Example-based 3D inpainting of point clouds using metric tensor and Christoffel symbols

Abstract

In this paper, we address the problem of 3D inpainting using example-based methods for point cloud data. 3D inpainting is a process of filling holes or missing regions in the reconstructed 3D models. Typically inpainting methods addressed in the literature fill missing regions due to occlusions or inaccurate scanning of 3D models. However, we focus on scenarios involving naturally existing damaged models which are partly broken or incomplete in artifacts at cultural heritage sites. We propose two example-based inpainting techniques, namely region of interest (ROI)-based and patch-based methods, to inpaint the missing regions of the damaged model. For both the methods, we represent the 3D model as a set of Riemannian manifolds in Euclidean space, to capture the inherent geometry using metric tensor and Christoffel symbols as geometric features and decompose into basic shape (such as spherical, conical and cylindrical) regions using decomposition algorithm derived from supervised learning. In ROI-based method, instead of using single similar example for inpainting, we select the most relevant regions that best-fit the missing region from the set of basic shape regions derived from n similar examples. And in patch-based method, we not only select the most relevant regions but cluster the regions into a set of patches. The best corresponding patches that match the missing region to be inpainted are considered to be the most relevant best-fit patches that cover the complete missing region. We demonstrate the performance of proposed inpainting methods on cultural heritage artifacts with varying complexities and sizes for both synthetically generated holes and real missing regions.