利用 SAV 算法绘制图像的曲率相关弹性弯曲总变化模型

IF 2.8 2区 数学 Q1 MATHEMATICS, APPLIED
Caixia Nan, Zhonghua Qiao, Qian Zhang
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引用次数: 0

摘要

图像内绘是图像处理领域中举足轻重的问题,人们在这一研究领域的建模、理论和数值分析方面做出了许多努力。本文针对内画问题提出了一种曲率依赖弹性弯曲总变化模型,其中相场框架中的弹性弯曲能量引入了几何信息,而总变化项则保持了内画边缘的锐利度,简称为弹性弯曲-TV 模型。基于标量辅助变量法,从理论上证明了能量的稳定性。此外,还采用了自适应时间步进算法,进一步提高了计算效率。数值实验说明了所提模型的有效性,并验证了我们的模型在图像绘制中的能力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Curvature-Dependent Elastic Bending Total Variation Model for Image Inpainting with the SAV Algorithm

Curvature-Dependent Elastic Bending Total Variation Model for Image Inpainting with the SAV Algorithm

Image inpainting is pivotal within the realm of image processing, and many efforts have been dedicated to modeling, theory, and numerical analysis in this research area. In this paper, we propose a curvature-dependent elastic bending total variation model for the inpainting problem, in which the elastic bending energy in the phase-field framework introduces geometric information and the total variation term maintains the sharpness of the inpainting edge, referred to as elastic bending-TV model. The energy stability is theoretically proved based on the scalar auxiliary variable method. Additionally, an adaptive time-stepping algorithm is used to further improve the computational efficiency. Numerical experiments illustrate the effectiveness of the proposed model and verify the capability of our model in image inpainting.

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来源期刊
Journal of Scientific Computing
Journal of Scientific Computing 数学-应用数学
CiteScore
4.00
自引率
12.00%
发文量
302
审稿时长
4-8 weeks
期刊介绍: Journal of Scientific Computing is an international interdisciplinary forum for the publication of papers on state-of-the-art developments in scientific computing and its applications in science and engineering. The journal publishes high-quality, peer-reviewed original papers, review papers and short communications on scientific computing.
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