Persistence in discrete Morse theory
نویسنده
چکیده
منابع مشابه
Topological analysis of discrete scalar data
This thesis presents a novel computational framework that allows for a robust extraction and quantification of the Morse-Smale complex of a scalar field given on a 2or 3dimensional manifold. The proposed framework is based on Forman’s discrete Morse theory, which guarantees the topological consistency of the computed complex. Using a graph theoretical formulation of this theory, we present an a...
متن کاملGraph Reconstruction by Discrete Morse Theory
Recovering hidden graph-like structures from potentially noisy data is a fundamental task in modern data analysis. Recently, a persistence-guided discrete Morse-based framework to extract a geometric graph from low-dimensional data has become popular. However, to date, there is very limited theoretical understanding of this framework in terms of graph reconstruction. This paper makes a first st...
متن کاملRGB image-based data analysis via discrete Morse theory and persistent homology
Understanding and comparing images for the purposes of data analysis is currently a very computationally demanding task. A group at Australian National University (ANU) recently developed open-source code that can detect fundamental topological features of a grayscale image in a computationally feasible manner. This is made possible by the fact that computers store grayscale images as cubical c...
متن کاملPersistence in sampled dynamical systems faster
We call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior, and to recover the eigenspaces of the endomorphism on homology induced by the self-map. The chain maps are constructed using ...
متن کاملCombinatorial Construction of Morse - Smale Complexes
Scientific data is becoming increasingly complex, and sophisticated techniques are required for its effective analysis and visualization. The Morse-Smale complex is an efficient data structure that represents the complete gradient flow behavior of a scalar function, and can be used to identify, order, and selectively remove features. This dissertation presents two algorithms for constructing Mo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011