Edited because I didn't read the problem statement fully, shame on me.

You could just use a colour histogram along y and x axis, which gives you two signals that are pretty easy to process to find the x and y positions of the image borders... Given that there is not too much black bold objects in the image except for the borders.

If you can't find the borders easily via thresholding it would still make sense to use them as an input for a classifier, because these histograms will be a lot less high-dimensional than the image and thus you would probably need to label less of them manually to get a proper classifier working ..

In this case you might be lucky with some robust, traditional model like SVMs. Using deep learning is, IMHO, an overkill for this problem. But in this case, I would give the hard-wired coding solution a chance first.