  This article introduces an application of Ghrist barcodes in the study of
persistent Betti numbers derived from vortex nerve complexes found in
triangulations of video frames. A Ghrist barcode is a topology of data
pictograph useful in representing the persistence of the features of changing
shapes. The basic approach is to introduce a free Abelian group representation
of intersecting filled polygons on the barycenters of the triangles of
Alexandroff nerves. An Alexandroff nerve is a maximal collection of triangles
with a common vertex in the triangulation of a finite, bounded planar region.
In our case, the planar region is a video frame. A Betti number is a count of
the number of generators in a finite Abelian group. The focus here is on the
persistent Betti numbers across sequences of triangulated video frames. Each
Betti number is mapped to an entry in a Ghrist barcode. Two main results are
given, namely, vortex nerves are Edelsbrunner-Harer nerve complexes and the
Betti number of a vortex nerve equals $k+2$ for a vortex nerve containing $k$
edges attached between a pair of vortex cycles in the nerve.
