Deep structure II. catastrophe theory

The previous chapter illustrates a number of approaches that explore the deep structure. However, there are a number of caveats. The edge focusing technique implicitly assumes that the edges for the signal can be located at the adjacent lower scale level in a small neighborhood around the location at the current scale. As mentioned, no formal scheme for defining the size and shape of the neighborhood is presented. Furthermore, this method ignores the problems encountered when edge points merge or split with increasing scale.