Planar Segmentation by Time-of-Flight Cameras

This article presents a new feature for detecting planarity when using range images on the principle of Time of Flight (ToF). We derive homogeneous linear conditions for Time-of-Flight images of 3 or 4 points to be the projection of collinear or coplanar points respectively. The crucial part in our equations is played by the D/d-ratios of the ToF-distance D(u, v) and the internal radial distance (IRD) d(u, v) for each pixel (u, v). The knowledge of the IRD d may be a consequence of an accurate lateral calibration of the camera, but this IRD can also be directly obtained. Consequently, the proposed planarity condition holds in principle for uncalibrated camera's. The elegance, efficiency and simplicity of our coplanarity constraint is illustrated in experiments on planarity tests and the segmentation of planar regions.