Mimetic finite difference methods in image processing
Mimetic finite difference methods in image processing
复制标题
图像处理中的模拟有限差分法
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
P. Blomgren
中科院分区：
文献类型：
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作者：
C. Bazan;M. Abouali;J. Castillo;P. Blomgren
我们介绍了使用模仿方法的成像社区，在机器视觉和图像处理和分析领域中无处不在的初始值问题的解决方案。基于偏微分方程的图像处理和分析技术包括一个主机的应用程序，如噪声去除和恢复，去模糊和增强，分割，边缘检测，修补，配准，运动分析等，因为他们良好的稳定性和效率的属性，半隐式有限差分和有限元方案的选择方法（在该顺序的偏好）。我们提出了一种新的方法，这些问题的数值解的基础上模仿的方法。模拟离散化方案保留了图像处理和分析方程中经常遇到的数学算子的连续性。这是主要的贡献因素，以改善性能的模拟方法的方法，相比上述两种流行的数值求解技术。为了评估所提出的方法的性能，我们采用Catte-Lions-Morel-Coll模型来恢复噪声图像，通过求解PDE与三个数值解方案。对于我们实验中使用的所有基准图像，以及应用的每个噪声水平，我们观察到，通过使用模仿方法恢复的最佳图像比通过其他两种测试方法恢复的最佳图像更接近无噪声图像。这些结果激发了进一步研究的应用程序的模拟方法的其他成像问题。数学科目分类：小学：68 U10;中学：65 L12。
We introduce the use of mimetic methods to the imaging community, for the solution of the initial-value problems ubiquitous in the machine vision and image processing and analysis fields. PDE-based image processing and analysis techniques comprise a host of applications such as noise removal and restoration, deblurring and enhancement, segmentation, edge detection, inpainting, registration, motion analysis, etc. Because of their favorable stability and efficiency properties, semi-implicit finite difference and finite element schemes have been the methods of choice (in that order of preference). We propose a new approach for the numerical solution of these problems based on mimetic methods. The mimetic discretization scheme preserves the continuum properties of the mathematical operators often encountered in the image processing and analysis equations. This is the main contributing factor to the improved performance of the mimetic method approach, as compared to both of the aforementioned popular numerical solution techniques. To assess the performance of the proposed approach, we employ the Catte-Lions-Morel-Coll model to restore noisy images, by solving the PDE with the three numerical solution schemes. For all of the benchmark images employed in our experiments, and for every level of noise applied, we observe that the best image restored by using the mimetic method is closer to the noise-free image than the best images restored by the other two methods tested. These results motivate further studies of the application of the mimetic methods to other imaging problems. Mathematical subject classification: Primary: 68U10; Secondary: 65L12.