Optical flow estimation under sparsity constraints

Emmanuel Froustey

Semester Project

Section of Mathematics, EPFL

January 2013

Abstract

The aim of this project was to develop optical flow estimation models in the framework of non-quadratic optimization. Physical constraints were imposed on the optical flow, such as sparsity of the curl or the divergence. These constraints occur for instance when observing irrotational or incompressible fluid flows.
The state-of-the art method to compute optical flow uses total variation regularization; but to take the physical constraints of the flow into account, we introduced and implemented new regularizers such as the L1 norm of curl and divergence. Applications of the developed optical flow methods include particle image velocimetry.

Fig1.gif Fig1. Example of curl-free motion Fig2.png Fig2. The ground truth optical flow associated to Fig1. Hue indicates orientation, saturation intensity.