Separating background and foreground optical flow fields by low-rank and sparse regularization

We present a method for separating background and foreground optical flow fields induced by observer´s egomotion and motion of objects, respectively. Optical flow is a vector field of instantaneous apparent motion computed from successive images. An optical flow field can be assumed as a linear combination with a few basis fields caused by translational and rotational egomotion and a spatially sparse optical flow field by the moving objects. We represent two-dimensional optical flow vectors as complex numbers and stack the fields as columns of a complex matrix. The low-rank component naturally corresponds to the egomotional background optical flow fields and the sparse component captures the moving foreground objects. We show that these components are successfully extracted from optical flow sequences by the robust PCA applied to the complex matrix.