Announcements
Project 2 winners
Think about Project 3
Guest lecture on Monday:  Aseem

Multiview stereo
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

Choosing the Baseline
What’s the optimal baseline?
Too small:  large depth error
Too large:  difficult search problem

The Effect of Baseline on Depth Estimation

Slide 5

Slide 6

Multibaseline Stereo
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

The visibility problem

Volumetric stereo

Discrete formulation:  Voxel Coloring

Complexity and computability

Issues
Theoretical Questions
Identify class of all photo-consistent scenes
Practical Questions
How do we compute photo-consistent models?

Slide 13

Reconstruction from Silhouettes (C = 2)

Volume intersection
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

Slide 18

Voxel Coloring Approach

Depth Ordering:  visit occluders first!

Panoramic Depth Ordering
Cameras oriented in many different directions
Planar depth ordering does not apply

Panoramic Depth Ordering

Panoramic Layering

Panoramic Layering

Compatible Camera Configurations

Calibrated Image Acquisition
Calibrated Turntable
360° rotation (21 images)

Voxel Coloring Results (Video)

Limitations of Depth Ordering
A view-independent depth order may not exist

Slide 29

Space Carving Algorithm
Space Carving Algorithm

Convergence
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

Which shape do you get?
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

Slide 33

Space Carving Algorithm
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

Multi-Pass Plane Sweep
Sweep plane in each of 6 principle directions
Consider cameras on only one side of plane
Repeat until convergence

Multi-Pass Plane Sweep
Sweep plane in each of 6 principle directions
Consider cameras on only one side of plane
Repeat until convergence

Multi-Pass Plane Sweep
Sweep plane in each of 6 principle directions
Consider cameras on only one side of plane
Repeat until convergence

Multi-Pass Plane Sweep
Sweep plane in each of 6 principle directions
Consider cameras on only one side of plane
Repeat until convergence

Multi-Pass Plane Sweep
Sweep plane in each of 6 principle directions
Consider cameras on only one side of plane
Repeat until convergence

Multi-Pass Plane Sweep
Sweep plane in each of 6 principle directions
Consider cameras on only one side of plane
Repeat until convergence

Space Carving Results:  African Violet

Space Carving Results:  Hand

House Walkthrough
24 rendered input views from inside and outside

Space Carving Results:  House

Space Carving Results:  House

Space Carving Results:  House

Other Approaches

Bibliography
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.

Bibliography
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.