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Recently, there has been a paradigm shift in stereo matching with learning-based methods achieving the best results on all popular benchmarks. The success of these methods is due to the availability of training data with ground truth; training learning-based systems on these datasets has allowed them to surpass the accuracy of conventional approaches based on heuristics and assumptions. Many of these assumptions, however, had been validated extensively and hold for the majority of possible inputs. In this paper, we generate a matching volume leveraging both data with ground truth and conventional wisdom. We accomplish this by coalescing diverse evidence from a bidirectional matching process via random forest classifiers. We show that the resulting matching volume estimation method achieves similar accuracy to purely data-driven alternatives on benchmarks and that it generalizes to unseen data much better. In fact, the results we submitted to the KITTI and ETH3D benchmarks were generated using a classifier trained on the Middlebury 2014 dataset.