Morphological approach to smoothing

Woon K. 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
    PublisherSociety of Photo-Optical Instrumentation Engineers
    Pages171-179
    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
    Volume3074
    ISSN (Print)0277-786X

    Other

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

    ASJC Scopus subject areas

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

    Fingerprint

    Dive into the research topics of 'Morphological approach to smoothing'. Together they form a unique fingerprint.

    Cite this