Persistence barcodes for shapes

G Carlsson, A Zomorodian, A Collins… - Proceedings of the 2004 …, 2004 - dl.acm.org
… simple shape descriptor that arises from persistent homology and carries information about
a shape. … To compare barcodes, we define a metric on the set of barcodes. We may now use …

Learning representations of persistence barcodes

CD Hofer, R Kwitt, M Niethammer - Journal of Machine Learning Research, 2019 - jmlr.org
persistent homology, the prevalent tool used in topological data analysis. As the summary
representations, referred to as barcodes … to use persistent homology on 2D shapes are twofold…

[PDF][PDF] Persistent homology: state of the art and challenges

M Kerber - International Mathematische Nachrichten, 2016 - geometrie.tugraz.at
… in question to be a geometric shape, possibly embedded in a … equivalent representation of
desired shapes, the goal is to find … the exact and approximate persistent barcode. Sheehy [61] …

Induced matchings of barcodes and the algebraic stability of persistence

U Bauer, M Lesnick - Proceedings of the thirtieth annual symposium on …, 2014 - dl.acm.org
… algebraic stability theorem for persistence barcodes [5… persistent homology. In contrast to
previous proofs, ours shows explicitly how a δ-interleaving morphism between two persistence

An entropy-based persistence barcode

H Chintakunta, T Gentimis, R Gonzalez-Diaz… - Pattern Recognition, 2015 - Elsevier
shape in 3D, which filtration should we choose for persistent homology computation? The
example shown in Fig. 1 of a conical shape … unveil much more information about the 3D shape. …

Vectorization of persistence barcode with applications in pattern classification of porous structures

Z Dong, C Hu, C Zhou, H Lin - Computers & Graphics, 2020 - Elsevier
Persistence barcode is a topological summary for persistent homology to exhibit topological
features with different persistencebarcode, organizes persistence Betti numbers in the form …

Harmonic Chain Barcode and Stability

S Parsa, B Wang - arXiv preprint arXiv:2409.06093, 2024 - arxiv.org
… Consequently, the homology class can be given the geometric shape of its … distinct barcode
from the persistence barcode, which is stable in the same sense as the persistence barcode. …

A framework for differential calculus on persistence barcodes

J Leygonie, S Oudot, U Tillmann - Foundations of Computational …, 2022 - Springer
… matching is cast into an optimization problem involving the barcodes of the shapes. [14…
barcodes, as an illustration of our framework on barcode vectorizations. We show that persistence

Tracking the Persistence of Harmonic Chains: Barcode and Stability

T Hou, S Parsa, B Wang - arXiv preprint arXiv:2412.15419, 2024 - arxiv.org
persistence barcode tracks the evolution of its homology groups. In this paper, we introduce
a new type of barcode, called the harmonic chain barcode… harmonic chain barcode is stable. …

Tropical coordinates on the space of persistence barcodes

S Kališnik - Foundations of Computational Mathematics, 2019 - Springer
… , barcodes are not well adapted for use by practitioners in machine learning tasks. We can
circumvent this problem by assigning numerical quantities to barcodes… space of barcodes and …