Invariant fitting of planar objects by primitives

The determination of invariant characteristics is an important problem in pattern recognition. Many invariants are known which have been obtained by the method of normalization. In this paper, we introduce a new approach of fitting planar objects by primitives using the method of normalization (e.g., fitting by lines, triangles, rectangles, circles, ellipses, super-quadrics, etc.). Objects and primitives are described by features, for example, by moments. The main advantage is that the normalization process provides us with a canonical frame of the object and the primitive. Therefore, the fit is invariant with respect to the transformation used. By this new method, an analytical fitting of non-analytical objects can be achieved, for example, fitting by polygons. Furthermore, the numerical effort can be reduced drastically by normalizing of the object and the primitive.