How to remove bridged lines/branches between lines in image?

Hi,

I would like to remove certain lines which are not the main parallel lines, that is, all the horizontally connected bridges and spurs.

This is my thinedImage:

I have tried disconnecting the branches by using:

bp=bwlookup(thinedImage,  makelut(@(x) sum(x(:))>=4 & x(5)==1,3)); %branch points?
 filteredIm=thinedImage&~bp;

I then try to perform a bwareaopen(filteredIm, 50) and get this:

Basically everything on the left hand side is fine, but I have removed too much from the right hand side. How do I keep the major line, removing only the smaller branches?

I have also tried using

 thinedImage - bwmorph(thinedImage, 'spur', Inf);

in the 2nd step, but that doesnt turn out too wel either.

[Walter Roberson]

Perhaps use hough() with a range of theta that are close to 0, and then houghlines() to detect lines at those angles?

[Edwin Sun]

Sorry, didnt get a chance to test it till now.

The hough transform only fit to certain sections of the line, not the whole line. Basically the output from hough() is a whole bunch of lines which make up the the line. Is there a way for the hough transform to be a bit more lenient?

Also the image in the question is one of the better ones from a set of data, and not all the datas are as straight.. some are a bit more zig zaggy.

Thanks