  Scale selection methods based on local extrema over scale of scale-normalized
derivatives have been primarily developed to be applied sparsely --- at image
points where the magnitude of a scale-normalized differential expression
additionally assumes local extrema over the domain where the data are defined.
This paper presents a methodology for performing dense scale selection, so that
hypotheses about local characteristic scales in images, temporal signals and
video can be computed at every image point and every time moment.
  A critical problem when designing mechanisms for dense scale selection is
that the scale at which scale-normalized differential entities assume local
extrema over scale can be strongly dependent on the local order of the locally
dominant differential structure. To address this problem, we propose a
methodology where local extrema over scale are detected of a quasi quadrature
measure involving scale-space derivatives up to order two and propose two
independent mechanisms to reduce the phase dependency of the local scale
estimates by: (i) introducing a second layer of post-smoothing prior to the
detection of local extrema over scale and (ii) performing local phase
compensation based on a model of the phase dependency of the local scale
estimates depending on the relative strengths between first- vs. second-order
differential structure.
  This general methodology is applied over three types of domains: (i) spatial
images, (ii) temporal signals and (iii) spatio-temporal video. Experiments show
that the proposed methodology leads to intuitively reasonable results with
local scale estimates that reflect variations in the characteristic scales of
locally dominant structures over space and time.
