Question about paper's equation (17). about optical-flow-filter HOT 5 CLOSED

I think I miss understand...

from optical-flow-filter.

Hi, did you solve the issue yourself?

from optical-flow-filter.

Not really ...

I have closed it because I traced the code and found that it just implements equation (17), so the equation in your paper must be right.

I think ^h\Delta\Phi should be ^h\Phi because:

in equation (12) is exactly same as brightness constancy constraint on wiki:

but equation (17) do not use the full flow... so I can't understand the equation.

If you can explain it to me, I will be super thankful.

Thanks for your help!

from optical-flow-filter.

The shape of Eq. (17) has to do with the filtering nature of the algorithm and the pyramidal structure. I will use Fig. (2) for my explanation.

The simplest filter loop (Fig 2.a) is at top level H-1. There, the full optical flow is predicted (Eq. 8) and estimated (Eq. 12), and the estimation equation is indeed the brightness constancy constraint plus a regularization term.

At lower pyramid levels (Fig 2.b), the first step is to compute the full flow for level h. This ^h\Phi^k is used to predict the values of the image and delta flow before the new measurements at time k+1 arrive. Notice that is not the image at previous time step, but something closer to . Under the brightness constancy constraint, any difference between the image at time k+1 and can be attributed to some small displacement which is what we want to calculate in the estimation stage (Eq 17).

I hope this helps.

from optical-flow-filter.

I'm closing this issue now.

from optical-flow-filter.