364 17 Reverse Engineering Using Optical Range Sensors
choice. Surfaces of 3-D objects usually consist of segments with low bandwidth and transients with high frequency between them. They have no “reasonable” shape, as it is preconditioned for linear filters.“Optimal” filters like Wiener or matched filters usually minimize the root mean square (RMS) error. Oscillations of the signal are allowed if they are small. For visualization or milling of surfaces curvature vari-ations are much more disturbing than small deviation from the ideal shape. A smoothing filter for geometric data should therefore mini-mize curvature variations and try to reinduce an error that is smaller than the original distortion of the data. These are the requirements we considered when we designed our new smoothing method.
We present a new method for calibration of optical 3-D sensors . An arbitrary polynomial is used as a calibration function. Its coefficients are determined by a series of measurements of a calibration standard with exactly known geometry. A set of flat surface patches is placed upon it. These intersect virtually at exactly known positions xi. After measuring the standard, an interpolating polynomial p with xi = p(x′can be found. Due to aberrations, the digitized surface patches are not i)
flat. Therefore polynomial surfaces are approximated to find the virtual intersection points x′i. In order to fill the whole measuring volume with such calibration points, the standard is moved on a translation stage and measured in many positions.
Figure 17.2: a Calibration standard with three tilted planes; and b eight range images of these planes.
Calibration of a range image with 512×540 points takes about 3 s on an Intel P166 CPU. Calibration error is less than 50 % of the measurement uncertainty of the sensor. It is sufficient to use a calibration polynomial of order 4, as coefficients of higher order are usually very close to zero.