While wide-angle lenses provide an expanded field of view (FoV), they exhibit severe nonlinear distortion near image boundaries, unnaturally stretching people in these regions. Existing methods mostly focus on facial regions, require high computational costs, and lack temporal modeling, resulting in incomplete full-body rectification, impractical real-time deployment, and noticeable inter-frame shakes. To tackle these issues, we propose \textbf{FastVC}, an efficient full-body video rectification framework driven by distortion-aware spatiotemporal learning. Grounded in lens physics, FastVC introduces a distortion-aware thin-plate spline (DA-TPS) module that nonlinearly remaps control points into a peripheral-dense layout, enabling more accurate geometric fitting without additional computational cost. We further develop a dual-level spatiotemporal learning scheme for causal and stable video rectification. At the model level, neighborhood spatiotemporal attention (NST) aggregates local context and selectively fuses historical features with low overhead. At the optimization level, sparse spatiotemporal supervision applies spatial alignment only to anchor frames, decoupling frame-wise accuracy from temporal stability. Besides, we contribute the first benchmark dataset for wide-angle full-body video correction. Extensive experiments show that FastVC achieves state-of-the-art rectification fidelity and visual stability at 57.0 FPS.

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