Algorithms for the Decomposition of Gray-Scale Morphological Operations

Ronald Jones, Imants Svalbe

    Research output: Contribution to journalArticleResearchpeer-review

    16 Citations (Scopus)


    The choice and detailed desian of structuring elements plays a pivotal role in the morphologic processing of images. A broad class of morphological operations can be expressed as an equivalent supremum of erosions by a minimal set of basis filters. Diverse morphological operations can then be expressed in a single, comparable framework. The set of basis filters are data-like structures, each filter representing one type of local change possible under that operation. The data-level description of the basis set is a natural starting point for the design of morphological filters. This paper promotes the use of the basis decomposition of gray-scale marphological operations to design and apply morphological filters. A constructive proof is given for the basis decomposition of general gray-scale morphological operations, as are practical algorithms to find all of the basis set members for these operations. Examples are given to illustrate the algorithms presented.

    Original languageEnglish
    Pages (from-to)581-588
    Number of pages8
    JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
    Issue number6
    Publication statusPublished - 1 Jan 1994


    • Gray-scale morphology
    • mathematical morphology
    • morphologic basis decomposition

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