Stability of invariant Fourier descriptors and its inference in the shape classification

Presents the study of a shape representation space by means of its identification to the invariants space. This approach has an algebraic meaning translated by the completion criterion for the set of invariants introduced by Crimmins (1982). The author introduces a new property for Fourier descriptors, the stability which expresses the fact that a low level divergence in the invariants does not induce a noticeable distortion of the shape. This stability gives a topologic meaning to the identification of the space shape with the space of invariants. A complete and stable set of Fourier descriptors with regard to the starting point and the direct group of similarities in the case of the planar closed contours is constructed