  In this work, we introduce Deep Bingham Networks (DBN), a generic framework
that can naturally handle pose-related uncertainties and ambiguities arising in
almost all real life applications concerning 3D data. While existing works
strive to find a single solution to the pose estimation problem, we make peace
with the ambiguities causing high uncertainty around which solutions to
identify as the best. Instead, we report a family of poses which capture the
nature of the solution space. DBN extends the state of the art direct pose
regression networks by (i) a multi-hypotheses prediction head which can yield
different distribution modes; and (ii) novel loss functions that benefit from
Bingham distributions on rotations. This way, DBN can work both in unambiguous
cases providing uncertainty information, and in ambiguous scenes where an
uncertainty per mode is desired. On a technical front, our network regresses
continuous Bingham mixture models and is applicable to both 2D data such as
images and to 3D data such as point clouds. We proposed new training strategies
so as to avoid mode or posterior collapse during training and to improve
numerical stability. Our methods are thoroughly tested on two different
applications exploiting two different modalities: (i) 6D camera relocalization
from images; and (ii) object pose estimation from 3D point clouds,
demonstrating decent advantages over the state of the art. For the former we
contributed our own dataset composed of five indoor scenes where it is
unavoidable to capture images corresponding to views that are hard to uniquely
identify. For the latter we achieve the top results especially for symmetric
objects of ModelNet dataset.
