A characterization of ellipses by discrete moments (Q2763607)

Let \(E\) be the elliptic region in the Euclidean plane defined by the inequality \(B^2(x-a)^2 + A^2(y-b)^2 \leq A^2 B^2\). The \textit{digitalization} \(D(E)\) of \(E\) is the set \(D(E) := E\cap Z^2\) of all points in \(E\) with integer coordinates. A typical problem of digital geometry is to characterize digital objects by a finite number of parameters. The author shows that digital ellipses can be efficiently characterized by the parameters \(R(E), X(E), Y(E)\) and \(XX(E)\) where \(R(E)\) is the number of digital points in \(E\), \(X(E)\) and \(Y(E)\) is respectively the sum of their \(x\)-coordinates (\(y\)-coordinates) and \(XX(E)\) is the sum of squares of \(x\)-coordinates of all points in \(D(E)\).NEWLINENEWLINEFor the entire collection see [Zbl 0977.00022].