The Method of Lucas and Kanade

 

The central point of this method is a model of constant velocities in a small spatial neighbourhood . Within this neighbourhood the following term is minimised:

Here, is a weighting function that favours the center part of .

With the abreviations

we obtain an implicit solution,

and, when is nonsingular, a closed form solution,

The matrix is singular when the gradient is constant in one or more directions over the neighbourhood . This can be interpreted as an instance of the ``aperture problem''.

The velocity estimates for most of the differential methods are more accurate for small displacements. Therefore, we also implemented an iterative version of this method where successive images are shifted by the amount of flow calculated in previous iterations in order to compensate the movements in the image and thereby yield more accurate results in the following iterations.