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Real-Time Tracking

Real-Time Tracking. Axel Pinz Image Based Measurement Group EMT – Institute of Electrical Measurement and Measurement Signal Processing TU Graz – Graz University of Technology http://www.emt.tugraz.at/~tracking http://www.emt.tugraz.at/~pinz axel.pinz@tugraz.at. Defining the Terms.

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Real-Time Tracking

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  1. Real-Time Tracking Axel Pinz Image Based Measurement Group EMT – Institute of Electrical Measurement and Measurement Signal Processing TU Graz – Graz University of Technology http://www.emt.tugraz.at/~tracking http://www.emt.tugraz.at/~pinz axel.pinz@tugraz.at

  2. Defining the Terms • Real-Time • Task dependent, “in-the-loop” • Navigation: “on-time” • Video rate: 30Hz • High-speed tracking: several kHz • Tracking • DoF: Degrees of Freedom • 2D: images, videos  2 / 3 DoF • 3D: scenes, object pose  6 DoF

  3. Example: High-speed, 2D

  4. Applications • Surveillance • Augmented reality • Surgical navigation • Motion capture (MoCap) • Autonomous navigation • Telecommunication • Many industrial applications

  5. Example: Augmented Reality [ARToolkit, Billinghurst, Kato, Demo at ISAR2000, Munich] http://www.hitl.washington.edu/research/shared_space/download/

  6. AgendaStructure of the SSIP Lecture • Intro, terminology, applications • 2D motion analysis • Geometry • 3D motion analysis • Practical considerations • Existing systems • Summary, conclusions

  7. 2D Motion Analysis • Change detection • Can be anything (not necessarily motion) • Optical flow computation • What is moving in which direction ? • Hard in real time • Data reduction required ! • Interest operators • Points, lines, regions, contours • Modeling required • Motion models, object models • Probabilistic modeling, prediction

  8. Change Detection [Pinz, Bildverstehen, 1994]

  9. Optical Flow (1) [Brox, Bruhn, Papenberg, Weickert] ECCV04 best paper award • Estimating the displacement field • Assumptions: • Gray value constancy • Gradient constancy • Smoothness • ... • Error Minimization

  10. Optical Flow (2) [Brox, Bruhn, Papenberg, Weickert] ECCV04 best paper award !! Not in real-time !!

  11. Interest Operators • Reduce the amount of data • Track only salient features • Support region – ROI (region of interest) Feature in ROI: Edge / Line Corner Blob Contour

  12. 2D Point Tracking[Univ. Erlangen, VAMPIRE, EU-IST-2001-34401] • Corner detection  Initialization • Calculate “cornerness” c • Threshold  sensitivity, # of corners • E.g.: “Harris” / “Plessey” corners in ROI • Cross-correlation in ROI

  13. 2D Point Tracking[Univ. Erlangen, VAMPIRE, EU-IST-2001-34401]

  14. Edge Tracking[Rapid 95, Harris, RoRapid 95, Armstrong, Zisserman]

  15. Blob Tracking[Mean Shift 03, Comaniciu, Meer]

  16. Contour Tracking[CONDENSATION 98-02, Isard, Toyama, Blake]

  17. CONDENSATION (2) • CONditional DENSity propagATION • Requires a good initialization • Works with active contours • Maintains / adapts a contour model • Can keep more than one hypothesis

  18. AgendaStructure of the SSIP Lecture • Intro, terminology, applications • 2D motion analysis • Geometry • 3D motion analysis • Practical considerations • Existing systems • Summary, conclusions

  19. Geometry • Having motion in images: • What does it mean? • What can be measured? • Projective camera • Algebraic projective geometry • Camera calibration • Computer Vision • Reconstruction from uncalibrated views • There are excellent textbooks [Faugeras 1994, Hartley+Zisserman 2001, Ma et al. 2003]

  20. Projective Camera (1) • Pinhole camera model: • p = (x,y)Tis the image ofP = (X,Y,Z )T • (x,y) ... image-, (X,Y,Z) ... scene-coordinates • o ... center of projection • (x,y,z) ... camera coordinate system • (x,y,-f) ... image plane x x P(X,Y,Z) f o z y y Z X p(x,y) Y

  21. Projective Camera (2) • Pinhole camera model: • If scene- = camera-coordinate system X f o Z x

  22. Projective Camera (3) • Frontal pinhole camera model: • (x,y,+f) ... image plane • Normalized camera: f=+1 P(X,Y,Z) f x x o p z y y Z X Y

  23. Projective Camera (4) • “real” camera: • 5 Intrinsic parameters (K) • Lens distortion • 6 Extrinsic parameters (M: R, t) •  … arbitrary scale

  24. Algebraic Projective Geometry [Semple&Kneebone 52] • Homogeneous coordinates • Duality points  lines • Homography H describes any transformation • E.g.: image  image transform: x’ = Hx • All transforms can be described by 3x3 matrices • Combination of transformations: Matrix product Translation Rotation

  25. Camera Calibration (1) • Recover the 11 camera parameters: • 5 Intrinsic parameters (K: fsx, fsy, fs, u0, v0) • 6 Extrinsic parameters (M: R, t) • Calibration target: • At least 6 point correspondences  • System of linear equations • Direct (initial) solution for K and M

  26. Camera Calibration (2) • Iterative optimization • K, M, lens distortion • E.g. Levenberg-Marquart • Practical solutions require more points • Many algorithms [Tsai 87, Zhang 98, Heikkilä 00] • Overdetermined systems • Robustness against outliers • E.g. RANSAC • Refer to [Hartley, Zisserman, 2001]

