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An amateur question. I take an image and average pixels over a window 3 by 3, thus obtaining a smoother image. Then I increase the averaging window size - obtain an image with even less details, but still with some low frequency details. Is there some theoretical upper limit, when there is no sense to increase the averaging window anymore, because I will loose any details. If yes, does this limit depend on the range of intensities [0,255] or on lowest frequencies, present in the image?

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Assume we're talking on Box Blur, the upper limit is basically by the image size.

As you wrote, when you increase the window size you generate a Low Pass Filter with lower cut off frequency.
How much details will remain depends on the spectrum of the image.

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