Optical Flow Estimation with Large Displacements: A Temporal Regularizer

The aim of this work is to propose a model for computing the optical flow in a sequence of images with a spatio–temporal regularizer explicitly designed for large displacements. We study the introduction of a temporal regularizer that expands the information beyond two consecutive frames. We propose to decouple the spatial and temporal regularizing terms to avoid an incongruous formulation between the data and smoothness term. We use the large optical flow constraint equation in the data term, the Nagel–Enkelmann operator for the spatial smoothness term and a newly designed temporal regularization. Our model is based on an energy functional that yields a partial differential equation (PDE). This PDE is embedded into a multipyramidal strategy to recover large displacements. A gradient descent technique is applied at each scale to reach the minimum. The numerical experiments show that thanks to this regularizer the results are more stable and accurate.