SLAM (Simultaneously Localization and Mapping) Presenter : Jeongkyun Lee

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

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

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

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

Fundamentals 5-point algorithm1) 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. Lepetit and 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

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 5-point algorithm3),4) & RANSAC3) Given 3 frames P3P algorithm & RANSAC3) Triangulation Re-triangulation using first & last observations Given 1 frames … P3P 5P 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.

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.

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

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.

Measurements Acquisition Filter-based SLAM MonoSLAM1) EKF-based Filter initialization Map management ( Generate & delete features ) Prediction Measurements acquisition Data association Update To easily explain…. Prediction Measurements Acquisition 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.

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

Measurements Acquisition Filter-based SLAM MonoSLAM Prediction Measurements Acquisition Update For Matching the patch by NCC at Max NCC value at > threshold Measurement Prediction of measurements Find measurements Active search1),2) : a covariance matrix for the 2D position of i th 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.

Measurements Acquisition 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.

Filter-based SLAM MonoSLAM Initialization of features Data association 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.

Comparison SfM-based Filter-based Initialization 5-point algorithm Delayed : SfM Undelayed : Inverse depth parameterization Measurement NCC matching (from extracted feature points) KLT tracker Active search (prediction & templete matching) Estimation technique LBA (after p3p algorithm) Kalman filtering (prediction & update) Tracking 3~400 points in a frame Working in real time within 100 landmarks.

Searching a large number (1000) of the re-projected features 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.

Other SLAMs PTAM (Parallel Tracking and Mapping) Features Experiments 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.

Topics Filter-based… Divergence Error accumulation Data association 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

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