Finding radius r of the overlappable sphere(s) in 3D image
A simpler solution and much more computationally efficient when compared to Hough Transform is to use the distance transform:


Find the surface of your spheres (i.e. the pixels that have value 1 and have at least one neighboring 0 pixel);
Compute the distance transform with respect to the spheres surface, but constrain the computation only to pixels that are internal to the spheres. The output will be a distance map;
The radius will be exactly the maximum value in your distance map.


Another advantage of this solution when compared to Hough transform is that it provides a much more precise value for the radius.