1. Synchronization and Calibration of Camera Networks from Silhouettes Sudipta N. Sinha Marc Pollefeys University of North Carolina at Chapel Hill, USA.

2. 2 Goal To recover the Calibration & Synchronization of a Camera Network from only Live Video or Archived Video Sequences.

3. 3 Motivation Easy Deployment and Calibration of Cameras. –No Offline Calibration ( Patterns, LED etc) –No physical access to environment Possibility of using unsynchronized video streams (camcorders, web-cams etc.) Applications in wide-area surveillance camera networks (3D tracking etc). Digitizing 3D events

4. 4 Why use Silhouettes ? Visual Hull (Shape-from-Silhouette) System Many silhouettes from dynamic objects Background segmentation Feature-based ? Features Matching hard for wide baselines Little overlap of backgrounds Few features on foreground

5. 5 Prior Work : Calibration from Silhouettes Epipolar Geometry from Silhouettes Porrill and Pollard, ’91 Astrom, Cipolla and Giblin, ’96 Structure-and-motion from Silhouettes Vijayakumar, Kriegman and Ponce’96 (orthographic) Furukawa and Ponce’04 (orthographic) Wong and Cipolla’01 (circular motion, at least to start) Yezzi and Soatto’03 (needs initialization) Sequence to Sequence Alignment Caspi, Irani,’02 (feature based)

6. 6 Our Approach Compute Epipolar Geometry from Silhouettes in synchronized sequences (CVPR’04). Here, we extend this to unsynchronized sequences. Synchronization and Calibration of camera network.

7. 7 Multiple View Geometry of Silhouettes Frontier Points Epipolar Tangents Always at least 2 extreme frontier points per silhouette Only 2-view correspondence in general. x1x1 x2x2 x’ 1 x’ 2

8. 8 Camera Network Calibration from Silhouettes 7 or more corresponding frontier points needed to compute epipolar geometry Hard to find on single silhouette and possibly occluded However, video sequences contain many silhouettes.

9. 9 Camera Network Calibration from Silhouettes If we know the epipoles, draw 3 outer epipolar tangents (need at least two silhouettes in each view) Compute an epipolar line homography H -T Epipolar Geometry F=[e] x H

10. 10 RANSAC-based algorithm Repeat { Generate a Hypothesis for the Epipolar Geometry Verify the Model } Refine the best hypothesis. Note : RANSAC is used to explore 4D space of epipoles apart from dealing with noisy silhouettes

11. 11 Compact Representation for Silhouettes Tangent Envelopes Store the Convex Hull of the Silhouette. Tangency Points for a discrete set of angles. Approx. 500 bytes/frame. Hence a whole video sequences easily fits in memory. Tangency Computations are efficient.

12. 12 RANSAC-based algorithm Generate Hypothesis for Epipolar Geometry Pick 2 corresponding frames, pick random tangents for each of the silhouettes. Compute epipoles. Pick 1 more tangent from additional frames Compute homography Generate Fundamental Matrix.

13. 13 RANSAC-based algorithm Verify the Model For all tangents Compute Symmetric Epipolar Transfer Error Update Inlier Count (Abort Early if Hypothesis doesn’t look Promising)

14. 14 What if videos are unsychronized ? For fixed fps video, same constraints are valid up to an extra unknown temporal offset. Add a random temporal offset to RANSAC hypothesis. Use multi-resolution approach: –Keyframes with slow motion, rough synchronization –ones with fast motion provide fine synchronization

15. 15 Computed Fundamental Matrices

16. 16 Synchronization experiment Total temporal offset search range [-500,+500] (i.e. ±15 secs.) Unique peaks for correct offsets Possibility for sub-frame synchronization # Promising Candidates Sequence Offset (# frames) # Iterations (In millions)

17. 17 Camera Network Synchronization Consider directed graph with offsets as branch value For consistency loops should add up to zero MLE by minimizing +3 -5 +8 +6 +2 0 ground truth in frames (=1/30s)

18. 18 From epipolar geometry to full calibration Solve for camera triplet (Levi and Werman, CVPR’03; Sinha et al. CVPR’04) Assemble complete camera network.

19. 19 Metric Cameras and Visual-Hull Reconstruction from 4 views Final calibration quality comparable to explicit calibration procedure

20. 20 Validation experiment: Reprojection of silhouettes

21. 21 Taking Sub-frame Synchronization into account Reprojection error reduced from 10.5% to 3.4% of the pixels in the silhouette Temporal Interpolation of Silhouettes. to appear (Sinha, Pollefeys, 3DPVT’04)

22. 22 Conclusion and Future Work Camera network calibration & synchronization just from dynamic silhouettes. Great for visual-hull systems. Applications for surveillance systems. Extend to active PTZ camera network and asynchronous video streams. Acknowledgments NSF Career, DARPA. Peter Sand, (MIT) for Visual Hull dataset.

23. 23 Computed Fundamental Matrices F computed directly (black epipolar lines) F after consistent 3D reconstruction (color)