Estimating the 3DoF rotation from a single RGB image is an important yet
challenging problem. Recent works achieve good performance relying on a large
amount of expensive-to-obtain labeled data. To reduce the amount of
supervision, we for the first time propose a general framework, FisherMatch,
for semi-supervised rotation regression, without assuming any domain-specific
knowledge or paired data. Inspired by the popular semi-supervised approach,
FixMatch, we propose to leverage pseudo label filtering to facilitate the
information flow from labeled data to unlabeled data in a teacher-student
mutual learning framework. However, incorporating the pseudo label filtering
mechanism into semi-supervised rotation regression is highly non-trivial,
mainly due to the lack of a reliable confidence measure for rotation
prediction. In this work, we propose to leverage matrix Fisher distribution to
build a probabilistic model of rotation and devise a matrix Fisher-based
regressor for jointly predicting rotation along with its prediction
uncertainty. We then propose to use the entropy of the predicted distribution
as a confidence measure, which enables us to perform pseudo label filtering for
rotation regression. For supervising such distribution-like pseudo labels, we
further investigate the problem of how to enforce loss between two matrix
Fisher distributions. Our extensive experiments show that our method can work
well even under very low labeled data ratios on different benchmarks, achieving
significant and consistent performance improvement over supervised learning and
other semi-supervised learning baselines. Our project page is at
this https URL

本文提出了一种利用矩阵费舍尔分布来建立旋转的概率模型，通过估计预测不确定性的信息熵来实现伪标签过滤的半监督旋转回归方法，并在不同基准测试中实现了显着和一致的性能提升。

FisherMatch: 基于熵过滤的半监督旋转回归

FisherMatch: Semi-Supervised Rotation Regression via Entropy-based  Filtering

This paper focuses on estimating probability distributions over the set of 3D
rotations ($SO(3)$) using deep neural networks. Learning to regress models to
the set of rotations is inherently difficult due to differences in topology
between $\mathbb{R}^N$ and $SO(3)$. We overcome this issue by using a neural
network to output the parameters for a matrix Fisher distribution since these
parameters are homeomorphic to $\mathbb{R}^9$. By using a negative log
likelihood loss for this distribution we get a loss which is convex with
respect to the network outputs. By optimizing this loss we improve
state-of-the-art on several challenging applicable datasets, namely Pascal3D+,
ModelNet10-$SO(3)$ and UPNA head pose.

文章通过使用深度神经网络学习输出矩阵费舍尔分布参数来实现在 3D 旋转集合（$SO (3)$）上估计概率分布；并使用负对数似然损失优化生成具有凸损失的模型从而在 Pascal3D +，ModelNet10-$SO (3)$ 和 UPNA 头部姿势等多个挑战性数据集上获取了 state-of-the-art 的结果。

用矩阵费歇尔分布进行概率方向估计

Probabilistic orientation estimation with matrix Fisher distributions

This paper focuses on a stochastic formulation of Bayesian attitude
estimation on the special orthogonal group. In particular, an exponential
probability density model for random matrices, referred to as the matrix Fisher
distribution is used to represent the uncertainties of attitude estimates and
measurements in a global fashion. Various stochastic properties of the matrix
Fisher distribution are derived on the special orthogonal group, and based on
these, two types of intrinsic frameworks for Bayesian attitude estimation are
constructed. These avoid complexities or singularities of the attitude
estimators developed in terms of quaternions. The proposed approaches are
particularly useful to deal with large estimation errors or large uncertainties
for complex maneuvers to obtain accurate estimates of the attitude.

本文提出了一种基于矩阵菲舍尔分布的随机贝叶斯态度估计方法，避开四元数表示法的复杂性和奇异性，对于复杂机动引起的大误差或大不确定性具有显著的提高。