Morphological decomposition of convex polytopes and its application in discrete image space

Syng Yup Ohn, E. K. Wong

    Research output: Contribution to journalConference articlepeer-review

    Abstract

    We present a new technique for the decomposition of convex structuring elements for morphological image processing. A unique feature of our approach is the use of linear integer programming technique to determine optimal decompositions for different parallel machine architectures. This technique is based on Shephard's theorem for decomposing Euclidean convex polygons. We formulated the necessary and sufficient conditions to decompose a Euclidean convex polygon into a set of basis convex polygons. We used a set of linear equations to represent the relationships between the edges and the positions of the original convex polygon and those of the basis convex polygons. This is applied to a class of discrete convex polygons in the discrete space. Further, a cost function was used to represent the total processing time for performing dilations on different machine architectures. Then integer programming was used to solve the linear equations based on the cost function. Our technique is general and flexible, so that different cost functions could be used, thus achieving optimal decompositions for different parallel machine architectures.

    Original languageEnglish (US)
    Article number413633
    Pages (from-to)560-564
    Number of pages5
    JournalProceedings - International Conference on Image Processing, ICIP
    Volume2
    DOIs
    StatePublished - 1994
    EventProceedings of the 1994 1st IEEE International Conference on Image Processing. Part 3 (of 3) - Austin, TX, USA
    Duration: Nov 13 1994Nov 16 1994

    ASJC Scopus subject areas

    • Software
    • Computer Vision and Pattern Recognition
    • Signal Processing

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