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Spacetime stereo is a promising technique for accurate 3D reconstruction based on randomly varying illumination and temporal integration of the stereo matching cost. In this paper we show that the standard spacetime stereo approach can be improved in terms of accuracy of disparity estimation and convergence speed by adoption of suitable matching algorithms based on adaptive support windows. We also present a practical and cost-effective 3D reconstruction system that deploys the proposed improved spacetime method together with cheap commercial off-the-shelf hardware (a PC, a stereo camera and a projector). Experimental results show that the proposed system can yield rapidly accurate 3D reconstruction of various types of objects and faces.