Nonlinear Evolutionary PDEBased Refinement of Optical Flow
Abstract
The goal of this paper is to propose two nonlinear variational models for obtaining a refined motion estimation from an image sequence. Both the proposed models can be considered as a part of a generalized framework for an accurate estimation of physicsbased flow fields such as rotational and fluid flow. The first model is novel in the sense that it is divided into two phases: the first phase obtains a crude estimate of the optical flow and then the second phase refines this estimate using additional constraints. The correctness of this model is proved using an Evolutionary PDE approach. The second model achieves the same refinement as the first model, but in a standard manner, using a single functional. A special feature of our models is that they permit us to provide efficient numerical implementations through the firstorder primaldual ChambollePock scheme. Both the models are compared in the context of accurate estimation of angle by performing an anisotropic regularization of the divergence and curl of the flow respectively. We observe that, although both the models obtain the same level of accuracy, the twophase model is more efficient. In fact, we empirically demonstrate that the singlephase and the twophase models have convergence rates of order $O(1/N^2)$ and $O(1/N)$ respectively.
 Publication:

arXiv eprints
 Pub Date:
 January 2021
 arXiv:
 arXiv:2102.00487
 Bibcode:
 2021arXiv210200487D
 Keywords:

 Computer Science  Computer Vision and Pattern Recognition;
 Mathematics  Analysis of PDEs;
 35A15;
 35J47;
 35Q68