Special Unitary Parameterized Estimators of Rotation

Core task: rotation estimation and learning in neural networks. The field encompasses diverse approaches to handling rotational transformations in deep learning, organized into several major branches. One branch focuses on rotation equivariance and invariance, where architectures such as Steerable Filters[1] and Vector Field Networks[12] build in geometric symmetries to ensure consistent behavior under rotation. Another branch addresses rotation representation and parameterization, exploring continuous representations like Rotation Continuity[2] and specialized parameterizations including quaternions and special unitary groups. Additional branches cover rotation-based self-supervised learning (e.g., Predicting Image Rotations[8]), 6D pose estimation for objects and spacecraft (Spacecraft Pose Rendering[5], Spacecraft Rendezvous Pose[10]), relative camera pose estimation (Relative Camera Pose[22]), and specialized applications ranging from remote sensing to machinery fault diagnosis. Theoretical foundations and training dynamics form yet another branch, examining how networks learn and represent rotational structure. Within the representation and parameterization branch, a particularly active line of work explores trade-offs between continuity, computational efficiency, and geometric fidelity. Some methods favor matrix-based representations analyzed through SVD Rotation Analysis[37] or address challenges with Unorthogonalized Matrices[6], while others adopt quaternion frameworks as in Quaternion Framework Pose[35]. SUPER[0] situates itself within the special unitary and quaternion parameterizations cluster, emphasizing structured algebraic representations that respect the manifold geometry of rotation groups. This contrasts with approaches like Rotation Continuity[2], which prioritize smooth, continuous mappings for gradient-based optimization, and differs from works such as Neural Euler Rotation[20] that explore alternative angle-based parameterizations. The choice of representation remains an open question, balancing mathematical elegance, learning stability, and downstream task performance across the diverse application domains represented in this taxonomy.