Fusing motion and color in particle filter

Question

I am trying to implement particle filter to track a car bounded by a box.

First i used color histogram as my likelihood function and implemented PF, where i was using the bhattacharya distance to get weights.

Later I used motion technique, In which i am subtracting the consecutive images, and then finding the contour in the image, which will be the object to be tracked(Camera is static), and I am using the gaussian distribution as the likelihood function to get weights and I have applied PF to it. Now I want to fuse both the techniques in one and use Particle filter .

How can i do it? I tried to search online, But I couldn't find any nice explanation or material.

Answer 1

If you can make the assumption that the two observations are independent then the the likelihood function you need is just the product of the two likelihood functions.

If for particle x, the likelihood of it in terms of the colour distribution is p(z_c|x) and the likelihood of it in terms of the motion contour is p(z_m|x) then the likeliood of both observations combined is

 p(z|x)
=p(z_c,z_m|x)
=p(z_m|z_c,x)p(z_c|x)
=p(z_c|z_m,x)p(z_m|x)

With the assumption of independence this becomes:

=p(z_c|x)p(z_m|x)

So just calculate the likelihoods as you have been doing and multiply them.

If you would rather not make this assumption then you need to specify p(z_m|z_c,x) or p(z_c|z_m,x).