1 Super Resolution Panospheric Imaging Trey Smith, Math for Robotics, Nov. 30, 1999 Panospheric Camera Can be thought of as a perspective camera with almost 180 degree field of view In “longitude” sees In “latitude” range is tunable, can be as large as – On a mobile robot, useful for localization (can track landmarks longer) Two major styles being championed by Columbia and CMU Already being used for immersive videos    

2 Super Resolution Panospheric Imaging Trey Smith, Math for Robotics, Nov. 30, 1999 Super Resolution: Problem Given: –k [n x n] images of the same scene –Overlap substantially –Offsets uniformly distributed modulo 1 pixel Produce: –One image with size on the order of [sqrt(k)n x sqrt(k)n] Classic application: satellite imagery Apply to panospheric images –Low panospheric angular resolution makes this a good fit More generally, could do 3D reconstruction

3 Super Resolution Panospheric Imaging Trey Smith, Math for Robotics, Nov. 30, 1999 Algorithm Register samples Minimize model error Form composite model

4 Super Resolution Panospheric Imaging Trey Smith, Math for Robotics, Nov. 30, 1999 Minimize Model Error Based on Bayesian principles Two error components –Deviation from prior assumption about the returned model. In general, prior tries to enforce smoothness Prior allows you to go to higher resolution than you have data for –Deviation from sample data e_i is the difference between the model pixel value and the value predicted by bilinear interpolation in sample i This gives us a vector error e. The error value is |e| 2.

5 Super Resolution Panospheric Imaging Trey Smith, Math for Robotics, Nov. 30, 1999 Preliminary Results