Comparing Different Fitting Strategies for Matching Two 3D Point Sets Using a Multivariable Minimizer
Sander Spanjaard, Joris S. M. Vergeest · 2001
Abstract Finding the best match of two geometric entities in 3D space is a key stage for purposes such as object recognition and reverse engineering. The reuse of existing freeform shapes during conceptual design is also an application. In this paper we compare different fitting strategies for matching two 3D point sets using a multivariable minimizer. The strategies are evaluated against speed, robustness and correctness of result. The fitting process aims at matching two point sets, a source point set and a template point set. The template point set is translated, rotated but also deformed during the fit, such that it gets placed into the neighborhood of the source point set and gets aligned to it as good as possible. The deformation of the template shape is controlled by shape parameters, which are varied to enhance the match. The engine behind the process is a multivariable function’s global minimum finder. Its objective is to minimize the Mean Directed Hausdorff Distance (MDHD) between the two point sets by altering the parameters of the template point set. One research question was whether or not a fully automated fitting process is feasible with our method. We performed numerical experiments with 3D scan data and a shape template defined by up to 8 free parameters. Four different strategies where used to do the fitting with one of them allowing user intervention. Comparing the strategies on total fit time, minimum MDHD and correctness of result a conclusion is drawn which strategy gives the highest chance on the best results. The relevance of the technology for shape reuse in conceptual design is also discussed.