Local Frequency Interpretation and Non-Local Self-Similarity on Graph for Point Cloud Inpainting

As 3D scanning devices and depth sensors mature, point clouds have attracted increasing attention as a format for 3D object representation, with applications in various fields such as tele-presence, navigation, and heritage reconstruction. However, point clouds usually exhibit holes of missing data, mainly due to the limitation of acquisition techniques and complicated structure. Further, point clouds are defined on irregular non-Euclidean domains, which are challenging to address especially with conventional signal processing tools. Hence, leveraging on recent advances in graph signal processing, we propose an efficient point cloud inpainting method, exploiting both the local smoothness and the non-local self-similarity in point clouds. Specifically, we first propose a frequency interpretation in graph nodal domain, based on which we derive the smoothing and denoising properties of a graph-signal smoothness prior in order to describe the local smoothness of point clouds. Second, we explore the characteristics of non-local self-similarity, by globally searching for the most similar area to the missing region. The similarity metric between two areas is defined based on the direct component and the anisotropic graph total variation of normals in each area. Finally, we formulate the hole-filling step as an optimization problem based on the selected most similar area and regularized by the graph-signal smoothness prior. Besides, we propose voxelization and automatic hole detection methods for the point cloud prior to inpainting. The experimental results show that the proposed approach outperforms four competing methods significantly, both in objective and subjective quality.