An extreme occurrence of the missing data

2. An extreme occurrence of the missing data W I D E B A S E L I N E – no point in more than 2 images!

3. zoom panorama Dominant planes no problem Difficult cases Coinciding camera centers

4. Some important, but very few matches Uneven image capture 26 images 325 image pairs

5. Uneven image capture

6. Our method can solve all previous examples.

7. Technical contribution of this paper Algorithm • matches – uncalibrated EG[Matas et al. BMVC’02] • focal length calibration • [Stewenius et al. CVPR’05], [NisterPAMI’04] [Chum] • EG importance • consistent rotations linearly • bundle adjustment with constrained rotations • consistent translations using SOCP[KahlICCV’05] • dense stereo [Kostkova & Sara BMVC’03]

8. Two-View Geometry Unaffected by a Dominant Plane. [Chum et al. CVPR'05] use inliers as a poolfor drawing samples in RANSAC on epipolar geometry Calibrated RANSAC and planes The six-point algorithm found only points on the wall. [Stewenius et al. CVPR’05]

9. mean focal length Partial calibration – unknown focal length The “six-point algorithm” on all pairs. [Stewenius et al. CVPR’05] Full calibration The “five-point algorithm” on all pairs. [Nister PAMI’04]

10. loosely coupled components – ambiguity! Consistent rotations – previous work [Uyttendaele et al., CG\&A '04] – dense video self-intersecting paths vanishing points [Martinec, Pajdla CVPR'05] – gluing projective reconstructions metric upgrade needed!

11. rotation matrices rotations w.r.t. a reference frame relative rotation consistent rotations Rotation registration into a reference frame

12.  orthonormal close to orthonormal rewrite as and solve large & sparse matrix well conditioned rotations – projection to orthonormal matrices Consistent rotations – solution eigenvalue problem global minimum fast: ~ 1 sec for 1000 image pairs

13. Refining rotations • in each partial reconstruction:

14. Refining rotations • in each partial reconstruction:

15. Refining rotations • in each partial reconstruction: replace rotations by the consistent ones,

16. change in relative rotation Refining rotations • in each partial reconstruction: replace rotations by the consistent ones,  reprojection errors grow  bundle adjustment needed

17. Refining rotations • in each partial reconstruction:

18. refine all reconstructions together, each in independant coordinate frame, but with corresponding rotations constrained to be same Refining rotations • in each partial reconstruction: re-estimate camera translations and points using [Kahl ICCV'05]

19. same rotations, translations unknown consistent rotations

20. low errors stability consistent rotations 0.8 / 18 pxl

21. Refining rotations refine 0.20 / 1.6 pxl consistent rotations 0.8 / 18 pxl

22. consistent translations [Kahl ICCV'05] 0.24 / 1.3 pxl refine 0.19 / 1.1 pxl Translations consistent rotations 0.8 / 18 pxl refine 0.20 / 1.6 pxl

23. Final reconstruction

24. Experiments ICCV’05 Contest finals mean / maximum error 3.01 / 4.87 meters

25. Experiments ICCV’05 Contest finals St. Martin rotunda – 104 images

26. importance support few data unevenimage capture use triplets Experiments ICCV’05 Contest finals St. Martin rotunda Head2 correct surface

27. Difficult scenarios: • only two-view matches recent results on 260 views practical algorithm • coinciding camera centers • uneven image capture, wide base-line Acknowledgements: • Ondrej Chum… code for EG unaffected by a dominant plane • Fred Schaffalitzki … code for the six-point algorithm (publicly available) • Lourakis et al. … base code for bundle adjustment (publicly available) • Jana Kostkova … routines for dense stereo • Richard Szeliski … the ICCV'05 Contest data (publicly available) Summary New algorithm for 3D reconstruction: • EG importance • consistent rotations linearly • bundle adjustment with constrained rotations