New formulations of the optical flow problem and of the digital inpainting problem are discussed and validated by numerical experiments. For determining optical flows, an optimal control approach is presented where the velocity field are interpreted as bilinear control functions of the optimal control problem of tracking a sequence of given frames. For digital inpainting, a new approach based on the solution of a Ginzburg--Landau equation is discussed. Advanced numerical techniques for the solution of these problems are presented and investigated.