An Equivalence Relation Between Morphological Dynamics and Persistent Homology in n-D

In Mathematical Morphology (MM), dynamics are used to compute markers proceed for example watershed-based image decomposition. At the same time, persistence is a concept coming from Persistent Homology (PH) and Morse Theory (MT) represents stability of extrema function. Since these concepts similar on functions, we studied their relationship found, proved, that they equal 1D functions. Here, propose extend this proof n-D, \(n \ge 2\), showing equality can be applied n-D images not only This step further show how much MM MT related.