Gap Filling Contours / Lines

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Faster method use connected componnet and find contours

1. Find all connected components by using find FindContour method
2. Store contour for every Region(Connected componnet CC)
3. calculate the Bounding Rect for every region (CC)
4. Loop in all region
5. For every region , find the nearest regions depending on the Bounding rect
6. now you have the suspected regions which can be connected to region, compare the two contours and find the mimimum distance between the two contours , if the minimum distance is smaller than threshould (say 10 pixel) then now you can draw line from Point1 in first contour and point2 in second contour , Point1 and Point2 are the points which satisfy the minmum distance calculated before.
7. repeat the proces for all regions

EDIT: you can find sample implemention code here

A simple solution could be to try a nearest neighbor approach, which may or may not work but will certainly be very slow. For every white pixel in the image find the nearest white pixels within a short distance range. If found, create a line between the two points. This could be speed up by skipping pixels;

An even simpler solution would be be to blur the image a few times, such that you would have a vague gray blur in the gap area. Then threshold the image such that anything not black becomes white.

I think, that an erosion and dilatation will do the job. And, as I see, you are using binary image, so you can just check if there is a white/black pixel in the window. BUT I'm not sure that will preserve the edges clear and sharp...