In this article, we propose to adapt the concept of medial axis (MA), largely studied on regular grids, to two-dimensional irregular isothetic grids. In a previous work, we introduced the extension of the squared Euclidean distance transformation to these structures, where cells may be defined with variables sizes and positions. We now propose an algorithm that computes a reduced discrete MA, that may be em- ployed for various classical grids in imagery. We also show the interest of our method for an adaptive MA construction based on a quadtree decomposition scheme.