7.7.10

Still progressing on this correlation/velocity estimate stuff. Clearly from the previous post, estimating the velocity at each stop is produces inconsistent results. I think the problem is that when the speed is relatively slow (<1 px/frame), consecutive frames look very similar, with only a few edge pixels changing. Thus there just isn't enough movement in the first few delays to show clear movement of the peak of the correlation image, maybe explaining why it takes a few delays for the estimated velocity to settle down to a reasonable number.

But based on how consistently the peak moves in that video I decided to just track its position as a function of the delay, instead of producing an estimate each time. Luckily, the peak position is very linear. Because the peak should move with the same velocity as the phase profile, I can do a linear regression and take the resulting slope as the velocity. The resulting estimate is close to the average of estimating a velocity each delay, but its more justified looking at a plot of the peak position vs delay.

This works equally well using the covariance matrix of a state space model to calculate the correlation image for each time lag. To make it even better I managed to vectorize the calculation so that Matlab doesn't yack all over the nested loops. It runs around 10x faster than before.

I'm not sure where all this is going. It seems to be working pretty well, but I'm not sure we'll be able to squeeze a paper out of it. Maybe if I manage to get results of flow using the WFS and the actual experiment that would be more interesting.