360 degree panorama photo or movie

Exhibit: table of content

Mathematics Math21a, Spring 2006
Multivariable Calculus
Oliver Knill, SciCtr 434, knill.harvard.edu

Unwrapping a 360 degree photos and movies

unwrapped photo

1. February 2006, Science Center D. Oliver Knill gives introduction lecture to Math21a of Spring 2006. Because of the relatively long exposure time in the lecture hall, Oliver got blurred during this "action shot". You can see the full panorama (JPG,JS,JAVA and QT versions) here.

original photo A special lense and mirror allows to take a 360 degree photo. To the left, you see the actual picture, the camera has taken. The picture above is the same, but in a different coordinate system.

Here is an example, where it is useful to know a bit of calculus or linear algebra. Because there is no unwrapping tool available for 360 degree movies, I had to write an unwrapper for movies myself. Reverse inegeneering the transformation was done by taking a few dozen points, note their coordinates in both pictures and find an interpolating map using curve fitting. I wrote the unwrapper as a C application. It is extremely fast. It turned out that the 360 mirror is done in such a way that the correspondence is given by an adaptation of polar coordinates. Having available an unwrapping tool, the movie can be transformed by splitting sound and picture, transform each picture and finally gluing together sound and picture again. Below you see to the left the movie taken by the camera and to the right the unwrapped movie. This was the first test. It needs still some tweeking. I still did not manage to coordinate sound and pictures completely yet for example.
360 degree mirror

This test movie was done on March 6th, 2006 in SC 434. The person buzzing and humming around the camera is Oliver.


Please send comments to math21a.harvard.edu
Oliver Knill, Math21a, Multivariable Calculus, Spring 2006, Department of Mathematics, Faculty of Art and Sciences, Harvard University