Reasoning about uncertain orientations is one of the core problems in many perception tasks such as object pose estimation or motion estimation. In these scenarios, poor illumination conditions, sensor limitations, or appearance invariance may result in highly uncertain estimates. In this work, we propose a novel learning based representation for orientation uncertainty. Characterizing uncertainty over unit quaternions with the Bingham distribution allows us to formulate a loss that naturally captures the antipodal symmetry of the representation. We discuss the interpretability of the learned distribution parameters and demonstrate the feasibility of our approach on several challenging real-world pose estimation tasks involving uncertain orientations.
The paper proposes a Brigham loss (based on the Brigham distribution) to model the uncertainty of orientations (an important factor for pose estimation and other tasks). This distribution has the necessary characteristics required to represent orientation uncertainty using quaternions (one way to represent object orientation in 3D) such as antipodal symmetry. The authors propose various additions such as using precomputed lookup tables to represent a simplified version of the normalization constant (to make it computationally tractable), and the use of Expected Absolute Angular Deviation (EAAD) to make the uncertainty of the Bingham distribution more interpretable. 
+Uncertainty quantification of neural networks is an important problem that I believe should gain more attention so I am happy to see papers such as this one. 
+Various experiments on multiple datasets show the efficacy of the method as well as out performing or showing comparable results to state-of-the-art
-In the caption for Table 1 the author’s write: “the high likelihood and lower difference between EAAD and MAAD indicate that the Bingham loss better captures the underlying noise.” How much difference between EAAD and MAAD is considered significant and why?
-In section 4.5 they write “While Von Mises performs better on the MAAD, we observe that there is a larger difference between the MAAD and EAAD values for the Von Mises distribution than the Bingham distribution. This indicates that the uncertainty estimates of the Von Mises distribution may be overconfident.” Same question as above. What amount of difference between MAAD and EAAD is considered significant and why?