Efficient Algorithms for Constructing a Pyramid from a Terrain

Jinhee CHUN  Kunihiko SADAKANE  Takeshi TOKUYAMA  

IEICE TRANSACTIONS on Information and Systems   Vol.E89-D   No.2   pp.783-788
Publication Date: 2006/02/01
Online ISSN: 1745-1361
DOI: 10.1093/ietisy/e89-d.2.783
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Section on Foundations of Computer Science)
Category: Computational Geometry
algorithm,  numeric data,  optimal reshaping,  unimodal approximation,  

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In [5], the following pyramid construction problem was proposed: Given nonnegative valued functions ρ and µ in d variables, we consider the optimal pyramid maximizing the total parametric gain of ρ against µ. The pyramid can be considered as the optimal unimodal approximation of ρ relative to µ, and can be applied to hierarchical data segmentation. In this paper, we give efficient algorithms for a couple of two-dimensional pyramid construction problems.