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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Serra, J., Kiran, B.R. (2015). Constrained Optimization on Hierarchies and Braids of Partitions. In: Benediktsson, J., Chanussot, J., Najman, L., Talbot, H. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2015. Lecture Notes in Computer Science(), vol 9082. Springer, Cham. https://doi.org/10.1007/978-3-319-18720-4_20
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DOI: https://doi.org/10.1007/978-3-319-18720-4_20
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18719-8
Online ISBN: 978-3-319-18720-4
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