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The key problems in a structured-light 3D scanner using a projector and camera are its geometric and radiometric calibration. A projector can be effectively represented using the familiar pin-hole model for cameras. However, since we cannot directly observe the projector plane, it cannot be calibrated like a camera. The first contribution of our paper is to develop a geometric calibration and 3D estimation method that utilises the projective geometric relationships available in a projector---camera pair, i.e., homography induced by a plane and invariance of cross-ratios. The low-dimensional parametric form of the homography averages out individual errors, resulting in a geometric calibration approach that is both simple to use and highly accurate. We present an extensive set of results to demonstrate the effectiveness of our approach and also characterise its accuracy. Second, we present a method for correcting systematic errors introduced due to the radiometric non-linearities present in commercial projectors. These errors are pronounced when only a few phase shifts are used in the sinusoidal coding scheme for structured-light scanners. We develop a cubic spline-based method to model and remove the effects due to these non-linearities. The efficacy of our model is demonstrated on real datasets.

Geometric and radiometric estimation in a structured-light 3D scanner