Abstract
Semi-global matching, originally introduced in the context of dense stereo, is a very successful heuristic to minimize the energy of a pairwise multi-label Markov Random Field defined on a grid. We offer the first principled explanation of this empirically successful algorithm, and clarify its exact relation to belief propagation and tree-reweighted message passing. One outcome of this new connection is an uncertainty measure for the MAP label of a variable in a Markov Random Field.
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- 1.
In the sense that nodes can take one of two possible labels.
- 2.
We will drop the indices in \(\varphi (d_{\mathbf {p}})\) and \(\varphi (d_{\mathbf {p}},d_{\mathbf {q}})\) as they are clear from the function inputs.
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- 4.
In terms of message passing on a factor graph, one variant represents factor-to-node messages, while the other gives node-to-factor messages.
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Acknowledgments
The research of A.D. and S.A. was partially supported by a Google grant. C.H. and F.A.H. gratefully acknowledge partial financial support by the HGS MathComp Graduate School, the RTG 1653 for probabilistic graphical models and the CellNetworks Excellence Cluster / EcTop.
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Drory, A., Haubold, C., Avidan, S., Hamprecht, F.A. (2014). Semi-Global Matching: A Principled Derivation in Terms of Message Passing. In: Jiang, X., Hornegger, J., Koch, R. (eds) Pattern Recognition. GCPR 2014. Lecture Notes in Computer Science(), vol 8753. Springer, Cham. https://doi.org/10.1007/978-3-319-11752-2_4
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