Image sequence interpolation using optimal control

Abstract

The problem of the generation of an intermediate image between two given images in an image sequence is considered. The problem is formulated as an optimal control problem governed by a transport equation. This approach bears similarities with the Horn \& Schunck method for optical flow calculation but in fact the model is quite different. The images are modelled in $BV$ and an analysis of solutions of transport equations with values in $BV$ is included. Moreover, the existence of optimal controls is proven and necessary conditions are derived. Finally, two algorithms are given and numerical results are compared with existing methods. The new method is competitive with state-of-the-art methods and even outperforms several existing methods.