Revisiting Horn and Schunck: Interpretation as Gauss-Newton Optimisation

In this paper we revisit the Horn and Schunck optical flow method [1], and focus on its interpretation as Gauss-Newton optimisation. We explicitly demonstrate that the standard incremental version of the Horn and Schunck (HS) method1 is equivalent to Gauss-Newton (GN) optimisation of the non-linearised energy, consisting of the sum of squared differences (SSD) criterion and diffusion regularisation. The formulation of incremental Horn and Schunck as Gauss-Newton optimisation has the following advantages. • The proposed interpretation reveals that the incremental HS minimises a non-linearised energy. This affects one of the major points of criticism, which is that HS is applicable only for small displacements, since it minimises a linearised energy. This common misapprehension is presumably caused since many works based on HS do not state explicitly the overall energy, but only the linearised approximations of the energy, which are used in every iteration. • Much simpler formulation and derivation of the HS method become possible please compare Figs. 1 and 2. • Embedding the formulation in the well-understood non-linear leastsquares (NLSQ) optimisation framework provides insight into the behaviour of the method.