OpticalFlow: eigenvalues cases

Question

I try to implement Lucas Kanade algorithm Matlab you can see here under Algorithm .

I don't understand after eigenvalues are computed in the case 2 :

Case 2: $λ_1≥τ$ , and , $λ_2<τ$

$A$ is singular (non invertible), the gradient flow is normalized to calculate $ u$ and $v$.

I don't understand what do they mean by gradient flow?

Answer 1

The answer is Page 7 here with 2 possibilties:

• from gradient constraint:

$s(x, t) = \dfrac{-I_{t}(x,t)}{\left\lVert\nabla I(x,t) \right\rVert}$, $n(x,t) = \dfrac{\nabla I(x,t)}{\left\lVert\nabla I(x,t) \right\rVert}$ with $\nabla I(x,t) = (I_x(x,t), I_y(x,t))^{T}$

Matlab : $(u, v)^T = s(x,t) \vec{n}$

• from "this" LS (least square) minimisation which is more sophisicated and might not be the implementation from matlab.