A hitherto unnoticed singularity of scale-space

A hitherto unnoticed singularity of scale space occurs only at isolated points in scale space. Thus it does not generically occur for single images, but it can occur occasionally in members of time sequences (say). It occurs at those critical points of the image at which the Laplacean of the illuminance vanishes (a nongeneric condition). The structure of scale space in an infinitesimal neighborhood of such a singularity is explored. The effect of the singularity of mappings between copies of an image at different levels of resolution is evaluated and checked with a numerical calculation