  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.
