Edge detection methods based on RBF interpolation

Edge detection is a widely used tool in signal/image processing with the aim of identifying abrupt changes or discontinuities in a signal/digital image. For the detection of jump discontinuities in 1D problems, we present an iterative method based on interpolation with Variably Scaled Kernels (VSKs). This is shown to outperform an existing iterative edge detection method based on multiquadric (MQ) radial basis function interpolation. To extend our purely one-dimensional edge detector to any dimension, we then introduce an innovative non iterative technique that detects jumps/edges by identifying the local maxima of the normalized absolute values of the RBF interpolant coefficients. The RBF interpolant is built-upon the compactly supported C2 Wendland function and exploits its advantageous properties to provide a robust and low-cost method. Numerical examples in 1D and 2D are included to illustrate its effectiveness and efficiency. In the context of edge detection for digital images, comparisons with Canny method are also presented.