Constrained Optimization on Hierarchies and Braids of Partitions

• Main Authors: Serra, Jean, Kiran, Bangalore Ravi
• Other Authors: Laboratoire d'Informatique Gaspard-Monge (LIGM), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS), Centre de Robotique (CAOR), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), ANR-10-BLAN-0205,KIDICO,Intégration des connaissances pour la convolution discrète, la segmentation et la reconstruction d'informations dans les images digitales(2010)
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2015
• Subjects: Hierarchies; Lagrange; Lattice; Optimization; [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV]; [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]; Garrido; Iceland
• Online Access: https://hal.archives-ouvertes.fr/hal-01134115; https://hal.archives-ouvertes.fr/hal-01134115/document; https://hal.archives-ouvertes.fr/hal-01134115/file/ConstrainedOptBraids_ISMM2015.pdf

International audience This theoretical paper provides a basis for the optimality of scale-sets by Guigues [6] and the optimal pruning of binary partition trees by Salembier-Garrido [11]. They extract constrained-optimal cuts from a hierarchy of partitions. Firstly, this paper extends their results to a larger family of partitions, namely the braid [9]. Secondly, the paper shows the dependence of valid constraint function values and multiplier values in a Lagrangian optimization framework. Lastly, but most importantly, it also proposes the energetic order and energetic lattice based solutions for the constraint optimization problem. This approach operates on a partition based constraint thus ensuring the existence of a valid multiplier and constraint value.