Several readers asked about the Gaussian kernel (filter). Note
that applying the Gaussian kernel (filter) is optional -- it
can be viewed as performing a kernel density estimation of p(d),
but is not strictly required. In fact, the radial measures
analyzed at the end of Section 4 are based on the unfiltered
p(d) (i.e. p(d) constructed from a straightforward histogram).

Using Gaussian filtered p(d) will affect the radial measures,
specifically the anisotropy, which is discussed at the end of
supplemental material Section B. In practice, I recommend not
to apply the Gaussian kernel, unless if there is concern about
the evaluation of p(d). This represents my personal view about
the treatment of the Gaussian kernel.