Learning rotations

Many problems in computer vision today are solved via deep learning. Tasks like pose estimation from images, point clouds or structure motion can all be formulated as a regression on rotations. However, there is no unique way of parametrizing rotations mathematically: matrices, quaternions, axis-angle representation Euler angles commonly used the field. Some them, however, present intrinsic limitations, including discontinuities, gimbal lock antipodal symmetry. These limitations may make learning neural networks challenging problem, potentially introducing large errors. Following recent literature, we propose three case studies: sanity check, 3D and an inverse kinematic problem. We do so by employing full geometric algebra (GA) description compare GA formulation with 6D continuous previously presented literature terms error reconstruction accuracy. empirically demonstrate that bivectors outperforms representation. The approach overcomes continuity issue representations does, but it also needs fewer parameters to learned offers enhanced robustness noise. hence provides broader framework for describing simple compact suitable tasks learning, showing high accuracy good generalizability realistic high-noise scenarios.