Morphological approach to smoothing

Woon Kyung Kim, S. M. Song

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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.

Original languageEnglish
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
EditorsStephen K. Park, Richard D. Juday
Place of PublicationBellingham, WA, United States
PublisherSociety of Photo-Optical Instrumentation Engineers
Pages171-179
Number of pages9
Volume3074
ISBN (Print)0819424897
Publication statusPublished - 1997 Dec 1
EventVisual Information Processing VI - Orlando, FL, USA
Duration: 1997 Apr 211997 Apr 22

Other

OtherVisual Information Processing VI
CityOrlando, FL, USA
Period97/4/2197/4/22

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

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  • Cite this

    Kim, W. K., & Song, S. M. (1997). Morphological approach to smoothing. In S. K. Park, & R. D. Juday (Eds.), Proceedings of SPIE - The International Society for Optical Engineering (Vol. 3074, pp. 171-179). Society of Photo-Optical Instrumentation Engineers.