Python Library For Computing Spatial Derivatives Of Optical Flow

I'm trying to compute a differential image velocity invariants (e.g. curl, divergence, deformation, etc) from a video using OpenCV in Python. To do that, I need to compute the spat

Solution 1:

This is the way I see it (I've worked with optical flow a little bit):

You want to compute the individual partial derivatives of the optical flow field; one for the x direction, and one for the y.

I'd attempt to solve the problem like so:

• Split your flow array/matrix into two matrices: x and y flow.
• For each of those, you could go the naive route and just do a simple difference: derivative = current_state - last_state. But this approach is very messy, as the derivative will be sensitive to the slightest bit of error.
• To counter that, you could approximate one chunk of your data points (maybe a whole row?) with a regression curve that is easily differentiable, like a polynomial.

The just differentiate that approximated curve and you're good to go.

You could also just smooth individual matrices and do a naive difference, which should be much faster than approximating data points, but should be more tolerant to error.