Next: Scale invariance. Up: Axiomatic scale-space formulations Previous: Non-creation of local extrema
If the semi-group structure per se is combined with a strong continuity
requirement with respect to the scale parameter,
then it follows from well-known results in functional analysis
the scale-space family must have an infinitesimal generator.
In other words, if a transformation operator
from the input signal
to the scale-space representation at any scale t is defined by
then under reasonable regularity requirements
there exists a limit case of this operator
(the infinitesimal generator)
Non-enhancement of local extrema:
Moreover, he showed that this scale-space formulation extends to discrete data as well as to non-symmetric temporal and spatio-temporal image domains.
Tue Jul 1 14:57:47 MET DST 1997