| Abstract | This report presents a novel method of calibrating a range camera equipped with a single scan axis. The method is based on the use of two sets of reference planes positioned at oblique angles to the range camera. Two techniques are proposed to implement this novel calibration method: lookup tables with linear interpolation and collinearity equation fitting. To demonstrate the calibration method, this report starts with an analytical treatment that allows the extraction of the projective transformation equations for a camera that uses the synchronized scanner geometry. These equations, which are based on the collinearity principle, form the basis of the calibration techniques and the derivation of a series of design guidelines for helping a designer conduct a preliminary study of a particular range camera. Parameters such as the size and shape of the volume of view, the camera precision, and an estimate of the shape of the probability distribution of the measurement error along the triangulation plane are derived. The first calibration technique uses the design guidelines to determine the number of reference planes necessary for the construction of look-up tables with linear interpolation. The second technique fits a canonical form of the collinearity equation, by a least-squares procedure, through measurements obtained from known displacements of a calibration bar oriented at oblique angles to the camera. This fitting procedure yields six parameters per angular increment of the scanning mirror along the laser plane. This latter technique is preferred over the former because of its robustness to outliers present in the raw data and the possibility of extrapolating near the measurement area. Also, it allows for the computation of the laser projector location. This is very useful in the extraction of the reflectance map of an object. The calibration technique based upon fitting a set of collinearity equations can be mapped to a very compact hardware implementation that has the potential of correcting an image in real time, i.e., up to video data rates. Finally, it presents a way to reduce systematic errors caused by the laser speckle originating from the interaction of the laser beam with the surface roughness of the calibration bar. Experimental results demonstrating this technique on a high-precision range camera are shown to compare favorably to theoretical prefictions. For a measurement area along the laser plane of 200 mm in depth by 125 mm in width, systematic errors (bias) are about two times better then those observed with a calibration technique based on look-up tables, i.e., down to 40 μm. The range precision is about the same for the two techniques, i.e., 40 μm. |
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