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I've got a high-resolution image segmentation, which I'm downsampling (and non-linearly deforming) to fit on an ROI image. I typically blur the high-res image before downsampling with a Gaussian-fwhm related to the downsampling factor. The result is high-res and low-res images with the same mean.

I'd like now for my high-res and low-res images to have the same sum. If I scale up the low-res image by the downsampling factor, will local sums be preserved across the image? Is there a better way to downsample and preserving local sums?

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    $\begingroup$ If I understand you correctly, that seems impossible! If my high resolution image is $[100\ 100]$ and my low resolution image is $[100]$ (same mean value) then there is no way the two can also have the same sum. Perhaps I'm missing something! :-? $\endgroup$ – Peter K. Aug 22 '13 at 14:38
  • $\begingroup$ Oh, I mean make another low-resolution image; one which preserves the mean, and the other which preserves the sum! $\endgroup$ – Andrew Wood Aug 22 '13 at 14:46
  • $\begingroup$ :-) Thanks. In that case, just scaling by the downsampling factor should get very close to what you need. It probably won't be precisely correct, though. $\endgroup$ – Peter K. Aug 22 '13 at 15:24
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Increase the gain of your filter by the downsampling factor.

You do this by multiplying the filter taps by the downsampling factor. This is equivalent to doing exactly what you have done before and then multiplying the results by the downsampling factor.

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