Describing shapes by geometrical-topological properties of real functions
Differential topology, and specifically Morse theory, provide a suitable setting for formalizing
and solving several problems related to shape analysis. The fundamental idea behind …
and solving several problems related to shape analysis. The fundamental idea behind …
A practical approach to Morse-Smale complex computation: Scalability and generality
The Morse-Smale (MS) complex has proven to be a useful tool in extracting and visualizing
features from scalar-valued data. However, efficient computation of the MS complex for large …
features from scalar-valued data. However, efficient computation of the MS complex for large …
Analysis of large-scale scalar data using hixels
One of the greatest challenges for today's visualization and analysis communities is the
massive amounts of data generated from state of the art simulations. Traditionally, the …
massive amounts of data generated from state of the art simulations. Traditionally, the …
Parallel computation of 2D Morse-Smale complexes
N Shivashankar, M Senthilnathan… - IEEE Transactions on …, 2011 - ieeexplore.ieee.org
The Morse-Smale complex is a useful topological data structure for the analysis and
visualization of scalar data. This paper describes an algorithm that processes all mesh …
visualization of scalar data. This paper describes an algorithm that processes all mesh …
Morse complexes for shape segmentation and homological analysis: discrete models and algorithms
Morse theory offers a natural and mathematically‐sound tool for shape analysis and
understanding. It allows studying the behavior of a scalar function defined on a manifold …
understanding. It allows studying the behavior of a scalar function defined on a manifold …
An entropy-based persistence barcode
In persistent homology, the persistence barcode encodes pairs of simplices meaning birth
and death of homology classes. Persistence barcodes depend on the ordering of the …
and death of homology classes. Persistence barcodes depend on the ordering of the …
Efficient computation of Morse-Smale complexes for three-dimensional scalar functions
The Morse-Smale complex is an efficient representation of the gradient behavior of a scalar
function, and critical points paired by the complex identify topological features and their …
function, and critical points paired by the complex identify topological features and their …
[PDF][PDF] Homological algebra and data
These lectures are a quick primer on the basics of applied algebraic topology with emphasis
on applications to data. In particular, the perspectives of (elementary) homological algebra …
on applications to data. In particular, the perspectives of (elementary) homological algebra …
A one‐dimensional homologically persistent skeleton of an unstructured point cloud in any metric space
Real data are often given as a noisy unstructured point cloud, which is hard to visualize. The
important problem is to represent topological structures hidden in a cloud by using skeletons …
important problem is to represent topological structures hidden in a cloud by using skeletons …
Computing Morse-Smale complexes with accurate geometry
Topological techniques have proven highly successful in analyzing and visualizing scientific
data. As a result, significant efforts have been made to compute structures like the Morse …
data. As a result, significant efforts have been made to compute structures like the Morse …