  27. What can be measured ... • … with a calibrated camera • Viewing directions • Angles between viewing directions • 3D reconstruction: more than 1 view required • … with uncalibrated camera(s) • Computer Vision research of the past decade • Hierarchy of geometries: Projective – oriented projective – affine – similarity – Euclidean

  28. AgendaStructure of the SSIP Lecture • Intro, terminology, applications • 2D motion analysis • Geometry • 3D motion analysis • Practical considerations • Existing systems • Summary, conclusions

  29. 3D Motion Analysis:Location and Orientation head coord. system R t scene coord. system 6 DoF pose in real-time Extrinsic parameters in real-time

  30. 3D Motion Analysis: • Tracking technologies, terminology • Camera pose (PnP) • Stereo, E, F, epipolar geometry • Model-based tracking • Confluence of 2D and 3D • Fusion • Kalman Filter

  31. Tracking Technologies (1) • Mechanical tracking • “Magnetic tracking” • Acoustic – time of flight • “Optical”  vision-based • Compass • GPS, … External effort required ! No „self-contained“ system [Allen, Bishop, Welch. Tracking: Beyond 15 minutes of thought. SIGGRAPH’01]

  32. Tracking Technologies (2)Examples [Allen, Bishop, Welch. Tracking: Beyond 15 minutes of thought. SIGGRAPH’01]

  33. Research at EMT:Hybrid Tracking – HT Combine 2 technologies: • Vision-based • Good results for slow motion • Motion blur, occlusion, wrong matches • Inertial • Good results for fast motion • Drift, noise, long term stability • Fusion of complementary sensors ! Mimicks human cognition !

  34. Vision-Based Tracking MoreTerminology • Measure position and orientation in real-time • Obtain trajectories of object(s) • Moving observer, egomotion – “inside-out” • Stationary observer – “outside-in Tracking” • Combinations of the above • Degrees of Freedom – DoF • 3 DoF (mobile robot) • 6 DoF (head tracking in AR)

  35. Inside-out Tracking • monocular • exterior parameters • 6 DoF from  4 points • wearable, fully mobile corners blobs natural landmarks

  36. Outside-in Tracking stereo-rig IR-illumination • no cables • 1 marker/device: • 3 DoF • 2 markers: 5 DoF • 3 markers: 6 DoF devices

  37. Camera Pose Estimation • Pose estimation: Estimate extrinsic parameters from known / unknown scene  find R, t • Linear algorithms [Quan, Zan, 1999] • Iterative algorithms [Lu et al., 2000] • Point-based methods • No geometry, just 3D points • Model-based methods • Object-model, e.g. CAD

  38. PnP(1)Perspective n-Point Problem • Calibrated camera K, C = (KKT)-1 • n point correspondences scene  image • Known scene coordinates of pi, and known distances dij= ||pi – pj || • Each pair (pi,pj) defines an angle  •  can be measured (2 lines of sight, calibrated camera)  constraint for the distance ||c –pi|| pi pj dij xi xj  c

  39. PnP (2) pi pj dij xi xj  c uj ui

  40. PnP (3) • P3P, 3 points: underdetermined, 4 solutions • P4P, 4 points: overdetermined, 6 equations, 4 unknowns 4 x P3P, then find a common solution • General problem: PnP, n points

  41. PnP (4) Once the xihave been solved: • project image points  scene p’i= xi K-1ui • find a common R, t for p’i pi (point-correspondences  solve a simple system of linear equations)

  42. Stereo Reconstruction z Elementary stereo geometry in “canonical configuration” 2 h … “baseline” b Pr - Pl … “disparity” d There is just column disparity Depth computation: P(x,y,z) Pz y Cl Cr x f Pl Pr h h xl=0 x=0 xr=0

  43. Stereo (2) • 2 cameras, general configuration: Epipolar geometry X Y ur ul v ll lr Cl el er Cr

  44. Stereo (3) • Uncalibrated cameras: Fundamental matrix F • Calibrated cameras: Essential matrix E • 3x3, Rank 2 • Many Algorithms • Normalized 8-point [Hartley 97] • 5-point (structure and motion) [Nister 03]

  45. Model-Based Tracking Confluence of 2D and 3D [Deutscher, Davison, Reid 01]

  46. 3D Motion Analysis: • Tracking technologies, terminology • Camera pose (PnP) • Stereo, E, F, epipolar geometry • Model-based tracking • Confluence of 2D and 3D • Fusion • Kalman Filter • General considerations • Kalman Filter •  EMT HT project

  47. General Considerations • We have: • Several sensors (vision, inertial, ...) • Algorithms to deliver pose streams for each sensor (at discrete times; rates may vary depending on sensor, processor, load, ...) • Thus, we need: • Algorithms for sensor fusion (weighting the confidence in a sensor, sensor accuracy, ...) • Pose estimation including a temporal model [Allen, Bishop, Welch. Tracking: Beyond 15 minutes of thought. SIGGRAPH’01]

  48. Sensor Fusion • Dealing with ignorance: • Imprecision, ambiguity, contradiction, ... • Mathematical models • Fuzzy sets • Dempster-Shafer evidence theory • Probability theory • Probabilistic modeling in Computer Vision • The topic of this decade ! • Examples: CONDENSATION, mean shift

  49. Kalman Filter (1) [Welch, Bishop. An Introduction to the Kalman Filter. SIGGRAPH’01] http://www.cs.unc.edu/~welch/kalman

  50. Kalman Filter (2) • Estimate a process • with a measurement xn ... State of the process zm ... Measurement p, v ... Process and measurement noise (zero mean) A ... n x n Matrix relates the previous with the current time step B ... n x l Matrix relates optional control input u to x H ... n x m Matrix relates state x to measurement z

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