Two standard object extraction methods Interactive Graph cuts [Boykov&Jolly ‘01] - Discrete formulation
- Computes min-cuts on N-D grid-graphs
Graph cuts (simple example à la Boykov&Jolly, ICCV’01)
Metrication errors on graphs
Cut Metrics : cuts impose metric properties on graphs
Our key technical result
Integral Geometry and Cauchy-Crofton formula
Cut Metric on grids can approximate Euclidean Metric
Cut metric in Euclidean case
Reducing Metrication Artifacts
Cut Metric in Riemannian case The same technique can used to compute edge weights that approximate arbitrary Riemannian metric defined by tensor D(p)- Idea: generalize Cauchy-Crofton formula
Convergence theorem
“Geo-Cuts” algorithm
Minimal surfaces in image induced Riemannian metric spaces (3D)
Our results reveal a relation between… Level Sets Graph Cuts [Osher&Sethian’88,…] [Greig et. al.’89, Ishikawa et. al.’98, BVZ’98,…]
Conclusions “Geo-cuts” combines geodesic contours and graph cuts. - The method can be used as a “global” alternative to variational level-sets.
Reduction of metrication errors in existing graph cut methods- stereo [Roy&Cox’98, Ishikawa&Geiger’98, Boykov&Veksler&Zabih’98, ….]
- image restoration/segmentation [Greig’86, Wu&Leahy’97,Shi&Malik’98,…]
- texture synthesis [Kwatra/et.al’03]
Theoretical connection between discrete geometry of graph cuts and concepts of integral & differential geometry
Geo-cuts (more examples)
Dostları ilə paylaş: |
