Novel Models and Efficient Methods for Surface Reconstruction and Fairing

Surface processing, such as surface reconstruction and surface fairing, is a cornerstone in 3D modeling, data visualization, and high level data processing. It has broad applications in urban reconstruction, medical imaging, and the emerging paradigm of metaverse, which recently has been attracting considerable attentions from a wide range of communities. For example, in urban reconstruction, surface processing algorithms use light
detection and ranging (LiDAR) data to build 3D urban models, which are important for urban planning and virtual tourism. A metaverse is a virtual world that aims to provide users with immersive experiences, for which surface processing becomes an indispensable tool in determining the quality of 3D models of real-life objects in the virtual world. To satisfy the increasing need of high-quality 3D models, effective and efficient surface processing methods are in high demand. The goal of this proposal is to develop novel mathematical models and fast numerical methods for surface reconstruction and fairing.

In practice, the point cloud data for surface reconstruction is often incomplete due to high light-absorption rate, and occlusions during scanning. Many existing methods may fail to recover certain surface features on an incomplete data set. Methods that can well reconstruct surfaces from incomplete data sets are still underdeveloped. Surface fairing aims to smoothen a noisy surface while preserving surface features, such as ridges and corners. Gaussian curvature has demonstrated to be an effective regularizer. But studies on Gaussian curvature for surface fairing are limited due to its complexity.

This proposal is divided into two parts. The first part involves designing new models for surface reconstruction from incomplete data sets and surface fairing. For surface reconstruction, the novel idea is to fit the data sets on the data-available regions and also infer surface features using neighboring information on data-missing regions. For surface fairing, we will use Gaussian curvature to design new regularizers so that the
faired surface can well preserve surface ridges and corners. Then, in the second part we focus on developing efficient numerical methods to tackle the challenging problems involved in our proposed models, which will break these problems down into several easy-to-solve subproblems. We test our methods to LiDAR data to construct 3D models of urban objects, and we envision our proposed methodology can contribute towards robust
and efficient strategies for surface processing tasks.