Tree Edit Distances from Singularity Theory

A representation based on the singularity structure of the gradient magnitude over scale is used as the atoms in a space of images. This representation is summarized as a rooted tree. The generic transitions of the functional of the scale space images are analysed and listed for the scale parameter and one free parameter. A distance measure between images is deduced soly from these generic transistions. The singular transitions are translated into the language of the tree transitions such that one generic transitions corresponds to one unit edit operation of the tree structure. The distance between two images is the size of the smallest set of edit operations necessary to transform the corresponding tree representations into each other.