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Collision recognition from a video part A

Collision recognition from a video part A . Students: Adi Vainiger , Eyal Yaacoby Supervisor: Netanel Ratner Laboratory of Computer Graphics & Multimedia Electrical Engineering faculty, Technion Semester: Winter 2012. Objective. Design a system with two main roles:

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Collision recognition from a video part A

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  1. Collision recognition from a videopart A Students: AdiVainiger, EyalYaacoby Supervisor: NetanelRatner Laboratory of Computer Graphics & Multimedia Electrical Engineering faculty, Technion Semester: Winter 2012

  2. Objective • Design a system with two main roles: • Recognize possible collision trajectories by vehicles, using a video taken from a camera directed toward the rear of the direction of driving • Alert the user so he can react accordingly • Part A goal: Design an algorithm for the system using MATLAB • Without taking into account real-time constraints

  3. Related Work • Mobileye[1] • Israeli company that developed an alerting system for car drivers • Front and rear cameras • Algorithm - based on changes of the vehicles’ width in the scene. • Our goal is similar but designed differently • Full reconstruction of the 3D world - enables accurate results.

  4. Background

  5. Feature Detection and Matching • Interest points detection • LaplacianPyramids (computed by DoG) • Interest points are the extrema in scale-space (x,y;s) [2] [3]

  6. Feature Detection and Matching • SIFT • Image descriptor - for each interest point • Grid – 4x4 • Scale Normalization – by level in pyramid • Orientation Normalization – by largest gradient • Gradient histogram per cell • By pixel gradient • 8 quantized directions • Descriptor size 4x4x8 = 128 dimensions [4]

  7. Feature Detection and Matching • SIFT • Matching • Closest neighbor by Euclidean distance between descriptors [5]

  8. Feature Detection and Matching • ASIFT • Affine extension of SIFT • ASIFT is much more accurate, gives more features • ASIFT is slower than SIFT (~50x) • We’ve used ASIFT for accuracy reasons

  9. Perspective Projection • Camera - Pinhole model • (X0, Y0 , Z0)  (U0, V0)

  10. Perspective Projection • Matrix Representation • Translation and Rotation • Projection • Ideal camera calibration matrix • Real camera calibration matrix • Final model of camera transformation • Using homogenous coordinates (Xf, Yf, Zf) = pinhole coordinates normalization

  11. 3D Reconstruction • Fundamental Matrix • Represents transformation between two frames • x - 2D point in frame 1 (projection of X in 3D world) • x‘ – 2D point in frame 2 (projection of same X) • Fx – epipolarline on frame 2 • Also the projection of the epipolar plane on frame 2 • Geometric constraint • Meaning: x‘ must be on the line Fx • rank(F) = 2 [6] X [6] l = Fx x x’

  12. 3D Reconstruction • Fundamental Matrix • Estimating using RANSAC • Generating many hypotheses (e.g. 500) • Choosing 8 random points • Estimating F using these 8 points (eight point algorithm) • Choosing the best hypothesis • Minimizes the sum of error for all points

  13. 3D Reconstruction • Estimating transformation between frames • Essential Matrix E • Similar to fundamental matrix, with normalized coordinates • Can be defined as • Satisfies • t,R - translation and Rotation between the two frames • Using SVD for E we get 4 Options • R is determined up to π degrees rotation (= 2 options) • t is determined up to sign (= 2 options)

  14. 3D Reconstruction • Triangulation • We now know the relative translation and Rotation (R’,t’) between the two frames • We set the first camera to be at the origin : • We can draw two lines in 3D space: from each interest point to camera center • Ideally, these two lines should intersect at the real 3D point • Realistically, due to noise, the two lines don’t intersect • We approximate by linearization and error minimization • is the reconstructed point [7]

  15. Our Approach

  16. Block Diagram

  17. Our Implementation • Feature Detection & Matching using ASIFT Feature Detection & Image Descriptors Frame 1 Matches Matching Interest Points Feature Detection & Image Descriptors Frame 2

  18. Our Implementation • 3D Reconstruction [*] Assuming the Calibration Matrix is known • Using the methods explained earlier • Out of 4 solutions, we eliminate 3 impossible ones: • Angular difference between the frames is larger than 180° • The reconstructed points are behind the camera 3D Reconstructed points Matches Triangulation [*] Estimating transformation between frames Fundamental Matrix

