Mechanical and hydro-mechanical properties of fracture surfaces and faults depend on the roughness of these surfaces. Roughness measures such as the Hurst exponent are used to measure roughness. Also anisotropy analysis of surfaces is of interest. Minkowski tensors of order 2 can be applied to measure roughness. The aim of my project is to establish stable roughness measures, compare those in terms of their qualitative and numerical properties. Moreover, one aim of my project is to establish structure function relationships between roughness measures and the corresponding mechanical properties.