@article{don_ghrist_2019,
abstract = {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 (also called a persistence barcode) is a topology of data pic- tograph 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 of 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 is 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.},
author = {Don, Arjuna P. H. and Peters, James F.},
date = {2019-04-01},
issn = {2247-6202},
journaltitle = {Theory and Applications of Mathematics \& Computer Science},
keywords = {1 - Classification, 1 - Video Frame Shape, 1 - Video analysis, 1 - Video identification, 2 - Alexandroff nerve, 2 - Barcode, 2 - Betti numbers, 2 - Ghrist barcode, 2 - Persistence barcode, 2 - Persistent homology, 3 - Video, 3 - Video frames},
langid = {english},
note = {Number: 1},
number = {1},
pages = {14--27--14--27},
rights = {Copyright (c) 2019 Theory and Applications of Mathematics \& Computer Science},
title = {Ghrist Barcoded Video Frames. Application in Detecting Persistent Visual Scene Surface Shapes captured in Videos},
url = {https://uav.ro/applications/se/journal/index.php/TAMCS/article/view/182},
urldate = {2021-04-15},
volume = {9}
}