Dense Multi-frame Optic Flow for Non-rigid Objects Using Subspace Constraints

In this paper we describe a variational approach to computing dense optic flow in the case of non-rigid motion. We optimise a global energy to compute the optic flow between each image in a sequence and a reference frame simultaneously. Our approach is based on subspace constraints which allow to express the optic flow at each pixel in a compact way as a linear combination of a 2D motion basis that can be pre-estimated from a set of reliable 2D tracks. We reformulate the multi-frame optic flow problem as the estimation of the coefficients that multiplied with the known basis will give the displacement vectors for each pixel. We adopt a variational framework in which we optimise a nonlinearised global brightness constancy to cope with large displacements and impose homogeneous regularization on the multi-frame motion basis coefficients. Our approach has two strengths. First, the dramatic reduction in the number of variables to be computed (typically one order of magnitude) which has obvious computational advantages and second, the ability to deal with large displacements due to strong deformations. We conduct experiments on various sequences of non-rigid objects which show that our approach provides results comparable to state of the art variational multi-frame optic flow methods.