Mathematical morphology is a classic field in set theory and digital image processing. Topological data analysis (TDA), on the other hand, is a rising field in both algebraic topology and machine learning. One-parameter persistent homology, a main tool in TDA, relies on having a one-parameter filtration which is a sequence of sets satisfying nested subset relations. It has been widely studied and applied. Recently, the theory of multi-parameter persistent homology has been proposed; however, real world applications or concrete examples of multi-parameter filtrations are very limited. In this talk, I will introduce a framework for constructing multi-parameter filtrations of binary images by using the classic opening/closing operations in mathematical morphology. The framework not only offers geometric insights, but also provides concrete examples to the TDA field. As an application, a denoising algorithm in digital images is developed based on the geometric and topological information extracted from the framework. This is a joint work with Yu-Min Chung at UNC Greensboro, and Sarah Day at College of William and Mary.