scholarly journals A framework for the construction of level set methods for shape optimization and reconstruction

2003 ◽  
pp. 301-329 ◽  
Author(s):  
Martin Burger
Keyword(s):  
Shape Optimization ◽  
Level Set ◽  
Level Set Methods

Multi-Layer Constrained Identification in Geophysics with Shape Optimization and Level Set Methods

2010 ◽  
Author(s):  
D. Papadopoulos ◽  
M. Behr ◽  
M. Herty ◽  
V. Rath ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Shape Optimization ◽  
Level Set ◽  
Level Set Methods

scholarly journals Reconstruction of Geophysical Layers with Shape Optimization and Level Set Methods

PAMM ◽  
2010 ◽  
Vol 10 (1) ◽  
pp. 587-588
Author(s):  
Dimitrios Papadopoulos ◽  
Michael Herty ◽  
Marek Behr ◽  
Volker Rath
Keyword(s):  
Shape Optimization ◽  
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.

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