Reproduce “Synchronizing Probability Measures on Rotations via Optimal Transport” on OpenResearch
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About this paper
Tolga Birdal, Michael Arbel, Umut Şimşekli, Leonidas Guibas
The method synchronizes distributions of plausible camera rotations rather than selecting one rotation per pair. It represents pairwise and absolute orientations as particles, compares implied and observed relative-rotation distributions, and optimizes them over a graph. In a rendered mug experiment, it achieved 4° best-match error and 19° median particle error. Its convergence guarantee is restricted to low-entropy, regularized maximum mean discrepancy.
Key insights
- Explicitly modeling pose estimates as probability measures directly handles multimodal ambiguities and propagates uncertainty, enhancing robustness beyond deterministic solutions.
- Optimal transport divergences provide a geometrically consistent way to compare and combine probability distributions on the rotation manifold.
- Riemannian Particle Gradient Descent offers a practical method to optimize non-parametric probability distributions on manifolds, enabling the discovery of multimodal solutions.
Summary by alphaXiv.
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