Optimal control based image sequence interpolation

This thesis includes my three-year doctoral research in the field of image sequence interpolation. The introduced interpolation methods are mainly based on finding an appropriate optical flow field, with which the objects in an initial image can be “transported” and “warped” to a certain time. To identify the optical flow field the interpolation problem is considered in the framework of optimal control governed by the transport equation. To improve the interpolation quality, the models are introduced so that the edges of the optical flow are preserved, the forward and backward interpolation are locally selected. Basically the smooth version of total variation and the active contours for segmentation are used. In the theoretical part, the solution theory of transport equation is investigated under different settings on the regularity of the optical flow, and applied in the proof of the existence of a minimizer to the associated minimization problems.