文章基本信息

标题：How to Apply a Filter Defined in the Frequency Domain by a Continuous Function
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作者：Thibaud Briand ; Jonathan Vacher
期刊名称：Image Processing On Line
电子版ISSN：2105-1232
出版年度：2016
卷号：6
页码：183-211
DOI：10.5201/ipol.2016.116
出版社：Image Processing On Line
摘要：We propose algorithms for filtering real-valued images, when the filter is provided as a continuous function defined in the Nyquist frequency domain. This problem is ambiguous because images are discrete entities and there is no unique way to define the filtering. We provide a theoretical framework designed to analyse the classical and computationally efficient filtering implementations based on discrete Fourier transforms (DFT). In this framework, the filtering is interpreted as the convolution of a distribution, standing for the filter, with a trigonometric polynomial interpolator of the image. The various plausible interpolations and choices of the distribution lead to three equally licit algorithms which can be seen as method variants of the same standard filtering algorithm. In general none should be preferred to the others and the choice depends on the application. In practice, the method differences, which come from the boundary DFT coefficients, are not visible to the naked eye. We demonstrate that claim on several experimental configurations by varying the input image and the considered filter. In some cases however, we discuss how the choice of the variant may affect fundamental properties of the filtering.