Dimensionality-Aware GICP: 4D Hilbert Curve Approach Using Hellinger Distance

This study proposes a novel approach that quantifies the local distribution of point clouds to define Dimensionality, incorporates it into the existing 3D coordinate system to construct a 4D coordinate system, and employs Hilbert Curve to efficiently improve registration speed. By analyzing the distributional characteristics of point clouds using Hellinger Distance and introducing Hilbert Curve-based nearest neighbor search, the proposed method reduces computational overhead while enhancing registration accuracy. The algorithm was evaluated on the Kitti and Stanford Bunny datasets [1], demonstrating lower performance compared to existing algorithms in the simple urban environment of the Kitti dataset but achieving outstanding registration performance in the complex structure of the Stanford Bunny dataset, even in cases involving partial overlaps and outliers. In particular, the combination of Dimensionality and Hilbert Curve-based search significantly improved registration quality and stability in complex datasets. This approach can be extended to LIO-based odometry systems or utilized in Color-based ICP applications.