This paper presents some optimal approaches to morphological top-hat transform. When using top-hat transform, size estimation of structuring elements is critical in performing tasks such as object segmentation. One typical example is the moving ball algorithm. Since the objects of particular interest possess various size measures, an optimal procedure for selecting structuring functions appears appropriate for the purpose of adaptive thresholding. An optimization design can result in a minimum error according to certain rules in error estimation. In this paper, three cases are considered. The first is the case where the cylindrical type of structuring elements and objects are investigated. The second is on a conical model where a cone is modeled as to optimize top-hat transform. The third case presents optimal algorithm via threshold area or umbra based on a cylindrical model. As is often typical in random geometric modeling, optimization leads very quickly to quite complicated mathematical expressions involving the distributions of the parameters.
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