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 s_{0}. 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

s_{i}=s_{0}^{.}(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

s

(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 s

(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 s

(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 s

(If you click on the image you will see the movie representing the focusing strategy)

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