Image manipulation using m-filters in a pyramidal computer model

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_k 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