Let $z_1,z_2,\dots, z_N$ be the vertices of a polygon $P$ in the complex plane. The complex moments $τ_k$ of the polygon are then defined as $$τ_k= \sum^N_{j=1} a_j z^k_j.$$ The shape-from moments problem is to reconstruct a planar polygon from a set of its complex moments, i.e one has to estimate the vertices and the ordering of the vertices. After the vertices $z_j$ have been estimated, there are several techniques for computing the coefficients $a_j$. The authors analyze the sensitivity of coefficients $a_j$ and introduce the sensitivity factor for each $a_j$ which are also used for sensitivty analysis of vertices. Experimental results with the generalized pencil method are given. These results confirm the proposed theoretical consideration.
Reviewer: Otu Vaarmann (Tallinn)