Question on tracking a moving ball using Kalman filter

Question

I want to learn to track a moving ball using Kalman filter. Although many tutorial are available, I still have some questions.

1. If we can extract the ball in each frame of the video sequence, we will know the position of the ball. Then, why do we need to use Kalman fiter anymore? What is the job of Kalman filter here?

2. Kalman filter: x(k+1) = A.x(k) + B.u(k) + noise

                 y(k) = C.x(k) + noise
   

Then, how do we define A, B, C ? suppose we want to track the moving ball?

3 . If we know the previous state x(k-1) and the measurement of the current state y(k), we can compute the estimated state. What is the "measurement" in case of tracking the moving ball?

Answer 1

well basically you use tracking method to follow the ball in your scene. You'd still have to detect the ball in each timestep.

(1)

Assume you come to a point where another ball comes into the scene. So you need to find a method to identify each ball. Make it worse and even let them cross each other or have obstacles in the way which might hide the ball for a little while.

Your tracking method (i.e. Kalman filter) will then continue its movement on the estimated trajectory, based on how the ball has moved before.

So if you just want to know where the ball is in each frame you don't need a tracking method, but if yo uwant to identify and follow one ball you'd need a tracker, i.e. a Kalman filter or for multi-object tracking I'd prefer a Particle Filter (http://en.wikipedia.org/wiki/Particle_Filter).

(2)

Can't help you here right now since I am not too far into the Kalman Filter right now. But basically A should be the transition matrix from step x(t-1) to x(t) and B should be the reference model. But as I've said if its likely you get more than one ball you might wanna have a look at the particle filter.

(3)

The measurement would be the position you measured on you image. Basically the midpoint of your ball. You'd use this measurement to correct the estimated path. So basically you compare the position the ball should be at at current timestep (depending on it's former movement) with it's actual position.

I hope that helps... if not, keep asking...

Answer 2

I will answer your questions one by one.

1. The Kalman filter is only used for estimation, it means reducing mistakes. When you are just tracking a single target, such as a ball, if you can detemine the position of the ball in each frame of the image, I think it is not necessary to use Kalman filter. However, in multi-target tracking ,if you need to match the same target in two consecutive frames, using Kalman filter can reduce mistakes.

2. For the principle of Kalman filter, I am not very clear.

3. I think "measurement" is the detection of the moving target in the current frame. The detected parameters include the target's centroid position and contour size.

These are my personal opinion. If there are anything wrong, I hope to be corrected.