Iterative closest geometric objects registration

In this paper, closed-form solutions are obtained for registering two sets of line segments, triangle patches, or even general simple geometric objects that are defined by a set of ordered points. Based on these new registration approaches, the iterative closest line segment registration (ICL) algorithm and the iterative closest triangle patch registration (ICT) algorithm are developed similar to the ICP algorithm. To simplify the mathematical representation, the concept of matrix scalar product is defined and some of its properties are given. The newly developed registration methods are tested. The test shows that the ICL algorithm and the ICT algorithm work much better than the conventional ICP algorithm considering that the ICL and the ICT algorithms are much less sensitive to the initial orientations of the object.