Motion from image and inertial measurements Dennis Strelow Carnegie Mellon University

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, On the web Related materials: these and related slides related papers movies VRML models at:

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Introduction (2) Fitzgibbon

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Introduction (3) Potential applications include: modeling from video Yuji Uchida

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Introduction (4) micro air vehicles (MAVs) AeroVironment Black WidowAeroVironment Microbat

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Introduction (5) rover navigation Hyperion Nister, et al.

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Introduction (6) search and rescue robots Rhex (movies:

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Introduction (7) NASA Personal Satellite Assistant (PSA)

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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Introduction (10) given these requirements, cameras are promising sensors… …and many algorithms for motion from images already exist

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Introduction (11) But, where are the systems for estimating the motion of: over the long term?

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Introduction (12) …and for automatically modeling rooms buildings cities from a handheld camera?

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Introduction (13) Motion from images suffers from some long- standing difficulties This work attacks these problems by… exploiting omnidirectional images exploiting image and inertial measurements robust image feature tracking recognizing previously mapped locations

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Outline Motion from images refresher bundle adjustment difficulties Motion from image and inertial measurements Robust image feature tracking Long-term motion estimation Conclusion

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from images: refresher (1) A two-step process is common: sparse feature tracking estimation

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from images: refresher (1) A two-step process is common: sparse feature tracking estimation Sparse feature tracking: inputs: raw images outputs: projections

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from images: refresher (2)

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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)

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from images: refresher (5)

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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)

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from images: bundle adjustment (1) From tracking, we have the image locations x ij for each point j and each image i

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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:

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from images: bundle adjustment (3)

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from images: bundle adjustment (4)

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from images: bundle adjustment (5) So, minimize: with respect to all the ρ i, t i, X j

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from images: bundle adjustment (5) So, minimize: with respect to all the ρ i, t i, X j

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from images: difficulties (3) Recursive methods suffer from: poor prior assumptions on the motion poor approximations in state error modeling

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from images: difficulties (4) Resulting errors are: gross local errors long term drift

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from images: difficulties (5)

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from images: difficulties (6) 151 images, 23 points manually corrected Lucas-Kanade

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from images: difficulties (7)  squares: ground truth points  dash-dotted line: accurate estimate  solid line: image-only, bundle adjustment estimate

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from image and inertial measurements: inertial sensors (1) inertial sensors can be integrated to estimate six degree of freedom motion

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from image and inertial measurements: inertial sensors (2) But many applications require small, light, and cheap sensors

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from image and inertial measurements: algorithms and results (4) batch algorithm minimizes a combined error:

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from image and inertial measurements: algorithms and results (5) image term E image is the same as before

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from image and inertial measurements: algorithms and results (6) inertial error term E inertial is:

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from image and inertial measurements: algorithms and results (6) inertial error term E inertial is:

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from image and inertial measurements: algorithms and results (6) inertial error term E inertial is:

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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)

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Motion from image and inertial measurements: algorithms and results (9)

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Outline Motion from images Motion from image and inertial measurements Robust image feature tracking smalls in brief Long-term motion estimation Conclusion

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Robust image feature tracking: smalls in brief (1) Lucas-Kanade has been the go-to feature tracker for shape-from-motion suitable for real-time subpixel accuracy general heuristics for handling large image motions

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Robust image feature tracking: smalls in brief (1) Lucas-Kanade has been the go-to feature tracker for shape-from-motion suitable for real-time subpixel accuracy general heuristics for handling large image motions …but not robust enough for “hands-free” motion estimation

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Robust image feature tracking: smalls in brief (2) smalls is a new feature tracker targeted at 6 DOF motion estimation combines aspects of correlation tracking and “extract and match” trackers exploits the rigid scene assumption eliminates the heuristics normally used with Lucas-Kanade SIFT is an enabling technology here

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Robust image feature tracking: smalls in brief (3) End analysis: allows hands-free SFM for many hard sequences can still be defeated by repeated texture or lack of texture Pointers to more information on smalls on the web page

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Outline Motion from images Motion from image and inertial measurements Robust image feature tracking Long-term motion estimation proof of concept system experiment Conclusion

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Long-term motion estimation: proof of concept system (2)

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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 }

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Long-term motion estimation: proof of concept system (5) {0, 1} {0}{0, 1, 2}{0, 1, …, 8}

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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, rollback Long-term motion estimation: proof of concept system (7) {0, 1} {0}{0, 1, 2}{0, 1, …, 8} 8 non-rollback States:

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, rollback Long-term motion estimation: proof of concept system (8) {0, 1} {0}{0, 1, 2} 8 {0, 1, 2, 3, 8} non-rollback pruned States:

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, rollback Long-term motion estimation: proof of concept system (9) {0, …, 6, 11, 12, 17, …, 20} non-rollback pruned States:

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Long-term motion estimation: experiment (1) CMU FRC highbay views; 945 images total

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Long-term motion estimation: experiment (2) CMU FRC highbay

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Long-term motion estimation: experiment (2) CMU FRC highbay (first forward pass: images 0-213)

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Long-term motion estimation: experiment (2) CMU FRC highbay (first forward pass: images 0-213)

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Long-term motion estimation: experiment (2) CMU FRC highbay (first forward pass: images 0-213)

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Long-term motion estimation: experiment (2) CMU FRC highbay (first backward pass: images )

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Long-term motion estimation: experiment (2) CMU FRC highbay (second forward pass: images )

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Long-term motion estimation: experiment (2) CMU FRC highbay (second backward pass: images )

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Long-term motion estimation: experiment (2) CMU FRC highbay (third forward pass: images )

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Long-term motion estimation: experiment (2) CMU FRC highbay (third backward pass: images )

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, rollback Long-term motion estimation: experiment (3) non-rollback pruned States: normally, the system produces a general tree of states

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Long-term motion estimation: experiment (4) … non-rollback rollback pruned States: for this example, the “rollback” states are restricted to the first forward pass

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Long-term motion estimation: experiment (5) movie…bottom half is smalls output:

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Long-term motion estimation: experiment (6) movie…top half is motion estimates:

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Long-term motion estimation: experiment (7) movie…top half is motion estimates:

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Outline Motion from images Motion from image and inertial measurements Robust image feature tracking Long-term motion estimation Conclusion remaining issues some previous work

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, 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

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Conclusion: some previous work (1) (CMU): trinocular stereo for Honda humanoid and Toyota highway obstacle detection (K 2 T, Inc.): architectural models from still images 1996 (U. of Illinois): Masters thesis, visualizing fMRI data with virtual reality

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Conclusion: some previous work (2) 1995 (Los Alamos): automatically delineating rib cage volumes in CT volumes 1994 (National Solar Observatory): tracking sunspot motion, measuring solar flare intensity 1993 (U. of Nebraska): AVHRR satellite image restoration

Dennis Strelow -- Motion estimation from image and inertial measurements – January 6, Thanks! Related materials: these and related slides related papers movies VRML models at: