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Stereo vision algorithms are important building blocks of self-driving applications. The two primary requirements of a self-driving vehicle are real-time operation and nearly 100% accuracy in constructing the 3D scene regardless of the weather conditions and the degree of ambient light. Sadly, most real-time systems as of today provide a level of accuracy that is inadequate and this endangers the life of the passengers; consequently, it is necessary to supplement such systems with expensive LiDAR-based sensors. We observe that for a given scene, different stereo matching algorithms can have vastly different accuracies, and among these algorithms there is no clear winner. This makes the case for a hybrid stereo vision system where the best stereo vision algorithm for a stereo image pair is chosen by a predictor dynamically, in real-time.We implement such a system called PredStereo in ASIC 1 that combines two diametrically different stereo vision algorithms, CNN-based and traditional, and chooses the best one at runtime. In addition, it associates a confidence with the chosen algorithm, such that the higher-level control system can be switched on in case of a low confidence value. We show that designing a predictor that is explainable and a system that respects soft real-time constraints is non-trivial. Hence, we propose a variety of hardware optimizations that enable our system to work in real-time. Overall, PredStereo improves the disparity estimation error over a state-of-the-art CNN-based stereo vision system by up to 18% (on average 6.25%) with a negligible area overhead (0.003mm 2 ) while respecting real-time constraints.