It's friday, Cable and I are continuing our series on applying Advanced Matrix Factorization and more to videos and other high dimensional datasets.

Today, we decided to perform a simple optical experiment. While most cameras have very nice lenses, we wanted to go for the dirty, uncalibrated, CSI style type of situation. Here, I built a "thing" made up of several concave "mirrors": i.e. lightbulbs (an idea we kind of tried in our DARPA Grand Challenge entry). The question here is simple: Can you use several reflecting round mirrors to evaluate the location of something in the scene reflected on those mirrors. Part of the answer revolves around removing the background from the moving scene. This is what we did in these two examples. We first show you the original scene and then the processed version with the low rank version at the top, and the sparse and noisy version at the bottom.

Original scene

Robust PCA using semiSoft GoDec

second original video

and here is the robust PCA decomposition

It does a pretty good job a separating the background from the moving figures. It's pretty obvious that the duplication of the same figure on several mirrors is likely to provide a good input for estimating the distance to the object of interest. A calibration run would be simple to run with a target moving around the camera once. Obviously this could be directly applicable to a compressive imaging camera.

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