Gauging the Repeatability of 3-D Imaging Systems by Sphere Fitting

Multiple scans of the same object acquired with a 3-D imaging system (e.g., a laser scanner) under the same experimental conditions could provide valuable information about the instrument's performance (e.g., repeatability, existence of bias). A geometrical primitive may be fitted to multiple data sets and the variances of the fitted object's parameters may be used to evaluate the instrument's repeatability. We test this procedure on simulated data as well on data acquired in a laboratory. Two different error functions (orthogonal and directional) are used to fit a sphere of known radius to the data. The spread of the sphere centers fitted with the directional function to simulated unbiased data is in agreement with the theoretically calculated variances of the fitted centers. For sphere centers fitted to simulated data with added bias and to the data acquired in a laboratory, the variances do not agree with the spread. This is interpreted as evidence that the data were not collected under repeatable conditions. The orthogonal fitting yields sphere centers in disagreement with theory both for the simulated and laboratory data sets and therefore, the choice of the error function is important.