Convective regularization for optical flow

TL;DR

This paper introduces a novel regularization term based on convective acceleration for optical flow, which better captures object motion and preserves edges, improving upon traditional quadratic models.

Contribution

It proposes using the nonconvex functional of convective acceleration as a regularizer in optical flow, demonstrating its edge-preserving and combined spatial-temporal benefits.

Findings

The convective acceleration regularizer acts as both spatial and temporal regularizer.

It has intrinsic edge-preserving properties.

Experimental results show improvements over basic quadratic models.

Abstract

We argue that the time derivative in a fixed coordinate frame may not be the most appropriate measure of time regularity of an optical flow field. Instead, for a given velocity field $v$ we consider the convective acceleration $v_t + \nabla v v$ which describes the acceleration of objects moving according to $v$. Consequently we investigate the suitability of the nonconvex functional $\|v_t + \nabla v v\|^2_{L^2}$ as a regularization term for optical flow. We demonstrate that this term acts as both a spatial and a temporal regularizer and has an intrinsic edge-preserving property. We incorporate it into a contrast invariant and time-regularized variant of the Horn-Schunck functional, prove existence of minimizers and verify experimentally that it addresses some of the problems of basic quadratic models. For the minimization we use an iterative scheme that approximates the original nonlinear problem with a sequence of linear ones. We believe that the convective acceleration may be gainfully introduced in a variety of optical flow models.