Computing visibility on a geometric object requires heavy computations since it requires to identify pairs of points that are visible to each other, i.e. there is a straight segment joining them that stays in the close vicinity of the object boundary. We propose to exploit a specific representation of digital sets based on lists of integral intervals in order to compute efficiently the complete visibility graph between lattice points of the digital shape. As a quite direct application, we show then how we can use visibility to estimate the normal vector field of a digital shape in an accurate and convergent manner while staying aware of the salient and sharp features of the shape.