SliceLRF: A Local Reference Frame Sliced along the Height on the 3D Surface

The local reference frame (LRF) plays a vital role in local 3D shape description and matching. Numerous LRF methods have been proposed in recent decades. However, few LRFs can achieve a balance between repeatability and robustness under exposure to a variety of nuisances, including Gaussian noise, mesh resolution variation, clutter, and occlusion. Additionally, most LRFs are heuristic and lack generalizability to different applications and data modalities. In this paper, we first define the degree of distinction to describe the distribution of 2D point clouds and explore the relationship between the relative deviation of the distinction degree and the LRF error through experiments. Based on Gaussian noise and a random sampling analysis, several factors that affect the relative deviation of the distinction degree and result in the LRF error are identified. A scoring criterion is proposed to evaluate the robustness of the point cloud distribution. On this basis, we propose an LRF method (SliceLRF) based on slicing along the Z-axis, which selects the most robust adjacent slices in the point cloud region by scoring criteria for X-axis estimation to improve the repeatability and robustness. SliceLRF is rigorously tested on four public benchmark datasets which have different applications and involve different data modalities. It is also compared with the state-of-the-art LRFs. The experimental results show that the SliceLRF has more comprehensive repeatability and robustness than the other LRFs under exposure to Gaussian noise and random sampling.