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Proceedings Paper

Morphological approach to smoothing
Author(s): Woonkyung Michael Kim; Samuel Moon-Ho Song
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Paper Abstract

In this paper, we present some fundamental theoretical results pertaining to the question of how many randomly selected labelled example points it takes to reconstruct a set in euclidean space. Drawing on results and concepts from mathematical morphology and learnability theory, we pursue a set-theoretic approach and demonstrate some provable performances pertaining to euclidean-set-reconstruction from stochastic samples. In particular, we demonstrate a stochastic version of the Nyquist Sampling Theorem - that, under weak assumptions on the situation under consideration, the number of randomly-drawn example points needed to reconstruct the target set is at most polynomial in the performance parameters and also the complexity of the target set as loosely captured by size, dimension and surface-area. Utilizing only rigorous techniques, we can similarly establish many significant attributes - such as those relating to robustness, cumulativeness and ease-of- implementation - pertaining to smoothing over labelled example points. In this paper, we formulate and demonstrate a certain fundamental well-behaving aspect of smoothing.

Paper Details

Date Published: 22 July 1997
PDF: 9 pages
Proc. SPIE 3074, Visual Information Processing VI, (22 July 1997); doi: 10.1117/12.280619
Show Author Affiliations
Woonkyung Michael Kim, Korea Univ. (South Korea)
Samuel Moon-Ho Song, Korea Univ. (South Korea)

Published in SPIE Proceedings Vol. 3074:
Visual Information Processing VI
Stephen K. Park; Richard D. Juday, Editor(s)

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