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<p><it>Abstract</it>—This paper presents how morphological transformations can be related to representations of a set on different lattices. A hierarchical definition of structuring element conveys to a class of multigrid transformations Ψ<sub>k</sub> that handle changes on discrete representations of regions. The transformations correspond to upward and downward processes in a hierarchical structure. Based on multigrid transformations, a method to delineate not-perfectly-isolated objects in an nxn image requiring O(log n) time is presented. The approach considers grey level regions as sets and processes through a pyramid to carry out geometric manipulations. Extending the concept of boundary to cope with hierarchical representations of a set, a second method which identifies the boundaries in an image is discussed.</p>
Mathematical morphology, multiresolution, image pyramids, image segmentation, parallel algorithms.

J. Alarcón, M. Montiel, A. Aguado and M. Garza-Jinich, "Image Manipulation Using M-filters in a Pyramidal Computer Model," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 17, no. , pp. 1110-1115, 1995.
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