We propose a method for the precise 3D see-through imaging, or transparent visualization, of the large-scale and complex point clouds acquired via the laser scanning of 3D cultural heritage objects. Our method is based on a stochastic algorithm and directly uses the 3D points, which are acquired using a laser scanner, as the rendering primitives. This method achieves the correct depth feel without requiring depth sorting of the rendering primitives along the line of sight. Eliminating this need allows us to avoid long computation times when creating natural and precise 3D see-through views of laser-scanned cultural heritage objects. The opacity of each laser-scanned object is also flexibly controllable. For a laser-scanned point cloud consisting of more than 10⁷ or 10⁸ 3D points, the pre-processing requires only a few minutes, and the rendering can be executed at interactive frame rates. Our method enables the creation of cumulative 3D see-through images of time-series laser-scanned data. It also offers the possibility of fused visualization for observing a laser-scanned object behind a transparent high-quality photographic image placed in the 3D scene. We demonstrate the effectiveness of our method by applying it to festival floats of high cultural value. These festival floats have complex outer and inner 3D structures and are suitable for see-through imaging.