If the radius is not known, then the locus of points in parameter space will fall on the surface of a cone. Each point (x,y) on the perimeter of a circle will produce a cone surface in parameter space. The triplet (a,b,R) will correspond to the accumulation cell where the largest number of cone surfaces intersect.
The drawing at the right illustrates the generation of a conical surface in parameter space for one (x,y) point. A circle with a different radius will be constructed at each level, r.
The search for circles with unknown radius can be conducted by using a three dimensional accumulation matrix.