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基于 Euler 弹性体和曲率的图像恢复模型。

Euler's elastica and curvature based model for image restoration.

机构信息

State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Center for Numerical Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu 210098, P. R. China.

出版信息

PLoS One. 2018 Sep 19;13(9):e0202464. doi: 10.1371/journal.pone.0202464. eCollection 2018.

DOI:10.1371/journal.pone.0202464
PMID:30231071
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC6145515/
Abstract

Minimization functionals related to Euler's elastica energy has a broad range of applications in computer vision and image processing. This paper proposes a novel Euler's elastica and curvature-based variational model for image restoration corrupted with multiplicative noise. It combines Euler's elastica curvature with a Weberized total variation (TV) regularization and gets a novel Euler's elastica energy and TV-based minimization functional. The combined approach in this variational model can preserve edges while reducing the blocky effect in smooth regions. The implicit gradient descent scheme is applied to efficiently finding the minimizer of the proposed functional. Experimental results demonstrate the effectiveness of the proposed model in visual improvement, as well as an increase in the peak signal-to-noise ratio, compared to the PDE-based methods.

摘要

与 Euler 弹性力学能量相关的极小化泛函在计算机视觉和图像处理中有广泛的应用。本文提出了一种新的基于 Euler 弹性力学和曲率的变分模型，用于恢复被乘性噪声污染的图像。它将 Euler 弹性力学曲率与 Weber 化全变差（TV）正则化相结合，得到了一个新的 Euler 弹性力学能量和基于 TV 的极小化泛函。这种变分模型中的组合方法可以在减少平滑区域块状效应的同时保留边缘。采用隐式梯度下降方案来有效地找到所提出泛函的最小值。实验结果表明，与基于偏微分方程的方法相比，该模型在视觉改善方面的有效性，以及峰值信噪比的提高。

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A New Variational Approach for Multiplicative Noise and Blur Removal.一种用于去除乘性噪声和模糊的新变分方法。
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