Point cloud rendering has a vital role in the user Quality of Experience for applications adopting point cloud based representations. While this is not a new area, it has recently become more relevant with the recent interest on point cloud coding by major standardization groups, notably JPEG and MPEG. The screened Poisson surface reconstruction is a state-of-the-art technique for generating a watertight surface mesh from the point cloud samples. While its screening component allows the surface to better fit the cloud points, this fitting may lead to undesired artifacts in the surface, notably when the point cloud is noisy. This paper proposes to improve this reconstruction method by making it more robust to noise by adopting a generalized Tikhonov regularization term. The proposed regularization approach smooths regions that should be flat while keeping the important details in the edges, thus creating more pleasant surface reconstructions.