Neumann, KaiKaiNeumannHildenbrand, DietmarDietmarHildenbrandStock, FlorianFlorianStockSteinmetz, ChristianChristianSteinmetzMichel, MaximilianMaximilianMichel2024-02-282024-02-282024https://publica.fraunhofer.de/handle/publica/46259310.1007/978-3-031-34031-4_9Geometrical 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.enBranche: Information TechnologyResearch Line: Computer graphics (CG)LTA: Machine intelligence, algorithms, and data structures (incl. semantics)Point cloudsRigid registrationConformal Geometric Algebra (CGA)conference paper