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completing characters to get their contour

Hi guys, at the moment I am working on OCR using opencv in c++. After processing my image I get something like this:

image description

The problem is that the pixels of the display have a big distance between each other so filtering results in not fully connected characters. I tried to play with dilate but it makes the characters way too big. Do you have an idea how to solve my problem?

I thought about writing my own little algorythm which connects contours (or their moments) if the distance between them is at a certain length but I am pretty sure there is an easier way which I just didn't think of yet.