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Presenter : Shiu , Jia-Hau Advisor : Wang, Sheng-Jyh

Simultaneous surveillance camera calibration and foot-head homology estimation from human detection 1 Author : Micusic & Pajdla. Presenter : Shiu , Jia-Hau Advisor : Wang, Sheng-Jyh. 1. 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Outline.

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Presenter : Shiu , Jia-Hau Advisor : Wang, Sheng-Jyh

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  1. Simultaneous surveillance camera calibration and foot-head homology estimation from human detection1 Author : Micusic & Pajdla Presenter : Shiu, Jia-Hau Advisor : Wang, Sheng-Jyh 1.2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition

  2. Outline • Introduction • Human Detection • Foot-head homology estimation • Conclusion

  3. Introduction • This paper uses people to calibrate the camera • Human contour detection (green) • Refined human detection with camera calibration parameters (blue) • Foot-head homology(o:foot,x:head)

  4. Concept • Objects are human • Estimate camera parameters by observing a person standing at several positions 3-D scene 2-D projection Image

  5. System Flow Sequential Images Human Detection Foot-head Homology Estimation Output

  6. System Flow Sequential Images Human Detection Foot-head Homology Estimation Output

  7. Background • Shape-based detector(Global search) • Detection rate drop significantly in presence of occluded humans • Part-based detector(Local search) C.Beleznai and H. Bischof. ,“Fast Human Detection in Crowded Scenes by Contour Integration and Local Shape Estimation”, In CVPR,2009.

  8. Background Left - Shape based : Template matching with head and body Right - Part based : Obtain foreground image by background subtraction Segmentation of detected human

  9. Result : Contour template

  10. Human Detection • Line edges model a human • Offline: Create around 1000 human contours based on 3D model and moving and rotating camera

  11. Draw foot-head lines in one image 2-D Image 3-D scene

  12. System Flow Sequential Images Human Detection Foot-head Homology Estimation Output

  13. Background : Camera Model

  14. Homography matrix One pair(2D-3D) of points 2 equation 11 DOF

  15. Simple Calibration Example • Measure 3-D position of special object points in 3-D scene z Correspond to camera 2-D point (30,30,40) (0,0,0) y (u1,v1) (0,30,0) (u2,v2) x

  16. Foot-head Homology Estimation • 1. Camera model : Shifted Homographies • 2. Focal length, Rotation, Translation • 3. Quadratic Eigenvalue Problem(QEP) • 4. Foot-head Homology

  17. Camera model • Extrinsic parameters rotation R and translation t

  18. Camera Parameters • Assumptions intrinsic parameters • Square pixels • No principal point offset : Image coordinate at center point (principal point) • No skew : angle of horizon axis and vertical axis = 90’ • Intrinsic parameters K = |f 0 0| |0 f 0| |0 0 1| y 90’ x

  19. (x3,y3,z0) z If x1,x2,x3,y1,y2,y3 are known Six points => 12 equation Compute homography of H (x1,y1,z0) (x2,y2,z0) (x3,y3,0) y (x1,y1,0) x (x2,y2,0)

  20. (x3,y3,z0) z If x1,x2,x3,y1,y2,y3 are unknown How to find homography of H? (x1,y1,z0) (x2,y2,z0) (x3,y3,0) y (x1,y1,0) x (x2,y2,0)

  21. (x3,y3,z0) z (0,0,0) & (0,0,z0) two point are known 4equation (0,0,z0) (x2,y2,z0) (x3,y3,0) y (0,0,0) x (x2,y2,0)

  22. (x3,y3,z0) z z (0,0,z0) (0,0,z0) (x3,y3,0) y1 y (0,0,0) x1 = x+dx1 y1 = y+dy1 x1 x (0,0,0)

  23. (0,0,z0) z z z (0,0,z0) x2 = x+dx2 y2 = y+dy2 (0,0,z0) (0,0,0) y1 y y2 (0,0,0) x1 = x+dx1 y1 = y+dy1 x2 x x1 (0,0,0)

  24. Shifted Homographies unknown add equation K = 1 6 4 K = 2 9 8 K = 3 12 12 3+3K unknown, Dof = 3+3K-1

  25. Shifted Homographies • The 3D point X = (x, y, z,1) can be simplified assuming x = 0 • ri : is the i-th column of R • 6+3K unknowns, K : number of detections

  26. Shifted Homographies

  27. Finding Homographies • This equation is extended with all the known point correspondences to form this equation: M contains all the point correspondences h contains h1, h2 and the unknown h3 of the homographies h is fixed for standard camera calibration

  28. Focal Length、Rotation and Translation

  29. form 3 equations Where equation unknown K = 1 3 4 K = 2 6 6

  30. Minimum Solution : two detectors case • The equations in (7) give Six equation with six unknown

  31. Overdetermined Solution • More than two homologies : solvable as a Quadratic Eigenvalue Problem (QEP) • Find scalars λ and nonzero vectors x, satisfying (λ2D3 + λD2 + D1)x = 0 • The authors create D1, D2, D3 using the known values in (7), λ = f.

  32. Overdetermined Solution • Solve With • D1, D2, D3 very sparse containing only:

  33. Solving QEP • One approach to solving the QEP : Convert it to a linear system (remove the f2): • Solving ( A - f B ) v = 0

  34. Foot-head Homology • Result of QEP : K, R, t, f • From this construct the homology HFH with uH ≃ HFH*uF • uH : image points of head • uF :image points of feet Hk uH (x0k,y0k,l) HFH uF Hk (x0k,y0k,0) Camera Image 3-D points

  35. Result

  36. Conclusion • Use 3D-2D point correspondences (model to contour) • Encode camera parameters that define relation between 3D 2D as a matrix H • Solve H and get the camera parameters

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