A new singularity index
We propose a new ratio index for the detection of impulse-like singularities in signals of arbitrary dimensionality. We show that the new singularity index responds strongly to singularities that are like impulses or smoothed impulses in cross section. For example, it responds strongly to curvilinear masses (ridges) in images, while responding minimally to edge-like singularities. The ratio index employs directional derivatives of gaussians, which makes the index naturally scalable.