If you don't care computational time, Hough Transform is a good solution to lines/line-segments detection in a binary image. parallel lines are lines with a same orientation.

once a line is extracted, those pixels along the line can be identifed. then removed. 

If you could post an example image, both grayscale and original, I'd be happy to help.

Firstly, you have to detect lines at all - eg. starting with the caculating 'oriented gradients' and gathering points of similar orientation to 'lines'. From the oriented gradients you already have the orientation of the lines, so finding parallel lines means comparing the orientation of the lines identified.

How to 'remove' these lines is another issue...

Regards

I'm guessing the issue here is that an operation that is simple in vectors is difficult if you convert to a "binary image" .... clearly after this conversion you have just a collection of pixels with 1/0 code and no global knowledge of how these pixels make a line ... and of course without knowing what is a line it is hard to removed related lines. Could you do this process BEFORE conversion to binary image? Of course if you have lines in point slope form the parallel ones are the ones with the same slope.

You could even tolerate small error ("almost" parallel line)

Finally, if you are doing this on a curved surface (the earth) you will have to be careful what you mean by parallel.

Like the other answers, I recommend a specific example so we can be more help.

Dear Abdelrahiem Ahmed Hashem,

Look the links, may be useful.

http://homepages.inf.ed.ac.uk/rbf/HIPR2/linedet.htm

https://books.google.az/books?id=cGXHLG1c_WUC&pg=PA688&lpg=PA688&dq=How+can+I+detect+the+parallel+lines+in+binary+image?&source=bl&ots=OGVbo7F5g3&sig=IYIQSrV8zJ0RqOwqB9O-4F6LL6s&hl=ru&sa=X&ved=0ahUKEwiMiJLH_vTOAhVBshQKHb5yBDMQ6AEIOjAE#v=onepage&q=How%20can%20I%20detect%20the%20parallel%20lines%20in%20binary%20image%3F&f=false

Regards, Shafagat

You can use pairwise geometrical histograms, check openCV

If you don't care computational time, Hough Transform is a good solution to lines/line-segments detection in a binary image. parallel lines are lines with a same orientation.

once a line is extracted, those pixels along the line can be identifed. then removed. 

iF those lines are a periodic pattern, a frequency filter can be used to removed them.

I recommend Hough Transform as already suggested by Xu.

Than you all my collegues above for your help.

You can use Hough Transform to detect lines first,

once you get the lines you should be able to recognize the parallel ones using line properties (same slope)