For many operations, distinguishing objects depends on the convention used to decide whether pixels are connected. There are two different conventions typically used: 4-connected or 8-connected neighborhoods.
In an 8-connected neighborhood, all of the pixels that touch the pixel of interest are considered, including those on the diagonals. This means that if two adjoining pixels are on, they are part of the same object, regardless of whether they are connected along the horizontal, vertical, or diagonal direction.