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About this paper
A. René Geist, Jonas Frey, Mikel Zobro, Anna Levina, Georg Martius
Researchers from the Max Planck Institute for Intelligent Systems and ETH Zurich present a comprehensive guide for selecting 3D rotation representations in neural networks. The work establishes that high-dimensional, continuously mapped representations like R9+SVD consistently outperform low-dimensional alternatives in rotation estimation tasks, providing clear recommendations for various learning scenarios.
Key insights
- For rotation estimation, low-dimensional representations (e.g., Euler angles, quaternions) fundamentally introduce discontinuities in the target function's mapping from SO(3) to the representation space, causing unstable gradient-based learning.
- Common 'fixes' like distance-picking metrics or half-space maps do not resolve the fundamental topological discontinuities of the underlying target function itself, offering only superficial improvements.
- High-dimensional representations, specifically R9+SVD and R6+GSO, circumvent these issues by providing a continuous mapping from SO(3) to a higher-dimensional Euclidean space, enabling more stable and effective gradient-based optimization.
Summary by alphaXiv.
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