sobel and letters

I have this problem with sobel filter:
when the sobel filter finds an edge of a line, it finds the initial up edge and the end edge , then,a line in the sobel filter have two edge?.
Is possible to eliminate this behaviour and show only the start edge?
i’m trying to filter some letters in a texture but the words after the sobel filter are enlarged and confused.


The down line is should be negative. so you could ignore every value thts below 0