Explicit representations of the global match distributions of pixel-wise
correspondences between pairs of images are desirable for uncertainty
estimation and downstream applications. However, the computation of the match
density for each pixel may be prohibitively expensive due to the large number
of candidates. In this paper, we propose Hierarchical Discrete Distribution
Decomposition (HD^3), a framework suitable for learning probabilistic pixel
correspondences in both optical flow and stereo matching. We decompose the full
match density into multiple scales hierarchically, and estimate the local
matching distributions at each scale conditioned on the matching and warping at
coarser scales. The local distributions can then be composed together to form
the global match density. Despite its simplicity, our probabilistic method
achieves state-of-the-art results for both optical flow and stereo matching on
established benchmarks. We also find the estimated uncertainty is a good
indication of the reliability of the predicted correspondences.

该研究提出了一种适用于光流和立体匹配的分层离散分布分解（HD^3）框架，通过分层地分解完整的匹配密度并估计每个层次上的局部匹配分布，最终组合得到全局匹配密度。尽管方法简单，但在光流和立体匹配的对比试验中取得了最优的效果，并发现估计的不确定性是预测对应的可靠度的很好指标。