The creation of high-quality alpha mattes as ground-truth data for video matting is typically a laborious task. The trade-off between accuracy, manual corrections, and capture constraints often produces erroneous results or is cost prohibitive. We propose PolarMatte, a fully computational alpha matte extraction method for images and video without compromise between quality and practicality. A single polarization camera is used to capture dynamic scenes backlit by an off-the-shelf LCD monitor. PolarMatte exploits the polarization channel to compute the per-pixel opacity of the target scene, including the transparency of fine-details, translucent objects, and optical/motion blur. We leverage polarization clues to robustly detect indistinguishable pixels, and extract the alpha matte value at polarized foreground reflections with a polarimetric matting Laplacian. Quantitative and qualitative evaluation demonstrate our ability to computationally extract ground-truth-quality alpha mattes without human labour.