The aim of this thesis is to investigate the applicability of two optimization algorithms in the context of Riemannian manifolds. More precisely, we use the steepest descent method and the nonlinear conjugate gradient (NCG) method to solve the shape from shading (SFS) problem in the shape space of triangular meshes. For this reason, we endow this shape space with an appropriate Riemannian inner product. Instead of steps along straight lines we shall take steps along geodesics with respect to the Riemannian metric. Moreover, we will have to use the concept of parallel displacement in order to apply the NCG-algorithm.The organization of the thesis is as follows. First, we concentrate on the theoretical studies which are necessary to implement the steepest descent algorithm and the NCG-algorithm in the shape space of triangular meshes. Afterwards, we apply these minimization algorithms to solve the SFS-problem for three different shapes. In addition, we compare the obtained results for certain Riemannian metrics in the shape space. Finally, a short chapter with remarks and an outlook to future research concludes the thesis.