Is there a metric to quantify edge information contained within different regions of an image

I have regions on an image (Rectangular ROI) which are passed to an an algorithm (The algorithm does edge segmentation to compute some metrics). I want to know if there is some metric I can use to choose quantify the edge quality and select the right ROI. I have attached a picture to explain the problem.The region in blue select a part of the vertical line , but the region in red does the same but contains noise from a horizontal feature (Being the bigger box it contains more statistics).

Answer 1

[Image Analyst]

You can find lines with hough or houghlines. If you take the profile across the edge you can fit a line through the middle part of the profile to get the slope of the edge.