  When designing and developing scale selection mechanisms for generating
hypotheses about characteristic scales in signals, it is essential that the
selected scale levels reflect the extent of the underlying structures in the
signal.
  This paper presents a theory and in-depth theoretical analysis about the
scale selection properties of methods for automatically selecting local
temporal scales in time-dependent signals based on local extrema over temporal
scales of scale-normalized temporal derivative responses. Specifically, this
paper develops a novel theoretical framework for performing such temporal scale
selection over a time-causal and time-recursive temporal domain as is necessary
when processing continuous video or audio streams in real time or when
modelling biological perception.
  For a recently developed time-causal and time-recursive scale-space concept
defined by convolution with a scale-invariant limit kernel, we show that it is
possible to transfer a large number of the desirable scale selection properties
that hold for the Gaussian scale-space concept over a non-causal temporal
domain to this temporal scale-space concept over a truly time-causal domain.
Specifically, we show that for this temporal scale-space concept, it is
possible to achieve true temporal scale invariance although the temporal scale
levels have to be discrete, which is a novel theoretical construction.
