  The computation of Lagrangian coherent structures (LCS) has established
itself as a prominent means to reveal significant geometric structures in
time-dependent vector fields. Their characterization, however, requires the
selection of a suitable time parameter for the construction of the flow map
that may not be known in advance. We present in this paper a continuous
time-scale framework for LCS extraction and visualization. Specifically, we
treat the time axis as a continuum from which a best temporal scale is
automatically determined at each spatial location for the extraction of LCS.
Beyond its effectiveness with vector fields we show that this method can be
successfully applied to improve the characterization of salient structures in
tensor fields and discrete maps. We present applications of our method to
problems spanning fluid dynamics, medical imaging, and orbital mechanics. The
results show that our approach can reveal important structural features that
are missed by existing LCS extraction methods.
