# Understanding Farneback Displacement Estimation

I am having some trouble in my attempt to understand some of the operations in the Farneback optical flow algorithm, and i would really appriciate if somebody could help me a bit along the way (and i hope i am able to express myself properly).

1. I have interpret the approximation part of the algorithm as following [seen in equation (1) to (3)]: A local signal model for each image pixel is found by approximating a quadratic polynomial, based on the pixel neighborhood. The approximated coefficients are found in A, b and c - while x = (x,y) is a running variable? The result is that the local signal model is a bivariate quadratic curve?

2. From the part 3.1 First Attempt: I am having trouble understanding the term A(x,y) = [A1(x,y) + A2(x,y)]/2. Is the (x,y) index related to the pixel coordinate where the expansion coefficients belong? I would have expected that A2 was belonging to an local signal model that was identical, but displaced, with respect to the local signal model which has the A1 expansion coefficient. I read equation (10) as: "Find the expansion coefficient A1 to pixel (1,1) in image 1, add it with expansion coefficient A2 to pixel (1,1) in image 2 - and divide by 2"?

3. The use of indexing in equation (10) to (13) is also making me insecure if we are talking about pixel coordinates. The same variables is used in equation (1), but i assume that this is running variables that is used to make the polynomial?

Kind regards VegardB