Abstract: Preserving connectivity is an important property commonly required for object discretization. Connectivity of a discretized object differs depending on how to discretize its original object. The morphological discretization is known to be capable of controlling the connectivity of a discretized object, by selecting appropriate structuring elements. The analytical approximation, which approximates the morphological discretization by a finite number of inequalities, on the other hand, is recently introduced to reduce the computational cost required for the morphological discretization. However, whether this approximate discretization has the same connectivity that the morphological discretization has is yet to be investigated. In this paper, we study the connectivity relationship between the morphological discretization and the analytical approximation, focusing on 2D explicit curves. We show that they guarantee the same connectivity for 2D explicit curves/surfaces.