The above image was taken by a security camera at a surburban Houston, Texas branch bank during a daring daylight robbery. It shows the reflections of two of the suspects and two hostages in a decorative silver ball that is 30 cm in horizontal diameter. The camera was 30 feet away.
The Chief Investigator, Texas Ranger Captain Billy Clyde Pucket (email@example.com), believes he knows who the suspects are, and he is trying to get an arrest warrant to bring then in for questioning and for a lineup in front of witnesses before they spend all the money they stole. State Superior Court Judge Roy Whaptner (firstname.lastname@example.org), however, refuses to issue the warrants because he cannot identify the suspects by comparing their mug shots (see below) to the picture, due to the geometric distortion produced by the spherical mirror.
Your job is to "unroll" the image so that the four faces appear relatively undistorted, and Capt. Pucket can convince Judge Whaptner to issue a bench warrant for the arrests. First try modeling the mirror as a sphere and using a mathematically-defined warp. If that result is still distorted, try using fiducial markings in the image to square it away. Click on the images to download GIF files. Send your results to ftp.texas.rangers.org/robbery/bank/bad-guys.