Uncertainty and Video Analysis

This is for commenter JimP. How do you take into account uncertainty when using video analysis? A great question. The first thing to think about is where does the uncertainty come from? My first guess would that it would be from the user. Where does the user click? Is it right on the object in each frame? Is the scale set correctly? I guess there could be other sources of error - maybe there are repeating frames that are a result of encoding. Maybe there is interlaced video frames.

Well, what to do? I will just look at one motion in particular and do the analysis several times. I am going to analyze the following video:

Horizontal Projectile Motion from Rhett Allain on Vimeo.

Note that you can download the video from vimeo (in the lower right hand of the video page). By repeatedly analyzing this video, I have an idea of the uncertainty due to the human input. Actually, I did this analysis 5 times before I realized a mistake I was making. So, let me show you the data I have from that. This is the velocity in the horizontal direction and the acceleration in the vertical direction that I obtained from fitting functions to the horizontal and vertical data.

The "RMS" is the root-mean square deviation of the data from the line fit. This is created from Tracker Video. If I use the standard error as the uncertainty, I get the following for the horizontal velocity and vertical acceleration:

So, I am not getting the expected value for the vertical acceleration. Maybe this is because in this shot, there is a small number of data points. Or it could possibly be due to some parallax or scaling issues. Either way, I still like this method of finding the uncertainty in these values. What is causing the uncertainty? Is it clicking error, or scaling error? It doesn't actually matter. This just gives me the uncertainty.

But what if I want to look at the uncertainty due to clicking on data points? For this next set, I did not scale the video (because that would add another layer of error). Here are the pixel values of the ball for the 8 times I did it. I have included all the data in case you want to play with it.

And here is the trajectory of the ball (in pixels vs. pixels) with error bars.

So, what can I say now? First, it seems like the uncertainty from clicking is less than 1% of the value. I don't think clicking uncertainty is going to be the problem. More likely, the uncertainty will come from other things - like where is the object? This is especially true for extended objects - like people.

If a student was doing a lab report with video analysis, probably the best thing to do would be to repeat the video analysis a few times and find the standard error and use that as the uncertainty.