Robust matching of affinely transformed objects

This paper presents a general robust solution for the problem of affine object matching, whereby an object can be given as a discrete point set, a set of lines, or a closed region. Let be given two such objects which are related by a general affine transformation (up to noise and maybe some additional distortions of the object). Then we can determine the six parameters a_ik of the affine transformation using some new general moment invariants. These invariants are global, but assigned locally to any object point. With these invariants and using the Hungarian method or dynamic programming it can be computed a weighted point reference list. The affine parameters a_ik can be calculated from this list using the method of the least absolute differences (LAD) method. Our approach is very robust against noise and distortions. The algorithm can be used also for all subgroups of the affine group. Additionally, it is an unifying approach for all classes of objects: Discrete point sets, sets of lines, and closed regions. Many well known algorithms have problems with the case of symmetries of the objects, our approach is stable against symmetries. Experimental results both on simulated and real objects validate the robustness of the algorithm. In the case of closed regions our algorithm performs better than SQUID F. Mokhtarian et al. (1996).