Why gaussian smoothing

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What are its advantages compared to other filters like median filter? Show older comments. MoonPie1 on 7 Jul Vote 0. Answered: lourci mohamedamine on 4 Feb Image Source: Wikimedia.

No complicated algorithms with multiple nested for loops needed. Some use cases might require you to conceal the identity of someone or to censor images that might contain material that might be inappropriate to certain audiences. Gaussian smoothing works well in these cases.

Gaussian smoothing produces an image that is rotationally symmetric. It is applied the same no matter what direction you go in. Smoothing increases signal to noise by the matched filter theorem. This theorem states that the filter that will give optimum resolution of signal from noise is a filter that is matched to the signal. In the case of smoothing, the filter is the Gaussian kernel.

Therefore, if we are expecting signal in our images that is of Gaussian shape, and of FWHM of say 10mm, then this signal will best be detected after we have smoothed our images with a 10mm FWHM Gaussian filter. The next few images show the matched filter theorem in action. First we can generate a simulated signal in a one dimensional set of data, by creating a Gaussian with FWHM 8 pixels, centered over the 14th data point:.

Thus, we smooth with a filter that is of matched size to the activation we wish to detect. This is of particular relevance when comparing activation across subjects. Here, the anatomical variability between subjects will mean that the signal across subjects may be expected to be rather widely distributed over the cortical surface. In such a case it may be wiser to use a wide smoothing to detect this signal. In contrast, for a single subject experiment, where you want to detect for example a thalamic signal, which may be in the order of a few mm across, it would be wiser to use a very narrow smoothing, or even no smoothing.

Sometimes you do not know the size or the shape of the signal change that you are expecting. In these cases, it is difficult to choose a smoothing level, because the smoothing may reduce signal that is not of the same size and shape as the smoothing kernel.

There are ways of detecting signal at different smoothing level, that allow appropriate corrections for multiple corrections, and levels of smoothing. Human Brain Mapping Why smooth?