small AR Workspaces, ACM International Symposium on Mixed and Augmented Reality, 2007.

18. Other SLAMs • PTAM (Parallel Tracking and Mapping) • Features • Matching : zero mean SSD • Key frame • > 20 frames from the last key frame. • Minimum distance away from the nearest key point. • Point initialization • Epipolar search • Data association refinement • Create new features in older keyframes. • Re-measure outlier measurements. • Experiments • Intel Core 2 Duo 2.66GHz, 600x480 pixels • 6000 point, 150 keyframes.

19. Beyond Spatial Pyramids: A New Feature Extraction Framework with Dense Spatial Sampling for Image Classification Topics • Filter-based… • Divergence • Relocalization • Multiple model • Resilience • Other filtering techniques • Error accumulation • Loop-closing • Combining LBA, visual odometry • Data association • 1-point RANSAC • ICNN, SCNN, JCBB • Dynamic environment • SLAMMOT (SLAM and Moving Object Tracking) • Multi-view, Sensor fusion • Application • Dense 3d reconstruction • AR • Deblurring

20. Thank you!