Appendix: Scene Flow Implementation Using Euler–Lagrange Equations

Abstract

Scene flow and the scene flow estimates have been introduced in Chap. 4. They are computed by minimizing an energy functional consisting of a data term and a smoothness term. This can be done by either using the refinement optical flow algorithm or using the calculus of variations, namely solving the associated Euler–Lagrange equations. In this chapter we outline step by step how the scene flow energy is minimized by calculus of variations, including the Euler–Lagrange equations and a multi-scale nested fixed point iteration scheme. In the second part of the chapter we provide helpful implementation details and show pseudo code of our implementation. The pseudo code is structured such that the implementation can be conducted on the CPU as well as on the GPU employing its parallel processing capabilities.