is the monopoly reduced/ lowered /shared?

"To erode a monopoly", or variants thereof, seem to be in common usage.

In the sense of being 'gradually destroyed,' it works in your example if Method 1 retains its monopoly in some parts of the imaging domain, but not for the entire domain. If Method 2 competes with Method 1 across the entire domain, Method 1 has lost it's monopoly.

You could also says that "Method 1 challenges the monopoly of Method 2" if Method 2 still has its monopoly but Method 1 has the potential to change that.