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I think this does what you want, but it's a bit unclear.

Create two empty images, one for work, one for results, both should be float type.

Zero the work image. Place a single pixel of <point height=""> in the appropriate place in the work image. Gaussian Blur. Add the work image to the result image.

Once you have done this for all the points, normalize the results image.

If this doesn't do what you want, then I'm not quite sure what you mean by "not overlapping".