Minimum cuts in hierarchical segmentations

Datum konání: 12.10.2011
Přednášející: Jean Serra
Odpovědná osoba: Šroubek

kdy: středa 12.10.2011 od 14:00
kde: místnost 25

Jean Serra, Center of Mathematical Morphology, University of Paris-Est

Minimum cuts in hierarchical segmentations

Most of the current segmentation techniques, in image processing, rest on hierarchies of transforms, and of the partitions that they induce. The final segmentation borrows its classes from the various levels by minimizing energy, or by reference to a connective criterion.

The efficiency of the approach depends on some conditions on the underlying energy, or connection. For example, when energy satisfies the condition of hierarchical increasingness, then the partitions of minimum energy can be characterized and computed easily. Moreover, these solutions form a complete lattice for the ordering of the partitions. Therefore, one can always take the (unique) largest solution, or act on the whole set of solutions according to some new criterion.

In addition, the energy often depends on a parameter (e.g. the relative weight of the smoothness term versus that of proximity to data). One can wonder whether the variation of this parameter can generate a hierarchy of all minimum cuts. Here the convenient energies are those that satisfy hierarchical increasingness, plus a condition of scale increasingness, which involves pairs of parameters.

A few examples illustrate these various points. They come from airborne photographs, from colour segmentation, from optimal coding and interactive lassos.