  We consider the class of selfsimilar Gaussian generalized random fields
introduced by Dobrushin in 1979. These fields are indexed by Schwartz functions
on $\mathbb{R}^d$ and parametrized by a self-similarity index and the degree of
stationarity of their increments. We show that such Gaussian fields arise in
explicit form by letting Gaussian white noise, or Gaussian random balls white
noise, drive a shift and scale shot-noise mechanism on $\mathbb{R}^d$, covering
both isotropic and anisotropic situations. In some cases these fields allow
indexing with a wider class of signed measures, and by using families of signed
measures parametrized by the points in euclidean space we are able to extract
pointwise defined Gaussian processes, such as fractional Brownian motion on
$\mathbb{R}^d$. Developing this method further, we construct Gaussian bridges
and Gaussian membranes on a finite domain, which vanish on the boundary of the
domain.
