The present paper is concerned with the numerical solution of multidimensional control problems of DieudonnéRashevsky type by discretization methods and large-scale optimization techniques. We prove first a convergence theorem wherein the difference of the minimal value and the objective values along a minimizing sequence is estimated by the mesh size of the underlying triangulations. Then we apply the proposed method to the problem of edge detection within raw image data. Instead of using an AmbrosioTortorelli type energy functional, we reformulate the problem as a multidimensional control problem. The edge detector can be built immediately from the control variables. The quality of our numerical results competes well with those obtained by applying variational techniques.