  We present a new definition of cosmic void and a publicly available code with
the algorithm that implements it. Underdense regions are defined as free-form
objects, called popcorn voids, made from the union of spheres of maximum volume
with a given joint integrated underdensity contrast.The method is inspired by
the excursion-set theory and consequently no rescaling processing is needed,
the removal of overlapping voids and objects with sizes below the shot noise
threshold is inherent in the algorithm. The abundance of popcorn voids in the
matter field can be fitted using the excursion-set theory provided the
relationship between the linear density contrast of the barrier and the
threshold used in void identification is modified relative to the spherical
evolution model. We also analysed the abundance of voids in biased tracer
samples in redshift space. We show how the void abundance can be used to
measure the geometric distortions due to the assumed fiducial cosmology, in a
test similar to an Alcock-Paczy\'nski test. Using the formalism derived from
previous works, we show how to correct the abundance of popcorn voids for
redshift-space distortion effects. Using this treatment, in combination with
the excursion-set theory, we demonstrate the feasibility of void abundance
measurements as cosmological probes. We obtain unbiased estimates of the target
parameters, albeit with large degeneracies in the parameter space. Therefore,
we conclude that the proposed test in combination with other cosmological
probes has potential to improve current cosmological parameter constraints.