  19. Recognition and DifferentiationBetween Static and Moving Objects • For N Frames creating N-1 reconstructions • Each reconstruction is between frames i and i-5 • Reconstructions Matching • For each 3D point in the newest reconstruction , finding the closest points in N-2 earlier reconstructions Dynamic Feature Points Variance Calculation for each point Reconstructions Matching Static Feature Points 3D Reconstructed points 3D Reconstructed points 3D Reconstructed points 3D Reconstructed points N-1

  20. Recognition and DifferentiationBetween Static and Moving Objects • Indicators • Dynamic points have greater epi-polar error • Dynamic points have higher variance (for each point and its matches) • Variance Normalization • We need to normalize by the expected error • Distance from camera - • Angle between triangulation lines - • Setting some threshold for each indicator • Points that have variance above the threshold – are Dynamic Point that have variance below the threshold – are Static Dynamic Feature Points Variance Calculation for each point Reconstructions Matching Static Feature Points 3D Reconstructed points 3D Reconstructed points 3D Reconstructed points 3D Reconstructed points N-1

  21. Collision Detection • Reconstruction by static points • More accurate reconstructions of the dynamic points than the ones we had • Estimate dynamic points scattering • On collision course, the reconstructed points are widely scattered • Counting how many balls are needed to cover all the points If greater than some threshold (e.g. 10), we assume some object is on a collision course Estimate dynamic points scattering Is there collision? Static Points Static Points שחזור העולם התלת-ממדי על פי הנקודות הסטטיות בלבד Static Points שחזור העולם התלת-ממדי על פי הנקודות הסטטיות בלבד Static Feature Points Reconstruction of the Dynamic points N-1 N Static Points Static Points Static Points Dynamic Feature Points N-1 N שחזור העולם התלת-ממדי על פי הנקודות הסטטיות בלבד שחזור העולם התלת-ממדי על פי הנקודות הסטטיות בלבד Estimating Fundamental Matrix by the Static points

  22. Results

  23. Synthetic Testing Environment

  24. 3D Synthetic World • Objects in picture are represented by trees (static objects) and cars (moving objects) • Each “tree” is a blue box • Each “car” is a green box • From each object we randomlychoose a predetermined number of 3D points (~64) • Vehicle represented by a moving camera • The camera is a pink pyramid • The camera has an angle relative to the moving direction • Takes a picture every 1/20 second • The interest points are the perspective projection of the chosen 3D points • Gaussian noise is added to the 2D projected points

  25. 3D Synthetic World • Scenarios • Creation - We chose 6 scenarios for testing – where the direction of the car changes. e.g. • Collision direction : • Same direction:

  26. 3D Synthetic World • Scenarios Reconstruction Results • Collision direction : • Same direction :

  27. 3D Synthetic World • Collision Detection Results : • Conclusions : • Setting the threshold to 10, we can correctly identify collision • 2% false negatives on collision scenario (collision but no alarm) • 12% false positives on the worst scenario (alarm but no collision)

  28. Synthetic Results • Tests - The error in 3D reconstruction by noise • Changing different parameters • Reconstruction based on Static vs. Static & Dynamic points • The error is significantly larger when dynamic points are included • Conclusion:Separation between static and dynamicobjects is crucial for a reliable 3D reconstruction • Implementation:We reconstruct the world using basedon the static points only after separation

  29. Synthetic Results • Frame rate : 1 - 20 per sec • The error is very largewhen comparingconsecutive frames • Conclusion: Reconstruction should be based on frames farther apart. The bigger difference between frames makes the noise less significant. • Implementation: Reconstruction is based on frames that are 5 frames apart

  30. Synthetic Results • Camera angle – 0 °-90° • The camera angle significantlyaffects the error - the larger theangle*, the smaller the error * relative to the forward direction • Conclusion: The camera angle creates a larger difference between frames, so the noise has less affect • Implementation: The camera should be positioned in an angle relative to the forward direction

  31. Synthetic Results • Trees position – distance from camera : 7-31 meters • The tree position significantlyaffects the error – the farther the tree , the less accurate the result • Number of interest points of each object : 32-128 • The more points – the merrier

  32. Movie Results • Two movie types • Camera on cyclist’s helmet • Camera on Roomba

  33. Movie Results • Calibration • Using an external toolbox for Matlab • Getting the calibration matrix K • Fixing radial distortion using an external algorithm

  34. Movie Results • Feature detection and matching • Dynamic points • Rolling shutter caused distortion due to the vibrations of Roomba • ASIFT misses the dynamic points in majority of movies • Solution: manual feature matching (using cpselect tool)

  35. Movie Results • Estimating Ego – motion using essential matrix • Rotation – • Camera was fixed to the robot during the shooting • Expecting rotation ~ 0 • The result was as expected • Translation – • The translation size was determined by us • Expecting angle between x-y axis 30° • The result was around 25° • Conclusion – • Ego motion is estimated correctly • Thus we assume Fundamental matrix and calibration of the camera are correct.

