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I have a grey valued image which is calculated as the mean of a series of images. The value of each pixel is therefore associated to a standard error.

The pixel values and the relative standard error (RSE) vary smoothly in pixel space, so that the pixels of a downscaled image resulting as the mean of the underlying downscaled images would exhibit a lower RSE. Meaning that a high resolution image is associated to high RSEs and a low resolution image to lower RSEs. However, the RSE vary in space.

Effectively this behaves like the trade-off of an uncertainty relation: Resolution in space vs resolution in the mean value.

For representing this I am looking for a way to divide the image into regions with constant RSEs, which would be larger in parts of the image with high RSEs and smaller in parts with low RSEs.

The aim would be to obtain irregularly sized superpixels with regular RSEs as opposed to my current image which contains pixels on a regular grid but with irregular RSEs.

This would be equivalent to downscaling the image but not on a regular grid. One approach I tried is agglomerative clustering of the pixels computing new distances in every step, but so far I couldn't find the right distance and objective functions to obtain a more or less regular map of superpixels (generally one big cluster would eat up its neighbours).

Do you know of any existing approach for this or if not which would be a good clustering method to apply? Would quadtrees help me?

Thanks a lot in advance!

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