Find center and radius of fisheye image

Hi Guys, I have a video from a fisheye camera with an image like this. Dont mind the cutout of the person. :)  I would like to find the center and radius of the circular fisheye image mage. I have tried just fitting a circle to the image, but the edge is very warped and reflections tend to bleed from the sides of the image so centering is difficult. I therefore need something better. I was therefore wondering if there was any way to find the contrast in the image andperhaps accumulate it over several video frames, to thereby detect what pixels contain world information and what contain bleeding. Kind regards Jesper