Analysis of top-hat selection transformation and some modified top-hat transformations

This paper analyzes the relationships between top-hat selection transformation and some modified top-hat transformations. Firstly, several top-hat transformations following different applications are reviewed. Then, the relationship between top-hat selection transformation and each other top-hat transformation is analyzed and proofed. Finally, we show that some other top-hat transformations may be derived from top-hat selection transformation. Moreover, different parameter specifications of top-hat selection transformation result in different types of top-hat transformations, which may generate efficient top-hat transformations for different application purposes. Therefore, top-hat selection transformation is useful for the research and application of top-hat transformation.