Noise effect is taken into account such that a scene can consist of noisy sub-parts of a model.
The matching is then to find the optimal mapping between the ARSs of the scene and the model. A gain functional is formulated to measure the goodness of fit and is to be maximized by using the relaxation labeling method. If all relations are invariants, the ARS is an invariant encapsulation of a shape, an object, or a scene.