We present a variational approach for surface reconstruction from a set of oriented points with scale information. We focus particularly on scenarios with non-uniform point densities due to images taken from different distances. In contrast to previous methods, we integrate the scale information in the objective and globally optimize the signed distance function of the surface on a balanced octree grid. We use a finite element discretization on the dual structure of the octree minimizing the number of variables. The tetrahedral mesh is generated efficiently from the dual structure, and also memory efficiency is optimized, such that robust data terms can be used even on very large scenes. The surface normals are explicitly optimized and used for surface extraction to improve the reconstruction at edges and corners