  Establishing dense correspondences between a pair of images is an important
and general problem. However, dense flow estimation is often inaccurate in the
case of large displacements or homogeneous regions. For most applications and
down-stream tasks, such as pose estimation, image manipulation, or 3D
reconstruction, it is crucial to know when and where to trust the estimated
matches.
  In this work, we aim to estimate a dense flow field relating two images,
coupled with a robust pixel-wise confidence map indicating the reliability and
accuracy of the prediction. We develop a flexible probabilistic approach that
jointly learns the flow prediction and its uncertainty. In particular, we
parametrize the predictive distribution as a constrained mixture model,
ensuring better modelling of both accurate flow predictions and outliers.
Moreover, we develop an architecture and training strategy tailored for robust
and generalizable uncertainty prediction in the context of self-supervised
training. Our approach obtains state-of-the-art results on multiple challenging
geometric matching and optical flow datasets. We further validate the
usefulness of our probabilistic confidence estimation for the task of pose
estimation. Code and models are available at
https://github.com/PruneTruong/PDCNet.
