Median variance in background subtraction

Question

I am facing some issues in implementation of the paper Statistical Background Subtraction for a Mobile Observer.

Question 1:

In Section 4.1, it talks about "... the median variance is computed over the entire image from the first components ..."

I am confused what the authors actually mean by this.

According to Stauffer & Grimson's paper Adaptive Background Mixture Models for Real-Time Tracking(1999), for every background model a variance gets initialized (say with value 36) and then it gets updated for each pixel. Should the median of the first model's variance across all the pixels for that frame should be taken?

                  OR

We compute the variance for each pixel based on its history of intensity values of those which belong to the first model and then take median of all these variances.

Question 2:

I am facing difficulty in understanding equation (12) in section 4.1

a) Is 'i' from 1 to H+1? If yes, how does the (H+1)th model fits in the equation?

i) Just after equation (13), P(A_1 | B_(H+1),M) is defined. Shouldn't rho_(H+1) = min(1, N_tot/N_max) instead of max which could make P(A_1 | B_(H+1),M) (-)ve?

ii) For the (H+1)th model should we have P(A_1 | B_(H+1),M) * P(B_(H+1) | N) to P(A_1 | Z,M) for equation (12)?

b) when H=1, does P(A1|Z,M) becomes 1?

My implementation is here.

Please check my trial in the MATLAB files which I have mentioned in my webpage.

Answer 1

Nice breakdown of it here: http://blog.damiles.com/2009/03/the-basics-of-background-substraction/

Its also in the opencv book.

code in opencv2 here: Background subtraction in opencv2

Answer 2

Question 1, first option, "Should the median of first model's variance across all the pixels for that frame be taken?".

Yes, it assumes that the variance of the background pixel is lower than the foreground. So the median of all variances will give acceptable variance for the background.