相关论文: On Median Filters for Motion by Mean Curvature

We present new level set methods for multiphase, anisotropic (weighted) motion by mean curvature of networks, focusing on wetting-dewetting problems where one out of three phases is stationary -- a good testbed for checking whether…

We present a robust and efficient numerical framework based on a median filter scheme for solving a broad class of interface-related optimization problems, from image segmentation to topology optimization. A key innovation of our work is…

We extend thresholding methods for numerical realization of mean curvature flow on obstacles to the anisotropic setting where interfacial energy depends on the orientation of the interface. This type of schemes treats the interface…

Modeling of a wide class of physical phenomena, such as crystal growth and flame propagation, leads to tracking fronts moving with curvature-dependent speed. When the speed is the curvature this leads to one of the classical degenerate…

We present an efficient scheme for level set mean curvature flow using a domain discretization and median filters. For this scheme, we show convergence in $L^\infty$-norm under mild assumptions on the number of points in the discretization.…

Image processing researchers commonly assert that "median filtering is better than linear filtering for removing noise in the presence of edges." Using a straightforward large-$n$ decision-theory framework, this folk-theorem is seen to be…

We introduce a new notion of viscosity solutions for the level set formulation of the motion by crystalline mean curvature in three dimensions. The solutions satisfy the comparison principle, stability with respect to an approximation by…

We present a second order accurate in time numerical scheme for curve shortening flow in the plane that is unconditionally monotone. It is a variant of threshold dynamics, a class of algorithms in the spirit of the level set method that…

We analyze the continuum limit of a thresholding algorithm for motion by mean curvature of one dimensional interfaces in various space-time discrete regimes. The algorithm can be viewed as a time-splitting scheme for the Allen-Cahn equation…

We present a generalization of the bilateral filter that can be applied to feature-preserving smoothing of signals on images, meshes, and other domains within a single unified framework. Our discretization is competitive with…

The threshold dynamics algorithm of Merriman, Bence, and Osher is only first order accurate in the two-phase setting. Its accuracy degrades further to half order in the multi-phase setting, a shortcoming it has in common with other related,…

Mean shift is a simple interactive procedure that gradually shifts data points towards the mode which denotes the highest density of data points in the region. Mean shift algorithms have been effectively used for data denoising, mode…

We introduce a method for computing interfacial motions governed by curvature dependent acceleration. Our method is a thresholding algorithm of the BMO-type which, instead of utilizing a diffusion process, thresholds evolution by the wave…

Median filtering is a cornerstone of computational image processing. It provides an effective means of image smoothing, with minimal blurring or softening of edges, invariance to monotonic transformations such as gamma adjustment, and…

We establish convergence results for a spatial semidiscretization of Mean Curvature Flow (MCF) for surfaces with fixed boundaries. Our analysis is based on Huisken's evolution equations for the mean curvature and the normal vector, enabling…

Differentiable particle filters provide a flexible mechanism to adaptively train dynamic and measurement models by learning from observed data. However, most existing differentiable particle filters are within the bootstrap particle…

Existing approaches for classifying dynamic graphs either lift graph kernels to the temporal domain, or use graph neural networks (GNNs). However, current baselines have scalability issues, cannot handle a changing node set, or do not take…

An analytic framework based on partial differential equations is derived for certain dynamic clustering methods. The proposed mathematical framework is based on the application of the conservation law in physics to characterize successive…

We introduce in this paper new and very effective numerical methods based on neural networks for the approximation of the mean curvature flow of either oriented or non-orientable surfaces. To learn the correct interface evolution law, our…

This paper considers and proposes some algorithms to compute the mean curvature flow under topological changes. Instead of solving the fully nonlinear partial differential equations based on the level set approach, we propose some…