Next: Non-enhancement of local extrema Up: Axiomatic scale-space formulations Previous: Causality.
Lindeberg  considered
the problem of characterizing those kernels in one dimension that
share the property of not introducing new local extrema in a signal
Such kernels have to be non-negative and unimodal.
Moreover, they can be completely classified.
He also imposed a semi-group structure
on the family of kernels,
which means that if two such kernels are convolved with
then the resulting kernel will be a member of the same family
Tue Jul 1 14:57:47 MET DST 1997