Stephan Didas is a member of the Fraunhofer-Institute of Techno- and Business-Mathematics.
Title: Higher Order Evolution Equations for Adaptive Image Simplification
Abstract:
Nonlinear diffusion filtering and regularisation methods are established tools for adaptive image simplification. Nevertheless, they show some limitations in practice if the image data is not piecewise constant. This drawback can be circumvented by using higher derivative orders in regularisation or PDE-based methods. With these methods, one can obtain piecewise polynomial approximations with higher degree of the given data. This approach can not only be used for grey-value images, but also for tensor-valued data. In this setting, there are some interesting open questions, for example concerning a suitable stability notion of methods for tensor data. Besides this application, we introduce higher order anisotropic filtering methods that generalise classical anisotropic edge-enhancing diffusion. This requires a generalisation of the well-known structure-tensor concept to higher derivative orders. Practical examples show that these methods are able to enhance ridges in image data, for example.
Contact: Jan Modersitzki
