Denoising the point cloud is fundamental for reconstructing high quality surfaces with details in order to eliminate noise and outliers in the 3D scanning process. The challenges for a denoising algorithm are noise reduction and sharp features preservation. In this paper, we present a new model to reconstruct and smooth point clouds that combine L1-median filtering with sparse L1 regularization for both denoising the normal vectors and updating the position of the points to preserve sharp features in the point cloud. The L1-median filter is robust to outliers and noise compared to the mean. The L1 norm is a way to measure the sparsity of a solution, and applying an L1 optimization to the point cloud can measure the sparsity of sharp features, producing clean point set surfaces with sharp features. We optimize the L1 minimization problem by using the proximal gradient descent algorithm. Experimental results show that our approach is comparable to the state-of-the-art methods, as it filters out 3D models with a high level of noise, but keeps their geometric features.
Keywords: 3D surface reconstruction; point cloud denoising; sparse representation.