Edge detection methods based on RBF interpolation
Radial basis function (in short: RBF) interpolation is a useful and popular tool for (multivariable or multivariate) function approximation. Other algorithms than interpolation are available, such as least-squares methods or quasi-interpolation, but for most applications, interpolation is the scheme of choice. In this article, edge detection methods are developed from the radial basis function spaces that are spanned by translates of a single rotationally invariant function, such as the famous multiquadric function \(\phi(r)=\sqrt{r^2+c^2}\). This multiquadric (but also other RBFs) offers an approach to the edge detection in more than one variable by the variable scale methods, where parameters such as the \(c\) in the multiquadric are adjusted in a recursive methds. Many numerical examples are given to show the usefulness of the new algorithms.
scientific article; zbMATH DE number 7006449
scientific article