1. Multi-view reconstruction
Vladimir Kolmogorov Yuri Boykov Carsten Rother
University College London
University of Western Ontario
Ratio minimization
- Q(·) assumed to be non-negative
- can handle:
- submodular / modular
- modular / submodular
(if numerator is negative for some x)
- some other
- including ratios of geometric functionals [B&K ICCV03, ICCV05]
- generalizing to 3D previous formulations: [Cox et al’96], [Jermyn,Ishikawa’01]
can be converted to a parametric max-flow problem
- Minimize for different l’s.
- Find l such that
Related to
isoperimetric
problem
(bias to circles)
solved efficiently via Newton's (Dinkelbach’s) method
Example 2: flux / length
or length / area
Example. 1
No shape bias !
One dominant solution
is a global optimizer for ratio
Theorem: other dominant configurations are optimal solutions for constrained ratio optimization problems
for
Example
Divergence of
photoconsistency
gradients
could be useful if unconstrained ratio minimizer is not a
practically useful solution (e.g. too small)
Visual-hull from photo-flux [Boykov&Lempitsky BMVC2006]
Best for
Applications of constrained ratio optimization (in 3D)
Segmentation
Surface fitting
Multi-view reconstruction
Optimizing ratio
for increasingly larger
lower bound on surface area
Optimizing ratio
for increasingly larger
lower bound on surface area
Divergence of
photoconsistency gradients [Boykov&Lempitsky BMVC2006]
Divergence of
estimated surface normals
[Lempitsky et.al. CVPR 2007]