Optical Flow Computation
by
L.Alvarez, J.Weickert and J.Sánchez

We use a modified version of  the Nagel and Enkelmann (1986) classical method for computation of the optical flow.
We avoid convergence to irrelevant local minima by embedding our method in a linear scale-space framework and using
a focusing strategy from coarse to fine scales. Our method avoids linearizations in the optical flow constraint, and it can
recover displacement fields that are far beyond the rypical 1 pixel limits that are characteristic for many differential
methods for optical flow recovery. We use a robust and efficient implicit numerical scheme to implement the method.
Ths resulting algorithm depends mainly on the next 4 parameters:

(1) The initial scale s0. It represents the standard deviation of the gaussian that we apply to the images in order
to init the focusing strategy.
(2) The decay ratio h. It represents the way that we choose the different scales in the focusing strategy. That is
si=s0.(h)i.
(3) The isotropy fraction s. It represents the balance in the Nagel operator, between the isotropic and anisotropic
diffusion.
(4) The regularization parameter a. It represents the balance between the optical flow constraint and the smoothness
of the flow.

For more details see the paper Reliable Estimation of Optical Flow for Large Displacements

Next we present several experiments to illustrate de algorithm. In you want to do your own experiments using our algorithm, you
can get here the Software with the algorithm implemented in different computer arquitectures. Figure 1. We present the computed flow (up) for a synthetic sequence (down) given by 4 squares
which move in different directions and with different velocities. The parameters are
s0=10., h=0.95, s=0.1 and  a=0.6.
(If you click on the image you will see the movie representing the focusing strategy) Figure 2. We present the computed flow (up) for a synthetic sequence (down) given in the Barron et al. survey paper.
The parameters are s0=10., h=0.95, s=0.1 and  a=0.6.
(If you click on the image you will see the movie representing the focusing strategy) Figure 3. We present the computed flow (up) for famous taxi sequence (down).
The parameters are s0=10., h=0.95, s=0.1 and  a=0.6.
(If you click on the image you will see the movie representing the focusing strategy) Figure 4. We present the computed flow (up) for famous Yosemite sequence (down).
The parameters are s0=5., h=0.95, s=0.1 and  a=0.6.
(If you click on the image you will see the movie representing the focusing strategy)

lalvarez@dis.ulpgc.es / updated October 1, 1999