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Explicit representations of the global match distributions of pixel-wisecorrespondences between pairs of images are desirable for uncertaintyestimation and downstream applications. However, the computation of the matchdensity for each pixel may be prohibitively expensive due to the large numberof candidates. In this paper, we propose Hierarchical Discrete DistributionDecomposition (HD^3), a framework suitable for learning probabilistic pixelcorrespondences in both optical flow and stereo matching. We decompose the fullmatch density into multiple scales hierarchically, and estimate the localmatching distributions at each scale conditioned on the matching and warping atcoarser scales. The local distributions can then be composed together to formthe global match density. Despite its simplicity, our probabilistic methodachieves state-of-the-art results for both optical flow and stereo matching onestablished benchmarks. We also find the estimated uncertainty is a goodindication of the reliability of the predicted correspondences.

Hierarchical Discrete Distribution Decomposition for Match Density Estimation