Abstract: The problem of finding an interpolating image between two given images in an image sequence is considered. An important application is video compression where currently techniques based on motion estimation are used. We formulate the problem as an optimal control problem governed by a transport equation, i.e. we aim at finding a flow field which transports the first image as close as possible to the second image. 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 the space of functions of bounded variation. 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. Especially, our model can deal with large displacements. This is joint work with Kanglich Chen, University Bremen.