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How to detect number of elements in a section of a given board

I have a board divided into various sections. E.g.

image description

and I want to count number of dots that are present in a section of this board, so that could have a final result of the kind:

A=0
B=0
C=1
D=0
E=6
F=0
G=0
H=2
I=4

The size and shapes of the various sections could be different, anyway the kind of patterns that board could have, are few and are already known, so It's not explicitly needed to have a system "smart enough to understand itself how to interpret board structure".

One of my co-worker suggested to use OpenCV, but don't know in what way I could use It to achieve this.

Reading the documentation I haven't clear how I have to use Its feature detection capabilities in order to count dots per section in a picture that reproduces the board pattern of interest.