An Efficient Boundary Integral Scheme for the MBO Threshold Dynamics Method via the NUFFT

Jiang, Shidong; Wang, Dong; Wang, Xiaoping

doi:10.1007/s10915-017-0448-1

Cited by 14 publications

(18 citation statements)

References 31 publications

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“…Various algorithms and rigorous error analysis have been introduced to refine and extend the original MBO and related methods for the aforementioned problems (see, e.g., [23], [38]- [42]). Adaptive methods based on non-uniform fast Fourier transform (NUFFT) [43], [44] have also been used to accelerate this type of method [45]. Generalized targetvalued diffusion-generated methods are recently developed in [46]- [48].…”

Section: Methodsmentioning

confidence: 99%

An efficient iterative thresholding method for image segmentation

Wang

Wei

et al. 2017

Journal of Computational Physics

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Abstract. We proposed an efficient iterative thresholding method for multi-phase image segmentation. The algorithm is based on minimizing piecewise constant Mumford-Shah functional in which the contour length (or perimeter) is approximated by a non-local multi-phase energy. The minimization problem is solved by an iterative method. Each iteration consists of computing simple convolutions followed by a thresholding step. The algorithm is easy to implement and has the optimal complexity O(N log N ) per iteration. We also show that the iterative algorithm has the total energy decaying property. We present some numerical results to show the efficiency of our method.

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Section: Methodsmentioning

confidence: 99%

An efficient iterative thresholding method for image segmentation

Wang

Wei

et al. 2017

Journal of Computational Physics

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“…In the following, we briefly review and extend an efficient boundary integral scheme for the free space heat solver with the initial data being the characteristic function of a bounded domain. The original scheme is introduced in [17] for smooth boundaries, and we extend the scheme here to treat nonsmooth boundaries. Then φ 1 , φ 2 , ψ 1 , and ψ 2 can be calculated as the weighted sum of these solutions.…”

Section: Vapormentioning

confidence: 99%

“…where the initial data χ D (x) is the characteristic function of some bounded domain D ∈ R d (d = 2, 3). In [17], we assume that the boundary ∂ D of D is smooth. For wetting dynamics, the boundary is often piecewise smooth due to the presence of the (possibly chemically patterned) solid surface.…”

Section: An Nufft-based Heat Solvermentioning

confidence: 99%

“…In this paper, we extend the boundary integral scheme for the threshold dynamics method developed in [17] for smooth material interfaces to nonsmooth material interfaces. The scheme discretizes the physical space only in a neighborhood of the interfaces and applies non-uniform fast Fourier transform (NUFFT) [8,9,15] to further accelerate the calculation.…”

Section: Introductionmentioning

confidence: 99%

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An Efficient Boundary Integral Scheme for the Threshold Dynamics Method II: Applications to Wetting Dynamics

2019

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In this paper, we extend the boundary integral scheme for the threshold dynamics method to treat the case where the material interface is nonsmooth and may undergo topological changes. The scheme is then applied to study the wetting dynamics in both two and three dimensions. Numerical experiments show that the scheme is more efficient as compared with the existing method using uniform grids, making accurate simulation of wetting dynamics on a chemically patterned solid surface in three dimensions within practical reach.

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“…It is usually implemented on uniform meshes so that a fast Fourier transform (FFT) method can be used. One exception is the work in [23], where a nonuniform FFT is applied.…”

Section: Introductionmentioning

confidence: 99%

An Adaptive Threshold Dynamics Method for Three-Dimensional Wetting on Rough Surfaces

Ying¹

2021

CiCP

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We propose an adaptive threshold dynamics method for wetting problems in three space dimensions. The method is based on solving a linear heat equation and a thresholding step in each iteration. The heat equation is discretized by a cellcentered finite volume method on an adaptively refined mesh. An efficient technique for volume conservation is developed on the nonuniform meshes based on a quicksorting operation. By this method, we compute some interesting wetting problems on complicated surfaces. Numerical results verify some recent theory for the apparent contact angle on rough and chemically patterned surfaces.

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An Efficient Boundary Integral Scheme for the MBO Threshold Dynamics Method via the NUFFT

Cited by 14 publications

References 31 publications

An efficient iterative thresholding method for image segmentation

An efficient iterative thresholding method for image segmentation

An Efficient Boundary Integral Scheme for the Threshold Dynamics Method II: Applications to Wetting Dynamics

An Adaptive Threshold Dynamics Method for Three-Dimensional Wetting on Rough Surfaces

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