How to segment with false edge in in image?
You could try "Non-maxima suppression" This is usually used on edge detectors to thin the edge to only one pixel. When there are lots of edges close together you basically pick the one with the largest gradient, and assume that is the true edge

Another technique that might be applicable is double thresholding. Some edge detectors (canny for instance) actually perform multiple detection's with different parameters.  "Strong edges" are found in the the higher threshold (and probably the lower one as well) weaker edges may only be found using the lower threshold, and are only "true" edges if they connect to one of the stronger edges. Maybe you could use your current edge detector as the weaker classifier, and then make one that is harder to satisfy. This might eliminate the false positives that are only detected by the weak detector (i hope that makes sense)

good luck