1. Multiway Cut for Stereo and Motion with Slanted Surfaces
Stan Birchfield and Carlo Tomasi
Stanford University

2. Fronto-parallel disparities
Motivation
Right
Left
Fronto-parallel disparities
(multiway-cut)
Slanted disparities
(multiway-cut +
affine estimation)

3. Previous Work PROGRAMMING Baker & Binford 1981 DYNAMIC
Ohta & Kanade 1985
Belhumeur & Mumford 1992, Geiger et al. 1995
Roy & Cox 1998
Boykov, Veksler, and Zabih 1998
PROGRAMMING
DYNAMIC
(1D)
MAXIMUM
FLOW
(2D)

4. Multiway-Cut Formulation
[Boykov, Veksler, Zabih 1998]
labels
labels
pixels
pixels

5. Multiway-Cut Algorithm
source
minimum cut
label
pixel
sink ?
Minimizes

6. Correspondence as Segmentation
With slanted surfaces, cannot search over disparities
computation (sub-pixel)
enforcing piecewise-continuity
computation (too many slants)
Instead, assign labels to pixels and parameters to labels
find affine
parameters
of regions
label
pixels

7. Finding Affine Parameters
dissimilarity
(Taylor series with truncation)
(Solve using Newton-Raphson)
image
gradient
unknown
parameters
image
difference
Affine warp with
epipolar constraint
2D Tracking
Affine warp

8. Handling Oversegmentation
Problem:
Solution:

9. Energy Minimization

10. Results
stereo
motion

11. 3D Reconstruction

12. Conclusions Algorithm: Abilities: Future work:
SEGMENT FIT COMBINE (assign labels) (find affine parameters) (fix oversegmentation)
Abilities:
Handles slanted surfaces
Finds segmentation and 3D geometry
Works for stereo and motion
Future work:
More complex cost function, to allow
discontinuities without intensity edges
untextured surfaces
shapes of regions to be taken into account