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)
Cut Metrics : cuts impose metric properties on graphs
Integral Geometry and Cauchy-Crofton formula
Cut metric in Euclidean case
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
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.
- 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)
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