Braids of Partitions

• Main Authors: Kiran, Bangalore Ravi, Serra, Jean
• Other Authors: 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), Laboratoire d'Informatique Gaspard-Monge (LIGM), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout (BEZOUT), Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), 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: Lattice; Optimization; Hierarchies; Dynamic Programming; [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV]; [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]; Iceland
• Online Access: https://hal.science/hal-01134114; https://hal.science/hal-01134114/document; https://hal.science/hal-01134114/file/Braids_ISMM2015.pdf

International audience In obtaining a tractable solution to the problem of extracting a minimal partition from hierarchy or tree by dynamic programming, we introduce the braids of partition and h-increasing energies, the former extending the solution space from a hierarchy to a larger set, the latter describing the family of energies, for which one can obtain the solution by a dynamic programming. We also provide the singularity condition for the existence of unique solution, leading to the definition of the energetic lattice. The paper also identifies various possible braids in literature and how this structure relaxes the segmentation problem.