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- W2884039401 abstract "Given a set S in $$mathbb {R}^n$$ , a $$(delta ,varepsilon )$$ -ball approximation of S is defined as a collection of balls that covers the morphological erosion of S (by a ball of radius $$varepsilon $$ ) and remains inside the morphological dilation of S (by a ball of radius $$delta $$ ). We study the problem of computing a $$(delta ,varepsilon )$$ -ball approximation when S is itself defined as a finite union of balls. This problem relates to geometric set cover problems but is however different in nature. It offers a new framework for reducing the size of a collection of balls while controlling both the inner and outer distance to the shape. We prove that computing a $$(delta ,varepsilon )$$ -ball approximation of minimum cardinality is NP-complete for $$n = 2$$ . Along the way, we study the boundary of unions of disks and their erosion, for which we derive a computational description." @default.
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- W2884039401 date "2018-07-20" @default.
- W2884039401 modified "2023-10-18" @default.
- W2884039401 title "( $$delta ,{varepsilon }$$ δ , ε )-Ball Approximation of a Shape: Definition and Complexity" @default.
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- W2884039401 doi "https://doi.org/10.1007/s00454-018-0019-8" @default.
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