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toni
2018-02-14 19:37:39 +01:00
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tex/chapters/mvg.tex
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@@ -16,7 +16,7 @@ where $\sigma$ is a smoothing parameter called standard deviation.
%In the discrete case the Gaussian filter is easily computed with the sliding window algorithm in time domain. %In the discrete case the Gaussian filter is easily computed with the sliding window algorithm in time domain.
If the filter kernel is separable, the convolution is also separable i.e. multi-dimensional convolution can be computed as individual one-dimensional convolutions with a one-dimensional kernel. If the filter kernel is separable, the convolution is also separable i.e. multi-dimensional convolution can be computed as individual one-dimensional convolutions with a one-dimensional kernel.
Because of $\operatorname{e}^{x^2+y^2} = \operatorname{e}^{x^2}\cdot\operatorname{e}^{y^2}$ the Gaussian filter is separable and can be easily applied to multi-dimensional signals. \todo{quelle} Because of $e^{x^2+y^2} = e^{x^2}\cdot e^{y^2}$ the Gaussian filter is separable and can be easily applied to multi-dimensional signals. \todo{quelle}
% TODO ähnlichkeit Gauss und KDE -> schneller Gaus = schnelle KDE % TODO ähnlichkeit Gauss und KDE -> schneller Gaus = schnelle KDE