Video stereo matching is the task of estimating consistent disparity maps from rectified stereo videos. There is considerable scope for improvement in both datasets and methods within this area. Recent learning-based methods often focus on optimizing performance for independent stereo pairs, leading to temporal inconsistencies in videos. Existing video methods typically employ sliding window operation over time dimension, which can result in low-frequency oscillations corresponding to the window size. To address these challenges, we propose a bidirectional alignment mechanism for adjacent frames as a fundamental operation. Building on this, we introduce a novel video processing framework, BiDAStereo, and a plugin stabilizer network, BiDAStabilizer, compatible with general image-based methods. Regarding datasets, current synthetic object-based and indoor datasets are commonly used for training and benchmarking, with a lack of outdoor nature scenarios. To bridge this gap, we present a realistic synthetic dataset and benchmark focused on natural scenes, along with a real-world dataset captured by a stereo camera in diverse urban scenes for qualitative evaluation. Extensive experiments on in-domain, out-of-domain, and robustness evaluation demonstrate the contribution of our methods and datasets, showcasing improvements in prediction quality and achieving state-of-the-art results on various commonly used benchmarks. The project page, demos, code, and datasets are available at: https://tomtomtommi.github.io/BiDAVideo/.

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