1

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 Difficult cases Coinciding camera centers panorama zoom Dominant planes no problem

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

5 Uneven image capture

6 Our method can solve all previous examples.

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

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

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

10 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! loosely coupled components – ambiguity!

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

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

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

17 Refining rotations in each partial reconstruction:

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

19 consistent rotations same rotations, translations unknown

/ 18 pxl consistent rotations low errors  stability

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

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

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 support Experiments ICCV’05 Contest finals Head2 St. Martin rotunda correct surfacesurface use triplets importance uneven image capture few data

27 Summary New algorithm for 3D reconstruction: EG importance consistent rotations linearly bundle adjustment with constrained rotations 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) Difficult scenarios: coinciding camera centers only two-view matches uneven image capture, wide base-line recent results on 260 views practical algorithm