How to create peaks at coordinates

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I think an easy way would be to smooth the image iteratively with a one-pixel diameter kernel, and only for the non-zero pixels.

Pseudocode:

repeat:
    for each pixel>0
        for each neighbor=0
            neighbor=pixel*0.8

Like this, you will have a small valley even between close points, but sometimes the transition won't be smooth.

Another way would be to create a gaussian blurred image and another image where you interpolate all the points (using for example a Delaunay triangulation). Then, for each pixel take the lower value.

gauss=gaussianblur(points,sigma)
delaunay=triangulate(points)
result=min(gauss, dealunay)

The disadvantage of this approach is that the triangulation isn't implemented in OpenCV (you have to do it yourself), and in some cases you can get artifacts.

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".