I'm trying to dewarp a small part of fisheye image. My fisheye camera has 180 degrees FOV. I get an input fisheye image in form of round area inside of rectangle frame. My camera gives me an opportunity to get the radius of this circle and coordinates of it's center inside of video frame. In this case it will be a reasonable solution to perform projection (move colored points) of flat 2-D fisheye image (circle) to 3-D hemisphere.
My question is: how to project correctly flat fisheye image (circle) to 3-D hemisphere (to warp colored points from circle area inside 2-D image around inner surface of 3-D hemisphere)? Will it be correct to just set Z-coordinate to all colored points of flat image in accordance with hemisphere equation, to rise points from image plane to hemisphere surface?
To make my question more clear I attached a picture with fisheye image and desired result.
