Python low-pass filter on list of Time/Position

2
votes

Let me first explain my goal and my problem. I have an object moving in circle inside of a bocal (a mice to be precise), and I need to know how many rotation it does in one minute. The movement isn't a perfect circle, and can be chaotic. It can stopped for several seconds, and start again moving.

But what I know, is that I have between 3 and 20 rotation per minute => Low frequency (between 0.05 Hz and 0.33 Hz).

I'm filming this object with a 30 fps camera during 30 minutes. With Python and OpenCV, I manage to extract the (X,Y) coordinates. Since 30 fps is a bit high for the frequency I'm looking for, I selected one frame on 15 in order to have a sampling frequency of 2 Hz.

The first problem, is that sometimes, I'm missing a point because OpenCV couldn't find the object. This is a problem I can't solve, since the point I'm tracking with an HSV color mask is sometimes hidden.

In fact, the data I have to filter are :

  • Frame, a list of the frame number. At the indice [i], I have the frame number corresponding to the X[i] and Y[i]
  • X, a list of the X coordinates
  • Y, a list of the Y coordinates

For instance, I have this kind of list :

  • Frame = [15, 90, 165, 180, 195, 210, 225, 300, 315, 375 ,405]
  • X = [395, 487, 389, 389, 358, 382, 373, 389, 397, 403, 446]
  • Y = [167, 211, 166, 173, 180, 185, 191, 223, 241, 231, 238]

This is the king of movement I get, as you can see, I need to filter the high frequency.

And now my problem : Even if I have some basics in filtering and coding, I don't know how to do it, and which library to use. I've read that scipy should have all the required function, but I don't know which one to use, and how.

I'm not sure, but I think I should do something like this :

  • Fourrier transformation
  • lowpass filtering
  • Inverse transformation

Could you please tell me if I'm right, and point me in the right direction for the coding part ?

Thanks for the help,

Mathieu

1
pythonscipyfrequencylowpass-filter
From your image I guess the chaotic and sometimes stopping behavior comes from observing an actual living thing (a mouse/souris). Maybe add such information so that people can have a better idea of what you're trying to achieve. – CodeMonkey
It is indeed a mice. As I explained, I can't change the fact that the data are chaotic, but I can erase all the little disturbing movement and focus on the general circular trajectory with a low-pass filter, – Mathieu
Yes, I was just saying it's better to state the whole problem, maybe someone else on here is observing mice (not me), but doesn't understand French. They could help you out much more easily. – CodeMonkey

1 Answers

0
votes

Before you delve into Fourier transforms, you could just apply a first or second order low-pass filter. You could first linearly interpolate your data, so that you can have a constant 2Hz frequency. Then you can apply a first order low pass filter to the data points.

y_k = a * x_k + (1-a) * y_km1, a in [0,1]

x_k are your observations, and y_k is your filtered estimate.

Then if this first prototype yields some useful results, you might be able to use some physical model to get a better estimator. A Kalman filter could make better use of your underlying physical reality. But for this you'd first need an idea how to model physical reality.

https://en.wikipedia.org/wiki/Kalman_filter

Here you can maybe also find a more close example in terms of tracking movements in computer vision: http://www.diss.fu-berlin.de/docs/servlets/MCRFileNodeServlet/FUDOCS_derivate_000000000473/2005_12.pdf