Abstract : The dynamic programming sub-structure of finding an optimal cut from a hierarchy of partitions was founded theoretically by the introduction of the energetic lattice. The braids of partitions define the largest partition family that preserves the energetic ordering and thus the dynamic programming substructure. Practically braids help relax the ill-posed segmentation problem while also provided the partition family over which multivariate problems can be defined. New problems include the search for a global optimum in hierarchies of partitions that are not indexed hierarchically.
