Project 2 winners | ||
Think about Project 3 | ||
Guest lecture on Monday: Aseem | ||
Readings | |||
S. M. Seitz and C. R. Dyer, Photorealistic Scene Reconstruction by Voxel Coloring, International Journal of Computer Vision, 35(2), 1999, pp. 151-173. | |||
http://www.cs.washington.edu/homes/seitz/papers/ijcv99.pdf |
What’s the optimal baseline? | ||
Too small: large depth error | ||
Too large: difficult search problem |
The Effect of Baseline on Depth Estimation
Basic Approach | |||
Choose a reference view | |||
Use your favorite stereo algorithm BUT | |||
replace two-view SSD with SSD over all baselines | |||
Limitations | |||
Must choose a reference view (bad) | |||
Visibility! | |||
CMU’s 3D Room Video |
Discrete formulation: Voxel Coloring
Theoretical Questions | ||
Identify class of all photo-consistent scenes | ||
Practical Questions | ||
How do we compute photo-consistent models? |
Reconstruction from Silhouettes (C = 2)
Reconstruction Contains the True Scene | |||
But is generally not the same | |||
In the limit (all views) get visual hull | |||
Complement of all lines that don’t intersect S |
Voxel algorithm for volume intersection
Color voxel black if on silhouette in every image | ||
for M images, N3 voxels | ||
Don’t have to search 2N3 possible scenes! |
Properties of Volume Intersection
Pros | ||
Easy to implement, fast | ||
Accelerated via octrees [Szeliski 1993] or interval techniques [Matusik 2000] | ||
Cons | ||
No concavities | ||
Reconstruction is not photo-consistent | ||
Requires identification of silhouettes |
Depth Ordering: visit occluders first!
Cameras oriented in many different directions | ||
Planar depth ordering does not apply |
Compatible Camera Configurations
Calibrated Turntable | |
360° rotation (21 images) |
Voxel Coloring Results (Video)
A view-independent depth order may not exist |
Space Carving Algorithm |
Consistency Property | |||
The resulting shape is photo-consistent | |||
all inconsistent points are removed | |||
Convergence Property | |||
Carving converges to a non-empty shape | |||
a point on the true scene is never removed |
The Photo Hull is the UNION of all photo-consistent scenes in V | ||
It is a photo-consistent scene reconstruction | ||
Tightest possible bound on the true scene |
The Basic Algorithm is Unwieldy | ||
Complex update procedure | ||
Alternative: Multi-Pass Plane Sweep | ||
Efficient, can use texture-mapping hardware | ||
Converges quickly in practice | ||
Easy to implement | ||
Sweep plane in each of 6 principle directions | ||
Consider cameras on only one side of plane | ||
Repeat until convergence |
Sweep plane in each of 6 principle directions | ||
Consider cameras on only one side of plane | ||
Repeat until convergence |
Sweep plane in each of 6 principle directions | ||
Consider cameras on only one side of plane | ||
Repeat until convergence |
Sweep plane in each of 6 principle directions | ||
Consider cameras on only one side of plane | ||
Repeat until convergence |
Sweep plane in each of 6 principle directions | ||
Consider cameras on only one side of plane | ||
Repeat until convergence |
Sweep plane in each of 6 principle directions | ||
Consider cameras on only one side of plane | ||
Repeat until convergence |
Space Carving Results: African Violet
24 rendered input views from inside and outside |
Volume Intersection | ||
Martin & Aggarwal, “Volumetric description of objects from multiple views”, Trans. Pattern Analysis and Machine Intelligence, 5(2), 1991, pp. 150-158. | ||
Szeliski, “Rapid Octree Construction from Image Sequences”, Computer Vision, Graphics, and Image Processing: Image Understanding, 58(1), 1993, pp. 23-32. | ||
Voxel Coloring and Space Carving | ||
Seitz & Dyer, “Photorealistic Scene Reconstruction by Voxel Coloring”, Proc. Computer Vision and Pattern Recognition (CVPR), 1997, pp. 1067-1073. | ||
Seitz & Kutulakos, “Plenoptic Image Editing”, Proc. Int. Conf. on Computer Vision (ICCV), 1998, pp. 17-24. | ||
Kutulakos & Seitz, “A Theory of Shape by Space Carving”, Proc. ICCV, 1998, pp. 307-314. |
Related References | ||
Bolles, Baker, and Marimont, “Epipolar-Plane Image Analysis: An Approach to Determining Structure from Motion”, International Journal of Computer Vision, vol 1, no 1, 1987, pp. 7-55. | ||
DeBonet & Viola, “Poxels: Probabilistic Voxelized Volume Reconstruction”, Proc. Int. Conf. on Computer Vision (ICCV) 1999. | ||
Broadhurst, Drummond, and Cipolla, "A Probabilistic Framework for Space Carving“, International Conference of Computer Vision (ICCV), 2001, pp. 388-393. | ||
Faugeras & Keriven, “Variational principles, surface evolution, PDE's, level set methods and the stereo problem", IEEE Trans. on Image Processing, 7(3), 1998, pp. 336-344. | ||
Szeliski & Golland, “Stereo Matching with Transparency and Matting”, Proc. Int. Conf. on Computer Vision (ICCV), 1998, 517-524. | ||
Roy & Cox, “A Maximum-Flow Formulation of the N-camera Stereo Correspondence Problem”, Proc. ICCV, 1998, pp. 492-499. | ||
Fua & Leclerc, “Object-centered surface reconstruction: Combining multi-image stereo and shading", International Journal of Computer Vision, 16, 1995, pp. 35-56. | ||
Narayanan, Rander, & Kanade, “Constructing Virtual Worlds Using Dense Stereo”, Proc. ICCV, 1998, pp. 3-10. |