It’s amazing what can be accomplished, out-of-pocket, with ubiquitous smart phone camera technology. Here’s an example of a simple wide angle catadioptric system produced with a standard phone camera and commonplace reflective ornament.
Although performed mostly for fun, this experiment provides an opportunity to demonstrate a simple photogrammetry math model expressed in the powerful language of geometric algebra (GA). Stellacore routinely utilizes GA in development of complex and custom sensor system models.
Techy Details
The photogrammetry math model, as described informally here, was implemented in a demonstration software application by combining various components of Stellacore’s available photogrammetry infrastructure.
The software application performs a basic “self-calibration” process that establish the relative geometry between the ball and camera and then reconstitutes the reflection geometry. Features identified in the reflected image are used to align the overall optical assembly with the local horizon and the rectified image is generated into a custom projection of interest (a cylindrical projection in above example).
Background and Motivation
The reflective ball experiment described above was motivated after observing the reflected scene in this intriguing photograph:
After some reflection:-) and a touch of research, the photograph was associated with one of these interesting sculptures (specifically, the one in the courtyard at the Vatican Museums).