Monocular, Boundary-Preserving Joint Recovery of Scene Flow and Depth

Variational joint recovery of scene flow and depth from a single image sequence, rather than from a stereo sequence as others required, was investigated in Mitiche et al. (2015) using an integral functional with a term of conformity of scene flow and depth to the image sequence spatiotemporal variations, and L2 regularization terms for smooth depth field and scene flow. The resulting scheme was analogous to the Horn and Schunck optical flow estimation method, except that the unknowns were depth and scene flow rather than optical flow. Several examples were given to show the basic potency of the method: it was able to recover good depth and motion, except at their boundaries because L2 regularization is blind to discontinuities which it smooths indiscriminately. The method that we study in this paper generalizes to L1 regularization the formulation of Mitiche et al. (2015) so that it computes boundary-preserving estimates of both depth and scene flow. The image derivatives, which appear as data in the functional, are computed from the recorded image sequence also by a variational method, which uses L1 regularization to preserve their discontinuities. Although L1 regularization yields non-linear Euler–Lagrange equations for the minimization of the objective functional, these can be solved efficiently. The advantages of the generalization, namely, sharper computed depth and three-dimensional motion, are put in evidence in experimentation with real and synthetic images, which shows the results of L1 versus L2 regularization of depth and motion, as well as the results using L1 rather than L2 regularization of image derivatives.