  We present a multimodal camera relocalization framework that captures
ambiguities and uncertainties with continuous mixture models defined on the
manifold of camera poses. In highly ambiguous environments, which can easily
arise due to symmetries and repetitive structures in the scene, computing one
plausible solution (what most state-of-the-art methods currently regress) may
not be sufficient. Instead we predict multiple camera pose hypotheses as well
as the respective uncertainty for each prediction. Towards this aim, we use
Bingham distributions, to model the orientation of the camera pose, and a
multivariate Gaussian to model the position, with an end-to-end deep neural
network. By incorporating a Winner-Takes-All training scheme, we finally obtain
a mixture model that is well suited for explaining ambiguities in the scene,
yet does not suffer from mode collapse, a common problem with mixture density
networks. We introduce a new dataset specifically designed to foster camera
localization research in ambiguous environments and exhaustively evaluate our
method on synthetic as well as real data on both ambiguous scenes and on
non-ambiguous benchmark datasets. We plan to release our code and dataset under
$\href{https://multimodal3dvision.github.io}{multimodal3dvision.github.io}$.
