1. Motion from image and inertial measurements Dennis Strelow Honeywell Advanced Technology Lab

2. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 2 On the web Related materials: these slides related papers movies VRML models at: http://www.dennis-strelow.com/umn

3. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 3 Introduction (1) From an image sequence, we can recover: 6 degree of freedom (DOF) camera motion without knowledge of the camera’s surroundings without GPS

4. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 4 Introduction (2) Fitzgibbon

5. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 5 Introduction (3) Potential applications include: modeling from video Yuji Uchida

6. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 6 Introduction (4) micro air vehicles (MAVs) AeroVironment Black WidowAeroVironment Microbat

7. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 7 Introduction (5) rover navigation Hyperion Nister, et al.

8. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 8 Introduction (6) search and rescue robots Rhex (movies: http://ai.eecs.umich.edu/Rhex/Movies)

9. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 9 Introduction (7) NASA Personal Satellite Assistant (PSA)

10. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 10 Introduction (8) For these problems, we want: 6 DOF motion in unknown environments without GPS or other absolute positioning

11. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 11 Introduction (8) For these problems, we want: 6 DOF motion in unknown environments without GPS or other absolute positioning using small, light, and cheap sensors

12. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 12 Introduction (8) For these problems, we want: 6 DOF motion in unknown environments without GPS or other absolute positioning using small, light, and cheap sensors over the long term

13. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 13 Introduction (9) Long-term motion estimation: absolute distance or time is long only a small fraction of the scene is visible at any one time

14. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 14 Introduction (10) given these requirements, cameras are promising sensors… …and many algorithms for motion from images already exist

15. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 15 Introduction (11) But, where are the systems for estimating the motion of: over the long term?

16. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 16 Introduction (12) …and for automatically modeling rooms buildings cities from a handheld camera?

17. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 17 Introduction (13) Motion from images suffers from some long- standing difficulties This work attacks these problems by… exploiting image and inertial measurements robust image feature tracking recognizing previously mapped locations exploiting omnidirectional images

18. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 18 Outline Motion from images refresher bundle adjustment difficulties Motion from image and inertial measurements Robust image feature tracking Long-term motion estimation Conclusion

19. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 19 Motion from images: refresher (1) A two-step process is common: sparse feature tracking estimation

20. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 20 Motion from images: refresher (1) A two-step process is common: sparse feature tracking estimation Sparse feature tracking: inputs: raw images outputs: projections

21. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 21 Motion from images: refresher (2)

22. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 22 Motion from images: refresher (3) Template matching: correlation tracking Lucas-Kanade (Lucas and Kanade, 1981) Extraction and matching: Harris features (Harris, 1992) Scale Invariant Feature Transform (SIFT) keypoints (Lowe, 2004)

23. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 23 Motion from images: refresher (4) The second step is estimation: inputs: projections outputs: 6 DOF camera position at the time of each image 3D position of each tracked point

24. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 24 Motion from images: refresher (5)

25. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 25 Motion from images: refresher (6) bundle adjustment (various, 1950’s) Kalman filtering (Broida, Chandrashekhar, and Chellappa, 1990) variable state dimension filter (VSDF) (McLauchlan, 1996) two- and three-frame methods (Hartley and Zisserman, 2000; Nister, et al. 2004)

26. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 26 Motion from images: bundle adjustment (1) From tracking, we have the image locations x ij for each point j and each image i

27. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 27 Motion from images: bundle adjustment (2) Suppose we also have estimates of: the camera rotation ρ i and translation t i at time of each image 3D point positions X j of each tracked point Then, we can compute reprojections:

28. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 28 Motion from images: bundle adjustment (3)

29. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 29 Motion from images: bundle adjustment (4)

30. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 30 Motion from images: bundle adjustment (5) So, minimize: with respect to all the ρ i, t i, X j

31. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 31 Motion from images: bundle adjustment (5) So, minimize: with respect to all the ρ i, t i, X j

32. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 32 Motion from images: difficulties (1) Estimation step can be very sensitive to… incorrect or insufficient image feature tracking camera modeling and calibration errors outlier detection thresholds sequences with degenerate camera motions

33. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 33 Motion from images: difficulties (2) Iterative batch methods have poor convergence or may fail to converge if: observations are missing the initial estimate is poor

34. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 34 Motion from images: difficulties (3) Recursive methods suffer from: poor prior assumptions on the motion poor approximations in state error modeling

35. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 35 Motion from images: difficulties (4) Resulting errors are: gross local errors long term drift

36. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 36 Motion from images: difficulties (5)

37. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 37 Motion from images: difficulties (6) 151 images, 23 points manually corrected Lucas-Kanade

38. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 38 Motion from images: difficulties (7)  squares: ground truth points  dash-dotted line: accurate estimate  solid line: image-only, bundle adjustment estimate

39. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 39 Outline Motion from images Motion from image and inertial measurements inertial sensors algorithms and results related work Robust image feature tracking Long-term motion estimation Conclusion

40. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 40 Motion from image and inertial measurements: inertial sensors (1) inertial sensors can be integrated to estimate six degree of freedom motion

41. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 41 Motion from image and inertial measurements: inertial sensors (2) But many applications require small, light, and cheap sensors

42. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 42 Motion from image and inertial measurements: inertial sensors (3) Integrating the outputs of these low grade sensors will produce drifting motion because of: noise unmodeled nonlinearities

43. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 43 Motion from image and inertial measurements: inertial sensors (4) And, we can’t even integrate until we can separate the effects of… rotation ρ gravity g acceleration a slowly changing bias b a noise n …in the accelerometer measurements

44. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 44 Motion from image and inertial measurements: inertial sensors (5) Image and inertial measurements are highly complementary With inertial measurements we can: decrease sensitivity in image-only estimates establish two rotation angles without drift establish the global scale

45. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 45 Motion from image and inertial measurements: inertial sensors (5) Image and inertial measurements are highly complementary With inertial measurements we can: decrease sensitivity in image-only estimates establish two rotation angles without drift establish the global scale …even with our low-grade sensors

46. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 46 Motion from image and inertial measurements: inertial sensors (6) With image measurements, we can: reduce the drift in integrating inertial data distinguish between… rotation ρ gravity g acceleration a bias b a noise n …in accelerometer measurements

47. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 47 Motion from image and inertial measurements: algorithms and results (1) This work has developed both: batch recursive algorithms for motion from image and inertial measurements

48. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 48 Motion from image and inertial measurements: algorithms and results (2) Gyro measurements: ω’, ω: measured and actual angular velocity b ω : gyro bias n: gaussian noise

49. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 49 Motion from image and inertial measurements: algorithms and results (3) Accelerometer measurements: ρ: rotation a’, a: measured and actual acceleration g: gravity vector b a : accelerometer bias n: gaussian noise

50. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 50 Motion from image and inertial measurements: algorithms and results (4) batch algorithm minimizes a combined error:

51. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 51 Motion from image and inertial measurements: algorithms and results (5) image term E image is the same as before

52. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 52 Motion from image and inertial measurements: algorithms and results (6) inertial error term E inertial is:

53. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 53 Motion from image and inertial measurements: algorithms and results (6) inertial error term E inertial is:

54. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 54 Motion from image and inertial measurements: algorithms and results (6) inertial error term E inertial is:

55. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 55 Motion from image and inertial measurements: algorithms and results (7) timeτ i-1 (time of image i - 1) t i-1 titi I(t i-1, …) τ i (time of image i) translation ( : translation estimate for image i – 1) ( : translation estimate for image i) ( : translation integrated from previous estimate)

56. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 56 Motion from image and inertial measurements: algorithms and results (8) time τ0τ0 translation τ1τ1 τ2τ2 τ5τ5 τ3τ3 τ4τ4 τ f-3 τ f-2 τ f-1

57. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 57 Motion from image and inertial measurements: algorithms and results (9)

58. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 58 Motion from image and inertial measurements: algorithms and results (10) I t (τ i-1, τ i,…, t i-1 ) depends on: τ i-1, τ i (known) all inertial measurements for times τ i-1 < τ < τ i (known) ρ i-1, t i-1 g b ω, b a camera linear velocities: v i

59. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 59 Motion from image and inertial measurements: algorithms and results (12)  dash-dotted line: batch estimate from image and inertial  solid line: image-only, bundle adjustment estimate  squares: ground truth points

60. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 60 Motion from image and inertial measurements: algorithms and results (13) IEKF for the same sensors, unknowns  dash-dotted line: batch estimate  solid line: IEKF estimate

61. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 61 Motion from image and inertial measurements: algorithms and results (14) Difficulties with IEKF for this application: prior assumptions about motion smoothness cannot model relative error between adjacent camera positions So, converting the batch algorithm into a variable state dimension filter (VSDF) is a promising future direction

62. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 62 Motion from image and inertial measurements: algorithms and results (15) IEKF assumptions on motion smoothness  dash-dotted line: batch estimate  solid line: IEKF estimate  right: IEKF propagation variances too strict  left: IEKF propagation variances just right

63. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 63 Motion from image and inertial measurements Recap: image, gyro, and accelerometer measurements batch algorithm recursive algorithm experiments evaluate batch and recursive algorithms establish basic facts about motion from image and inertial measurements

64. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 64 Outline Motion from images Motion from image and inertial measurements Robust image feature tracking Lucas-Kanade and real sequences The “smalls” tracker Long-term motion estimation Conclusion

65. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 65 Robust image feature tracking: Lucas- Kanade and real sequences (1) Combining image and inertial measurements improves our situation, but… we still need accurate feature tracking tracking some sequences do not come with inertial measurements

66. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 66 Robust image feature tracking: Lucas- Kanade and real sequences (2) better feature tracking for improved 6 DOF motion estimation remaining results will be image-only

67. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 67 Robust image feature tracking: Lucas- Kanade and real sequences (3) Lucas-Kanade has been the go-to feature tracker for shape-from-motion minimizes a correlation-like matching error using general minimization evaluates the matching error at only a few locations subpixel resolution

68. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 68 Robust image feature tracking: Lucas- Kanade and real sequences (4) Additional heuristics used to apply Lucas- Kanade to shape-from-motion: task:heuristic: choose features to trackhigh image texture identify mistracked, occluded, no-longer-visible convergence, matching error handle large motionsimage pyramid

69. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 69 Robust image feature tracking: Lucas- Kanade and real sequences (5) But Lucas-Kanade performs poorly on many real sequences…

70. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 70 Robust image feature tracking: the “smalls” tracker (1) smalls is a new feature tracker targeted at 6 DOF motion estimation exploits the rigid scene assumption eliminates the heuristics normally used with Lucas-Kanade SIFT is an enabling technology here

71. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 71 Robust image feature tracking: the “smalls” tracker (2) First step: epipolar geometry estimation use SIFT to establish matches between the two images get the 6 DOF camera motion between the two images get the epipolar geometry relating the two images

72. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 72 Robust image feature tracking: the “smalls” tracker (3)

73. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 73 Robust image feature tracking: the “smalls” tracker (4)

74. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 74 Robust image feature tracking: the “smalls” tracker (5) Second step: track along epipolar lines use nearby SIFT matches to get initial position on epipolar line exploits the rigid scene assumption eliminates heuristic: pyramid

75. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 75 Robust image feature tracking: the “smalls” tracker (6) Third step: prune features geometrically inconsistent features are marked as mistracked and removed clumped features are pruned eliminates heuristic: detecting mistracked features based on convergence, error

76. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 76 Robust image feature tracking: the “smalls” tracker (7) Fourth step: extract new features spatial image coverage is the main criterion required texture is minimal when tracking is restricted to the epipolar lines eliminates heuristic: extracting only textured features

77. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 77 Robust image feature tracking: the “smalls” tracker (8)

78. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 78 Robust image feature tracking: the “smalls” tracker (9) left: odometry onlyright: images only average error: 1.74 m maximum error: 5.14 m total distance: 230 m

79. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 79 Robust image feature tracking: the “smalls” tracker (10) Recap: exploits the rigid scene and eliminates heuristics allows hands-free tracking for real sequences can still be defeated by textureless areas or repetitive texture

80. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 80 Outline Motion from images Motion from image and inertial measurements Robust image feature tracking Long-term motion estimation proof of concept system experiment Conclusion

81. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 81 Long-term motion estimation: proof of concept system (1) Image-based motion estimates from any system will drift: if the features we see are always changing given sufficient time if we don’t recognize when we’ve revisited a location

82. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 82 Long-term motion estimation: proof of concept system (2)

83. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 83 Long-term motion estimation: proof of concept system (3) To limit drift: recognize when we’ve returned to a previous location exploit the return A proof of concept system demonstrates these capabilities

84. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 84 Long-term motion estimation: proof of concept system (4) “smalls” tracker state: 2D feature history for images in I variable state dimension filter (VSDF) state for images in I: 6 DOF camera positions, covariances for images in I 3D positions for features visible in I SIFT keypoints for image i n system state S image indices: I = {i 1, …, i n }

85. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 85 Long-term motion estimation: proof of concept system (5) 012345678 {0, 1} {0}{0, 1, 2}{0, 1, …, 8}

86. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 86 rollback Long-term motion estimation: proof of concept system (6) 012345678 {0, 1} {0}{0, 1, 2}{0, 1, …, 8} non-rollback States:

87. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 87 rollback Long-term motion estimation: proof of concept system (7) 012345678 {0, 1} {0}{0, 1, 2}{0, 1, …, 8} 8 non-rollback States:

88. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 88 rollback Long-term motion estimation: proof of concept system (8) 012345678 {0, 1} {0}{0, 1, 2} 8 {0, 1, 2, 3, 8} non-rollback pruned States:

89. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 89 rollback Long-term motion estimation: proof of concept system (9) 012345678 891011 121314 151617 181920 {0, …, 6, 11, 12, 17, …, 20} non-rollback pruned States:

90. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 90 Long-term motion estimation: proof of concept system (10) When to “roll back”? examine the camera covariances for the current state and the candidate rollback state check the number of SIFT matches extend from the candidate state examine the camera covariances for the current state and the resulting extended state

91. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 91 Long-term motion estimation: experiment (1) CMU FRC highbay views; 945 images total

92. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 92 Long-term motion estimation: experiment (2) CMU FRC highbay

93. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 93 Long-term motion estimation: experiment (2) CMU FRC highbay (first forward pass: images 0-213)

94. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 94 Long-term motion estimation: experiment (2) CMU FRC highbay (first forward pass: images 0-213)

95. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 95 Long-term motion estimation: experiment (2) CMU FRC highbay (first forward pass: images 0-213)

96. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 96 Long-term motion estimation: experiment (2) CMU FRC highbay (first backward pass: images 214-380)

97. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 97 rollback Long-term motion estimation: experiment (3) 012345678 891011 121314 151617 181920 non-rollback pruned States: normally, the system produces a general tree of states

98. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 98 Long-term motion estimation: experiment (4) … 01234567 13141514 16171817 non-rollback rollback pruned States: for this example, the “rollback” states are restricted to the first forward pass 89 10111214 213

99. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 99 Long-term motion estimation: experiment (5) movie…bottom half is smalls output:

100. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 100 Long-term motion estimation: experiment (6) movie…top half is motion estimates:

101. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 101 Long-term motion estimation: experiment (7) movie…top half is motion estimates:

102. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 102 Outline Motion from images Motion from image and inertial measurements Robust image feature tracking Long-term motion estimation Conclusion remaining issues

103. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 103 Conclusion: remaining issues all: system is experimental, not optimized for speed image and inertial: VSDF “smalls”: integration of gyro, more robustness to poor texture needed long-term: “roll back” space, computation grow with sequence length

104. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 104 Thanks! Related materials: these slides related papers movies VRML models at: http://www.dennis-strelow.com/umn

105. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 105 Motion from omnidirectional images (1)

106. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 106 Motion from omnidirectional images (2)

107. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 107 Motion from omnidirectional images (3)

108. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 108 Motion from omnidirectional images (4)

109. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 109 Motion from omnidirectional images (5) left: non-rigid cameraright: rigid camera squares: ground truth points solid: image-only estimates dash-dotted: image-and-inertial estimates

110. Dennis Strelow -- Motion estimation from image and inertial measurements -- March 22. 2006 110 Motion from omnidirectional images (6) In this experiment: omni images conventional images + inertial have roughly the same advantages But in general: inertial has some advantages that omni images alone can’t produce omni images can be harder to use