[IPOL announce] new article: How to Apply a Filter Defined in the Frequency Domain by a Continuous Function
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Mon Nov 7 15:41:03 CET 2016
A new article is available in IPOL: http://www.ipol.im/pub/art/2016/116/
Thibaud Briand, and Jonathan Vacher,
How to Apply a Filter Defined in the Frequency Domain by a Continuous
Function,
Image Processing On Line, 6 (2016), pp. 183–211.
https://doi.org/10.5201/ipol.2016.116
Abstract
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.
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