Statistical Analysis of Two 3-D Registration and Modeling Strategies

The paper deals with the registration and modeling of multiple 3-D proole maps acquired from diierent viewpoints by light striping. We analyze the propagation of measurement and calibration errors to the registration parameters and further to the reconstructed model of the scene consisting of planar patches. The analysis is performed for two strategies. In the rst strategy, the maps are registered simultaneously using the Levenberg-Marquardt method to update the registration parameters and the model computed afterwards while in the second one, the maps are registered sequentially against the model reconstructed up till then using the method of unit quaternions to update the registration parameters. Our statistical analysis thus combines the registration and modeling steps, and in registration, we determine the corresponding points either on the parametric domains of the maps or as closest points in 3-D using the information from the parametric domain to restrict the search for the closest points. We also point out the precise estimation of the covariance matrix of the solution given by the Levenberg-Marquardt method. We illustrate the results of our analysis with real data from a scale model of an urban area.