In this thesis we present a method to estimate the surface orientation of a 3D object. The general technique is called Photometric Stereo (PS) since we use several 2D images taken from the same location while the illumination changes for each image. Therefore, we use the varying intensities for each pixel to estimate the surface normal vector. In order to compute the estimation of the surface normals we used a variational approach and derived an energy functional depending on the Cartesian depth z. This energy functional is like a cost function that we want to minimise to obtain a good estimation of the shape of the test object. For the minimisation technique we used the method of Maurer et al. [MJBB15] to overcome the difficulties in the minimisation of the energy functional and efficiently reach a global minimum. Further, we present three variants of this model that use different illumination models and two model extensions. Finally, we compare the performances of all the variants of the PS model in different experiments.