LGSur-Net: A Local Gaussian Surface Representation Network for Upsampling Highly Sparse Point Cloud

We introduce LGSur-Net, an end-to-end deep learning architecture, engineered for the upsampling of sparse point clouds. LGSur-Net harnesses a trainable Gaussian local representation by positioning a series of Gaussian functions on an oriented plane, complemented by the optimization of individual covariance matrices. The integration of parametric factors allows for the encoding of the plane's rotational dynamics and Gaussian weightings into a linear transformation matrix. Then we extract the feature maps from the point cloud and its adjoining edges and learn the local Gaussian depictions to accurately model the shape's local geometry through an attention-based network. The Gaussian representation's inherent high-order continuity endows LGSur-Net with the natural ability to predict surface normals and support upsampling to any specified resolution. Comprehensive experiments validate that LGSur-Net efficiently learns from sparse data inputs, surpassing the performance of existing state-of-the-art upsampling methods. Our code is publicly available at https://github.com/Rangiant5b72/LGSur-Net.