Terrain Point Cloud Inpainting via Signal Decomposition

TL;DR

The paper tackles holes in terrain point clouds where boundaries are irregular or ill-defined. It introduces a terrain-specific signal decomposition into a low-frequency component $L$ represented by a B-spline surface $\mathcal{S}(u,v)$ and a high-frequency component $H$ captured as a relative height map, converting 3D inpainting into a 2D image inpainting plus surface fitting problem. The method automatically localizes holes using the height map, performs robust low-frequency surface fitting, and then reconstructs fine details by solving a gradient-domain Poisson inpainting guided by patch matching, followed by 3D reconstruction using Halton-driven sampling. Experiments on real terrains show superior geometric fidelity (GPSNR/NSHD) over traditional and learning-based baselines, though computational cost remains a limitation to address in future work.

Abstract

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.

Figures (15)

• Figure 1: In outdoor scenes, the combination of trees and low-rise buildings often presents significant challenges for terrain reconstruction using a 3D acquisition technique called oblique photography. Upon filtering out these extraneous objects, complex-shaped or no-well-defined holes remain. (a) An overhead perspective of the terrain point cloud. (b) After applying filters, both vegetation and low-rise buildings are effectively eliminated, thereby exposing holes within the terrain. Irregular boundary holes are marked with blue boxes, while holes lacking well-defined boundaries are marked with green boxes.
• Figure 2: Core idea of our method.
• Figure 3: A comparison is made between the DEM method and our method from a lateral perspective. In this comparison, the original signal is depicted in green, the low-frequency component $L$ is represented in blue, and the high-frequency component $H$ is depicted in yellow
• Figure 4: The pipeline of our method.
• Figure 5: Illustration of point projection onto a surface. $q_1$ and $q_2$ represent the projection points of $p_1$ and $p_2$, respectively. $p_1$ and $p_2$ reside on opposite sides of $\mathcal{S}$ and exhibit different projection directions.