The Theory of Braids and Energetic Lattices II - Constrained Optimization by Disseminated Energy

B Ravi Kiran (1) , Jean Serra (2)

1 CAOR - Centre de Robotique
2 Mines Paris - PSL (École nationale supérieure des mines de Paris)

Give a hierarchy of segmentations, the optimal cut problem consists in extracting the partition with the least energy, solved greedily by a dynamic program. The energy is composed of two terms : fidelity term (how well the local model fits the image) and regularization/constraint term(how simple the partition is). The energetic lattice was introduced as a basis for the dynamic programming substructure. At no moment the energy of a complete partition is ever calculated. In view of the local nature of the dynamic program substructure, in this study we introduce three constraint models : Multiplier constrained, Cut constrained, Class constrained , each of which has a equivalent representation as an energetic lattice and captures the constraint on the solution space of partitions in different ways.

Domaines: Optimisation et contrôle [math.OC]

B Ravi Kiran, Jean Serra. The Theory of Braids and Energetic Lattices II - Constrained Optimization by Disseminated Energy. 2016. ⟨hal-01538632⟩