See attached solution.
For linking the bottom lines, you can look at edge linking http://www.peterkovesi.com/matlabfns/#edgelink
Or you could try to do a cluster analysis on the lines and find common y values. Like if you knew there were 9 lines, you could use kmeans to get the centroids in the y direction and then use bwmorph(binaryImage, 'endpoints') to get the endpoints of all the line segments and then use imline() to burn a line connecting endpoints to the closest endpoint of another line in the sane y zone. I don't have code for that but it's pretty straightforward so try it.
