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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.

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contents
Contents
  • What is SLAM
  • SfM-based SLAM
  • Filter-based SLAM
  • Comparison
  • Other SLAMs
  • Research topics
what is slam
What is SLAM
  • Simultaneously Localization and Mapping

Unknown Environment

Given only images

Unknown Pose

what is slam1
What is SLAM
  • How to localize & map
    • Structure-from-Motion based
    • Filtering based

Pay attention to :

Initialization

Measures ( Matching features )

Localization & Mapping

fundamentals
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

fundamentals1
SfM-based SLAMFundamentals
  • 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

sfm based slam
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.

sfm based slam1
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 slam2
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 slam3
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.

filter based slam
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.

filter based slam1
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

filter based slam2
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.

filter based slam3
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 slam4
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.

other slams
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 slams1
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.
topics
Beyond Spatial Pyramids: A New Feature Extraction Framework with Dense Spatial Sampling for Image ClassificationTopics
  • 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