title: On the Relationship between Variational Level Set-Based and SOM-Based Active Contours.
abstract: 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.
authors.affiliation: Department of Mathematics, Faculty of Science, University of Assiut, Assiut 71516, Egypt ; IMT Institute for Advanced Studies, Piazza S. Francesco 19, 55100 Lucca, Italy.
authors.forename: Mohammed M
authors.initials: MM
authors.lastname: Abdelsamea
authors.affiliation: IMT Institute for Advanced Studies, Piazza S. Francesco 19, 55100 Lucca, Italy.
authors.forename: Giorgio
authors.initials: G
authors.lastname: Gnecco
authors.affiliation: Robert Gordon University, Garthdee House, Garthdee Road, Aberdeen AB10 7QB, UK.
authors.forename: Mohamed Medhat
authors.initials: MM
authors.lastname: Gaber
authors.affiliation: Robert Gordon University, Garthdee House, Garthdee Road, Aberdeen AB10 7QB, UK.
authors.forename: Eyad
authors.initials: E
authors.lastname: Elyan
mesh_terms: D006801:Humans; D008962:Models, Theoretical; D016571:Neural Networks, Computer; D010363:Pattern Recognition, Automated / Q000379:methods*; D012718:Set, Psychology