Optical Flow Example
I have a conceptual doubt in Optical Flow. The brightness constancy constraint states that ∂I/∂x vx + ∂I/∂y vy + ∂I/∂t = 0
The example is a 2*2 image [1 0 ; 0 0] at time t. Now, suppose at time t+1, it is shifted by [a a] pixels (suppose a is fractional and less than 1 ). Then the new image is [(1-a)(1-a) a(1-a) ; (1-a)*a a*a].
Now, if we fit the values in the original equation, Ix = Iy = -1 and It = -2*a + a*a at (1,1). (I have used Ix(x,y) = I(x+1,y) - I(x,y))
which makes ∂I/∂x vx + ∂I/∂y vy + ∂I/∂t = a*a - 4*a. If a is very small, even then it can be approximated to 4*a which is not zero. Help me out.
I have a conceptual doubt in Optical Flow. The brightness constancy constraint states that ∂I/∂x vx + ∂I/∂y vy + ∂I/∂t = 0
The example is a 2*2 image [1 0 ; 0 0] at time t. Now, suppose at time t+1, it is shifted by [a a] pixels (suppose a is fractional and less than 1 ). Then the new image is [(1-a)(1-a) a(1-a) ; (1-a)*a a*a].
Now, if we fit the values in the original equation, Ix = Iy = -1 and It = -2*a + a*a at (1,1). (I have used Ix(x,y) = I(x+1,y) - I(x,y))
which makes ∂I/∂x vx + ∂I/∂y vy + ∂I/∂t = a*a - 4*a. If a is very small, even then it can be approximated to 4*a which is not zero. Help me out.
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