Relations between nonlinear filters in digital image processing

数字图像处理中非线性滤波器之间的关系

• 批准号: 5333820
• 负责人: Professor Dr. Joachim Weickert
• 金额: --
• 依托单位: Saarland Informatics Campus (SIC)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2001
• 资助国家: 德国
• 起止时间: 2000-12-31 至 2008-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5333820?language=en
• 关键词: Relations; between; nonlinear; filters; digital

Nonlinear filters are very popular for image restoration, since they allow denoising without deterioration of edges. Although many different methodologies have been developed in parallel, their connections have hardly been studied so far. In this project we intend to examine the relations between three important classes of nonlinear filters, namely local discrete filters, diffusion filters and wavelet techniques. We will analyse these relations not only theoretically but we will also study numerical implementations and perform practical evaluations. In order to derive a unifying description of the three classes, we investigate formulations in terms of unconstrained optimization problems, discrete weighted averaging methods and parabolic partial differential equations (PDEs). We will compare the different techniques both for synthetical images as well as for widely used real-world test images.

非线性过滤器在图像恢复中非常受欢迎，因为它们允许在不恶化边缘的情况下进行降解。尽管已经并行开发了许多不同的方法，但到目前为止，几乎没有研究它们的连接。在这个项目中，我们打算检查三个重要类的非线性过滤器之间的关系，即局部离散过滤器，扩散过滤器和小波技术。我们将不仅从理论上分析这些关系，而且还将研究数值实施并进行实际评估。为了得出三个类的统一描述，我们根据不受约束的优化问题，离散的加权平均方法和抛物线偏微分方程（PDES）进行研究。我们将比较综合图像以及广泛使用的现实测试图像的不同技术。