How to remove noise using morphological filtering

I have two groups of dots that both contain noise between them:

The line that separates the two groups in the picture is diagonal in shape. I tried to use morphological filtering on this image to remove the noise between these two groups but failed.

This is the code that I tried to run on this image:

from skimage.morphology import opening, square

new_image = opening(image, square(3))

It did remove a little bit of noise, but not enough for them to become two distinct groups.

I am using DBSCAN on the new_image and DBSCAN still treats them as one group.

I would like to know whether I am giving the correct argument to the function opening. Or maybe there is some other way (better way) to remove the noise between the two groups?