Determining the 2- or 3-dimensional similarity transformation between a point set and a model made of lines and arcs

A description is given of an efficient, robust algorithm for determining the best transformation, meaning either a similarity or a congruence, in two or three dimensions, between a point set and a model consisting of line and circle segments, assuming the desired transformation is small. Although convergence to a correct match cannot be guaranteed, several figures of merit for the congruence allow wrong convergences to be detected. The image and the model are constructed of different elements, i.e. points versus line and circle segments, which is well suited for the applications discussed. If this feature is undesirable, however, the algorithm can be adapted to match two sets of segments or two sets of points. Experimental results are presented for the case of a similarity in 2D using line segments only