Unified form for multi-scale top-hat transform based algorithms

Multi-scale operation has been one efficient way to improve the performance of top-hat transform. The key of multi-scale top-hat transform is appropriately organizing and using multi-scale top-hat transform to extract the multi-scale image features. If a unified form of multi-scale top-hat transform can be proposed, the application of multi-scale top-hat transform could be focused on the decision of some functions of the unified form. This would simplify the algorithm design. In this paper, a unified form of multi-scale top-hat transform based algorithms is given. To prove the unified form, some applications of multi-scale top-hat transform based algorithms are integrated into the unified form by specifying the key functions of the unified form. These examples not only prove the unified form, but also provide the way of how to determine the key functions of the unified form for different applications.