  Establishing robust and accurate correspondences between a pair of images is
a long-standing computer vision problem with numerous applications. While
classically dominated by sparse methods, emerging dense approaches offer a
compelling alternative paradigm that avoids the keypoint detection step.
However, dense flow estimation is often inaccurate in the case of large
displacements, occlusions, or homogeneous regions. In order to apply dense
methods to real-world applications, such as pose estimation, image
manipulation, or 3D reconstruction, it is therefore crucial to estimate the
confidence of the predicted matches.
  We propose the Enhanced Probabilistic Dense Correspondence Network, PDC-Net+,
capable of estimating accurate dense correspondences along with a reliable
confidence map. 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 an enhanced 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 tasks of pose
estimation, 3D reconstruction, image-based localization, and image retrieval.
Code and models are available at https://github.com/PruneTruong/DenseMatching.
