GAAlign: Robust Sampling-Based Point Cloud Registration Using Geometric Algebra

Geometrical 3D data is often represented in form of point clouds. A common problem is the registration of point clouds with shared underlying geometry, for example to align two 3D scans. This work presents GAAlign, a new formulation of a geometric algebra (GA) based algorithm that aims to solve this problem. While the algorithm itself is a gradient descent based approach, the implementation takes advantage of GAALOP, which had to be extended with a specific, so far unsupported GA, namely projective GA. The proposed new robust registration algorithm uses a geometric algebra based motor estimation algorithm in the context of a stochastic gradient descent inspired algorithmic structure and achieves state-of-the-art results. When using synthetically disturbed input data the results show, that GAAlign either outperforms other used algorithms (outliers) or is comparable to the best (Gaussian noise) while having a significantly better
runtime as soon as the number of correspondences increases. When used in a real world pipeline, GAAlign also performs on the same level or above compared to state-of-the-art algorithms.