Let $(M,g)$ be a Riemannian manifold with non-empty boundary. Is there any notion of injectivity radius on $(M,g)$ in points away from the boundary? By this I mean points lying in $M- \partial M$. What about geodesics or the exponential map in points away from the boundary? I am actually intrested in the description of the injectivity radius if there is one. Do you know a good reference? Hope for answers.