Lucas-Kanade-Algorithm in 1D
Ok, get the solution, the sigmoid-funtion should be updated during the iterations:

x0 = 0
v = 0
# now starting with newton-method iterations
for i=1:10
    I_t = σ(x0 + v) - g(x0) # temporal derivative !!! sigmoid-function should be updatetd here
    I_x = dσ(x0)  # spatial derivative does not change
    v = v - (I_t/I_x)
    print("$(v) \n")
end