Apparaît dans la collection : 2019 - T1 - WS1 - Variational methods and optimization in imaging

In the metamorphosis model the space of images is equipped with a Riemannian metric measuring both the cost of transport of image intensities and the variation of them along motion lines. In this talk a recently introduced variational time discretization to compute discrete geodesics and a discrete exponential map will be reviewed. The classical metamorphosis model considers images as square-integrable functions and thus is non-sensitive to image features such as sharp interfaces or fine texture patterns. To resolve this drawback, we treat images not as intensity maps. Instead, we consider two different approaches based on convolutional neural networks methodology. In an image analysis approach, we use deep CNN features to treat local structures and semantic information and morph images via a morphing in feature space. Alternatively, in an image synthesis approach, we take into account learned rotational invariant kernels for sparse image representation and morph images in the space of this representation. This is joint work with Alexander Effland, Thomas Pock, Erich Kobler.