2014
DOI: 10.1088/1674-1056/23/2/028702
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Application of radial basis functions to evolution equations arising in image segmentation

Abstract: In this paper, radial basis functions are used to obtain the solution of evolution equations which appear in variational level set method based image segmentation. In this method, radial basis functions are used to interpolate the implicit level set function of the evolution equation with a high level of accuracy and smoothness. Then, the original initial value problem is discretized into an interpolation problem. Accordingly, the evolution equation is converted into a set of coupled ordinary differential equa… Show more

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Cited by 2 publications
(2 citation statements)
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“…Besides, the MLS shape functions Ξ¦ i (𝑦 j ) used in Eqs. ( 16), ( 17), (21), and ( 23) can also be computed only once, then the matrices 𝑀 1 , 𝑀 2 , and 𝑀 3 at each iteration can be assembled easily.…”
Section: Discretization and Numerical Implementationmentioning
confidence: 99%
See 1 more Smart Citation
“…Besides, the MLS shape functions Ξ¦ i (𝑦 j ) used in Eqs. ( 16), ( 17), (21), and ( 23) can also be computed only once, then the matrices 𝑀 1 , 𝑀 2 , and 𝑀 3 at each iteration can be assembled easily.…”
Section: Discretization and Numerical Implementationmentioning
confidence: 99%
“…Some MLS-based meshless methods, such as the element-free Galerkin method, the h-p meshless method, and the meshless local Petrov-Galerkin method have been developed and achieved remarkable success in solving a broad range of physical problems. [18][19][20][21] They are the domain type, as the FEM, in which the problem domain is discretized by nodes.…”
Section: Introductionmentioning
confidence: 99%