Surface Reconstruction from Noisy Point Cloud Using Directional G-norm.

We propose a method to reconstruct surface from noisy point cloud data, by obtaining a clean zero level set of their signed distance function (SDF). Due to the noise in the given point cloud, the distance function is oscillatory and lacks smoothness, especially near the data point. We denoise the SDF using a modified G-norm along the tangential direction of the input point cloud data. While there is abundant work for obtaining a smooth surface from a noisy data, our contribution is to provide an insight into how noisy data corrupts reconstruction of surfaces, through extracting the noisy component from the distance function directly. We apply Augmented Lagrangian Method to optimize the objective energy function and solve the subproblems. We present various numerical results to validate the proposed method.