scholarly journals Enablers for high-order level set methods in fluid mechanics

2015 ◽  
Vol 79 (12) ◽  
pp. 654-675 ◽  
Author(s):  
Francky Luddens ◽  
Michel Bergmann ◽  
Lisl Weynans
Keyword(s):  
Fluid Mechanics ◽  
Level Set ◽  
Level Set Methods ◽  
High Order

scholarly journals Level set methods for detonation shock dynamics using high-order finite elements

2017 ◽  
Author(s):  
V. A. Dobrev ◽  
F. C. Grogan ◽  
T. V. Kolev ◽  
R Rieben ◽  
V. Z. Tomov
Keyword(s):  
Finite Elements ◽  
Level Set ◽  
Level Set Methods ◽  
High Order ◽  
Shock Dynamics ◽  
Detonation Shock

Reconstructing 3D Buildings from LIDAR Using Level Set Methods

2013 ◽  
Author(s):  
Saad R. Khattak ◽  
Daniel S. Buckstein ◽  
Andrew Hogue
Keyword(s):  
Level Set ◽  
Level Set Methods

scholarly journals On the Relationship between Variational Level Set-Based and SOM-Based Active Contours

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
Mohammed M. Abdelsamea ◽  
Giorgio Gnecco ◽  
Mohamed Medhat Gaber ◽  
Eyad Elyan
Keyword(s):  
Level Set ◽  
Active Contour ◽  
Active Contours ◽  
Level Set Methods ◽  
Energy Functional ◽  
Self Organizing Maps ◽  
Complex Shapes ◽  
Variational Level Set ◽  
Preservation Property ◽  
The Relationship

Most Active Contour Models (ACMs) deal with the image segmentation problem as a functional optimization problem, as they work on dividing an image into several regions by optimizing a suitable functional. Among ACMs, variational level set methods have been used to build an active contour with the aim of modeling arbitrarily complex shapes. Moreover, they can handle also topological changes of the contours. Self-Organizing Maps (SOMs) have attracted the attention of many computer vision scientists, particularly in modeling an active contour based on the idea of utilizing the prototypes (weights) of a SOM to control the evolution of the contour. SOM-based models have been proposed in general with the aim of exploiting the specific ability of SOMs to learn the edge-map information via their topology preservation property and overcoming some drawbacks of other ACMs, such as trapping into local minima of the image energy functional to be minimized in such models. In this survey, we illustrate the main concepts of variational level set-based ACMs, SOM-based ACMs, and their relationship and review in a comprehensive fashion the development of their state-of-the-art models from a machine learning perspective, with a focus on their strengths and weaknesses.

On the existence and evaluation of Stokes phenomena in fluid mechanics

2021 ◽  
pp. 1-27
Author(s):  
Nik Alexandrakis
Keyword(s):  
Fluid Mechanics ◽  
Simple Proof ◽  
Travelling Waves ◽  
High Order ◽  
Singularly Perturbed ◽  
Type Model ◽  
Underlying Theory ◽  
Stokes Constant ◽  
Splitting Constant ◽  
Stokes Phenomena

A singularly perturbed, high order KdV-type model, which describes localized travelling waves (“solitons”) is being considered. We focus on the Inner solution, and detect Stokes phenomena that are crucial as to whether we can obtain a suitable solution. We provide a simple proof that the corresponding Stokes constant is non-zero. Also, we evaluate this splitting constant numerically by using two methods that are induced by the underlying theory.

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