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?