[IPOL announce] new article: How to Apply a Filter Defined in the Frequency Domain by a Continuous Function

[announcements about the IPOL journal]

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.