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 …
[PDF][PDF] Position: Topological Deep Learning is the New Frontier for Relational Learning
Topological deep learning (TDL) is a rapidly evolving field that uses topological features to
understand and design deep learning models. This paper posits that TDL may complement …
understand and design deep learning models. This paper posits that TDL may complement …
The topology toolkit
This system paper presents the Topology ToolKit (TTK), a software platform designed for the
topological analysis of scalar data in scientific visualization. While topological data analysis …
topological analysis of scalar data in scientific visualization. While topological data analysis …
Reeb graphs for shape analysis and applications
Reeb graphs are compact shape descriptors which convey topological information related to
the level sets of a function defined on the shape. Their definition dates back to 1946, and …
the level sets of a function defined on the shape. Their definition dates back to 1946, and …
Robust on-line computation of Reeb graphs: simplicity and speed
Reeb graphs are a fundamental data structure for understanding and representing the
topology of shapes. They are used in computer graphics, solid modeling, and visualization …
topology of shapes. They are used in computer graphics, solid modeling, and visualization …
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 …
Interactive exploration and analysis of large-scale simulations using topology-based data segmentation
Large-scale simulations are increasingly being used to study complex scientific and
engineering phenomena. As a result, advanced visualization and data analysis are also …
engineering phenomena. As a result, advanced visualization and data analysis are also …
Understanding the structure of the turbulent mixing layer in hydrodynamic instabilities
D Laney, A Mascarenhas, P Miller… - IEEE Transactions on …, 2006 - ieeexplore.ieee.org
When a heavy fluid is placed above a light fluid, tiny vertical perturbations in the interface
create a characteristic structure of rising bubbles and falling spikes known as Rayleigh …
create a characteristic structure of rising bubbles and falling spikes known as Rayleigh …