Terrain point cloud inpainting via signal decomposition

The rapid development of 3D acquisition technology has made it possible to obtain point clouds of real-world terrains. However, due to limitations in sensor acquisition technology or specific requirements, point clouds often contain defects such as holes with missing data. Inpainting algorithms are widely used to patch these holes. However, existing traditional inpainting algorithms rely on precise hole boundaries, which limits their ability to handle cases where the boundaries are not well-defined. On the other hand, learning-based completion methods often prioritize reconstructing the entire point cloud instead of solely focusing on hole filling. Based on the fact that real-world terrain exhibits both global smoothness and rich local detail, we propose a novel representation for terrain point clouds. This representation can help to repair the holes without clear boundaries. Specifically, it decomposes terrains into low-frequency and high-frequency components, which are represented by B-spline surfaces and relative height maps respectively. In this way, the terrain point cloud inpainting problem is transformed into a B-spline surface fitting and 2D image inpainting problem. By solving the two problems, the highly complex and irregular holes on the terrain point clouds can be well-filled, which not only satisfies the global terrain undulation but also exhibits rich geometric details. The experimental results also demonstrate the effectiveness of our method.