Towards Robust Probabilistic Modeling on SO(3) via Rotation Laplace Distribution

Area of Science:

• Computer Vision
• Machine Learning
• Geometric Deep Learning

Background:

• Estimating 3 Degrees of Freedom (3DoF) rotation from single RGB images is a challenging computer vision task.
• Probabilistic rotation modeling offers uncertainty information but common distributions like Bingham and matrix Fisher are sensitive to outliers (e.g., 180° errors).

Purpose of the Study:

• To propose a novel rotation Laplace distribution on SO(3) for robust probabilistic rotation estimation.
• To demonstrate the effectiveness of the proposed distribution in handling outliers, noise, and imperfect annotations.
• To extend the approach to a mixture model for multi-modal rotation solutions, particularly for symmetric objects.

Main Methods:

• Developed a novel rotation Laplace distribution inspired by the multivariate Laplace distribution, designed for SO(3).
• Introduced a rotation Laplace mixture model to address multi-modal rotation scenarios.
• Evaluated the proposed methods on rotation regression tasks, including semi-supervised settings with noisy pseudo-labels.

Main Results:

• The proposed rotation Laplace distribution shows robustness to outlier predictions and small noises, improving convergence.
• The method demonstrates advantages in semi-supervised rotation regression due to its tolerance for imperfect annotations.
• The rotation Laplace mixture model effectively captures multi-modal rotation solution spaces for symmetric objects.

Conclusions:

• The novel rotation Laplace distribution and its mixture model achieve State-of-the-Art performance in rotation regression tasks.
• The proposed approach offers significant improvements over both probabilistic and non-probabilistic baselines, particularly in challenging conditions.