Approximation of planar point sets by point configurations

Abstract

The paper is devoted to planar linear point sets having hierarchical structure. Point configurations arise naturally in several areas of computational geometry. In the
paper, the linear approximation of planar point configurations is discussed. Planar point configuration is considered as a fuzzed and deformed image of some ideal
configuration. Also, it may be considered as random realizations of ideal one. Pure images and deformed ones are described by the same hierarchical structures.
The structure of approximating configuration is determined a priory. Image approximation is realized by mean of least square restoration. The correspondence of the structures is one of the parameters of approximation. Identification procedure is realized by linear transformations. Similarity transformations as general ones are used in the calculations.