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Constrained Optimization on Hierarchies and Braids of Partitions

Abstract : 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.
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Contributor : Bangalore Ravi Kiran <>
Submitted on : Friday, March 22, 2019 - 12:10:27 AM
Last modification on : Wednesday, February 3, 2021 - 7:54:28 AM
Long-term archiving on: : Sunday, June 23, 2019 - 12:12:36 PM


  • HAL Id : hal-01134115, version 1


Jean Serra, Bangalore Ravi Kiran. Constrained Optimization on Hierarchies and Braids of Partitions. International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, May 2015, Rejkavik, Iceland. ⟨hal-01134115⟩



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