Apparent contours and their Legendrian deformations

After reviewing the notion of apparent contours of a smooth map $\varphi$ from a compact manifold $N$ to another manifold $M$, we recall the construction of an associated Legendrian subvariety in the space of contact elements of the goal manifold $M$ and we study various examples. The main result is that, in some sense, non-trivial Legendrian deformations of apparent contours do not exist: In the space of contact elements of a real projective space, the set of the Legendrian submanifolds obtained in this way is closed under Legendrian isotopy.