  36. Movie Results • Reconstruction of the world

  37. Movie Results • Recognition and Differentiation Between Static and Moving Objects • Epi-polar error • The epi-polar error does not correlate well with the expected result • We get a lot of static points with a high error and some dynamic points with a low error • We have decided not to use it

  38. Movie Results • Recognition and Differentiation Between Static and Moving Objects • Variance • Measuring variance among several 3D reconstructions • Distant objects have a high variance • Using un-normalized variance, We cannot distinguish between distant and dynamic points

  39. Movie Results • Recognition and Differentiation Between Static and Moving Objects • Normalized Variance • 1) Distance from camera - • Threshold = 0.05 • 2) Angle between triangulation lines – • Threshold = 3.3e-6 • We get better results than previous methods • Still, there are scenes where it doesn’t work as expected

  40. Summary and Conclusions • There were several major problems in the project • 1) Matching features of moving objects • Doesn’t work, largely due to the vibrations in video capturing • In a real scenario, we expect much less vibrations • 2) Classifying static and moving objects • Even the best algorithm fails on many cases • A form of tracking (e.g. KLT) can help solve this problem • 3) Long running time (~3 minutes per frame) • Most of the time is spent on ASIFT • A faster feature matching algorithm can resolve this

  41. Summary and Conclusions • Further research • Using a tracking algorithm (e.g. KLT) • Should solve the matching problem • Much better classification between static and moving objects • Identifying vehicles • An algorithm that recognizes vehicles (e.g. Viola and Jones) • Allows focusing only on interesting objects instead of the entire frame • Accurate triangulation • Using the full polynomial error estimation instead of the linear approximation

  42. Thank you for Listening

  43. Appendices

  44. Appendix A : Essential Matrix • SVD for essential matrix • The SVD can be represented in 2 ways: • Overall: 4 options

  45. Appendix B : Triangulation • Approximation of the reconstruction of the 3D point in presence of noise • The homogeneous interest points in frames 1 and 2 should satisfy the equations: • Due to noise there is no solution - as • We would like to minimize , s.t • The solution is the singular vector with the lowest singular value out of the SVD of A .

  46. Static Point Reconstruction Appendix C : Static &Moving Objects Dynamic Point Reconstruction Low Variance High Variance

  47. Appendix D: Collision Detection • Collision course • On a collision course,the lines between the camera centers and theobject are almostparallel • Thus, the reconstructions will be very distant from one another • We identify this by measuring dynamic points scattering • Note - This property is not unique to collision courses

  48. Appendix E: Collision Detection • Clustering Algorithm • We want to count how many balls are needed to cover all the reconstructed points • While there are points remaining: • Choose a random point • Draw a ball around it • Remove all points inside the ball • The number of balls used is the result of the algorithm • This is used as a metric for points scattering • We implemented a k-medoids algorithm • Produced almost the same results, but performance was much worse – we chose the above random algorithm [8]

  49. Appendix F: Triangulation ambiguity • Uncertainty of reconstruction depends on the angle between the triangulation rays • Reconstructed points has more ambiguity along the ray as the rays become more parallel • Forward\ backward motion – rays almost parallel , thus reconstruction is even more weak Less ambiguity Higher ambiguity

  50. References • [1] E.Dagan, O.Mano, G. P. Stein, A.Shashua, Forward Collision Warning with a Single Camera, 2004 • [2] Mikhail Sizintsev, http://www.cse.yorku.ca/~sizints • [3] http://www.scholarpedia.org/article/File:Strandvagen2-Laplace1500pts.png • [4] David G. Lowe, "Distinctive image features from scale-invariant keypoints,"International Journal of Computer Vision, 60, 2 (2004), pp. 91-110. • [5] http://www.scholarpedia.org/article/SIFT • [6] http://www.consortium.ri.cmu.edu/projMultiView.php • [7] Hartley and Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. p.311 • [8] http://en.wikipedia.org/wiki/K-medoids

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