A discontinuity does not sound like something for which a statistical parameter like the roughness is suitable for, that sounds more like something for which a profile extraction and analysis would be suitable.
If you still want to get the roughness for a selected area on an image, you can do that e.g. with Gwyddion in the following steps:
1) Load the image, subtract baseline and correct for error lines if you haven't already done that.
2) Use the "edit mask" functions, in my version that's a red rectangle symbol in the bottom options group. Select the area(s) you want to be included in the evaluation.
3) Select "statistical quantities" (the button with the variables) and tick the option "include masked area only". Then you should get RA and RQ for your selected range.
The joint roughness coefficient (JRC) proposed by Barton [1], has been widely used in engineering practice. The JRC value scales the joint roughness in the range from 20 (rough) to 0 (smooth) and can be determined either by tilt, push or pull tests on rock samples.
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