Progress

This plot here is finally a sign of progress. I had the idea of using the variance of the image as an objective function before, but for some reason the standard var() command on the vectorized image I(:) didn't work well. I stumbled on the std2() function while looking for ways to filter the image to use the moment of inertia idea (which I still think has some promise).

With a single mode (constant command across all actuators), the standard dev. of the image peaks nicely around a maximum, and unlike the max intensity the curve has nonzero slope for all command values (see 3.23.09). I'm not sure yet if the maximum corresponds to the maximum intensity, but even if it doesn't then some linear combo of the 2 should work well as an objective.

Some things to look into tomorrow:

1. Multiple modes: this is the big question. Just because the std2() function is smooth for a single mode, there's no guarantee it behaves nicely when multiple modes are used.

2. Max intensity vs. max std2(): do they correspond to the same value? I know they're close right now, so some linear combo of the 2 should work nicely.

3. Log-concavity?: the plot of std2 vs. u (the command constant) looked almost Gaussian, which is log-concave. Maybe this is too? If so that might dramatically improve convergence.

4. Speed up convergence: right now it sucks.

Also, there's no possible way to make canned tuna into a satisfying meal. That is all.