A Probabilistic Rotation Representation for Symmetric Shapes With an
  Efficiently Computable Bingham Loss Function
Hiroya Sato Takuya Ikeda Koichi Nishiwaki
In recent years, a deep learning framework has been widely used for object
pose estimation. While quaternion is a common choice for rotation
representation, it cannot represent the ambiguity of the observation. In order
to handle the ambiguity, the Bingham distribution is one promising solution.
However, it requires complicated calculation when yielding the negative
log-likelihood (NLL) loss. An alternative easy-to-implement loss function has
been proposed to avoid complex computations but has difficulty expressing
symmetric distribution. In this paper, we introduce a fast-computable and
easy-to-implement NLL loss function for Bingham distribution. We also create
the inference network and show that our loss function can capture the symmetric
property of target objects from their point clouds.