Sep 2026· Balkan Journal of Electrical and Computer Engineering· Vol 14· 0 citations· 13 references
TL;DR
A new phase field model for image decomposition and smoothing based on a modification of the Cahn-Hilliard equation which allows only the decomposition of phase values into multiple layers.
Abstract
In this paper we propose a new phase field model for image decomposition and smoothing based on a modification of the Cahn-Hilliard equation. The Cahn-Hilliard equation was first formulated as the minimization of a free energy that reflects the topological events, phase coarsening and separation processes. We replaced the energy density in this equation with the derivative of a new convex energy which allows only the decomposition of phase values into multiple layers. This system, although based on a variational formulation does not require the solution of an optimization problem and its main advantage is the flexibility it provides in designing decomposition algorithms. Within this framework, we developed several algorithms based on order statistics for image smoothing and decomposition.
We propose a novel domain decomposition framework based on energy minimization, applicable to a wide class of linear and nonlinear partial differential equations. This energy-minimizing domain decomposition (EMDD) method addresses problems whose solutions are minimizers of an energy functional, either unconstrained or...
M. Hassan, Benjamin Stamm, Lambert Theisen· 0 citations
A discretisation based on a second-order consistent Grünwald Letnikov scheme is introduced and some numerical simulations aiming to denoise images corrupted by impulsive noise are shown, which can be well modeled by the Laplace distribution.
A. Lanza, A. Leaci, S. Morigi et al.· Journal of Convex Analysis· 0 citations
We propose a Gauss-map variation (GMV) model for image denoising that measures the spatial variation of the tangent-plane projectors of the scaled image graph. We establish an equivalent representation of the regularizer in terms of the corresponding Gauss map and, using differential geometric tools including tubular c...
In this article, we analyze a recently introduced kinetic model based on Hegselmann-Krause-type interaction dynamics describing consensus-based image segmentation in the mean-field regime, where particle density depends on spatial coordinates and the normalized gray level (feature) value. The model is formulated as an...
Abramo Agosti, P. Colli, Elisabetta Rocca et al.· 0 citations
We propose an algorithm based on iteratively reweighted norm strategy for image edge preservation. In order to achieve the purpose of boundary enhancement, we obtain a regularization operator through an adaptive process in the outer iteration and derive a Tikhonov regularization problem. An effective hybrid regularizat...
Le Li, Zhengsheng Wang, Meng-Ying Wu· Journal of Mathematical Stud...· 0 citations
Plug-and-Play methods are among the state-of-the-art approaches for image reconstruction, but they do not scale well with the image size. We propose a multiresolution block-coordinate Plug-and-Play algorithm that decomposes the image into wavelet blocks and applies a block-wise denoiser network to only a subset of bloc...
Edgar Desainte-Maréville, Marion Foare, Paulo Gonçalves et al.· 0 citations
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