Morphological approach to smoothing

Woon K. Kim, S. M. Song

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

1 Citation (Scopus)


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
PublisherSociety of Photo-Optical Instrumentation Engineers
Number of pages9
ISBN (Print)0819424897
Publication statusPublished - 1997
EventVisual Information Processing VI - Orlando, FL, USA
Duration: 1997 Apr 211997 Apr 22

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X


OtherVisual Information Processing VI
CityOrlando, FL, USA

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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