monocular concurrent recovery of structure and motion scene flow

This paper describes a variational method of joint three-dimensional structure and motion scene flow recovery from a single image sequence. A basic scheme is developed by minimizing a functional with a term of conformity of scene flow and depth to the image sequence spatiotemporal variations, and quadratic smoothness regularization terms. The data term follows by re-writing optical velocity in the optical flow gradient constraint in terms of scene flow and depth. As a result, this problem statement is analogous to the classical Horn and Schunck optical flow formulation except that it involves scene flow and depth rather than image motion. When discretized, the Euler-Lagrange equations give a large scale sparse system of linear equations in the unknowns of the scene flow three coordinates and depth. The equations can be ordered in such a way that its matrix is symmetric positive definite such that they can be solved efficiently by Gauss-Seidel iterations. Experiments are shown to verify the scheme’s validity and efficiency.