Regularised Diffusion-Shock Inpainting.

We introduce regularised diffusion-shock (RDS) inpainting as a modification of diffusion-shock inpainting from our SSVM 2023 conference paper. RDS inpainting combines two carefully chosen components: homogeneous diffusion and coherence-enhancing shock filtering. It benefits from the complementary synergy of its building blocks: The shock term propagates edge data with perfect sharpness and directional accuracy over large distances due to its high degree of anisotropy.

Connections Between Numerical Algorithms for PDEs and Neural Networks.

We investigate numerous structural connections between numerical algorithms for partial differential equations (PDEs) and neural architectures. Our goal is to transfer the rich set of mathematical foundations from the world of PDEs to neural networks. Besides structural insights, we provide concrete examples and experimental evaluations of the resulting architectures.

Designing rotationally invariant neural networks from PDEs and variational methods.

Partial differential equation models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the input results in a corresponding rotation of the output, which is desirable in applications such as image analysis. Convolutional neural networks (CNNs) do not share this property, and existing remedies are often complex.

Hamster organotypic modeling of SARS-CoV-2 lung and brainstem infection.

SARS-CoV-2 has caused a global pandemic of COVID-19 since its emergence in December 2019. The infection causes a severe acute respiratory syndrome and may also spread to central nervous system leading to neurological sequelae. We have developed and characterized two new organotypic cultures from hamster brainstem and lung tissues that offer a unique opportunity to study the early steps of viral infection and screening antivirals.

Robustness of brain tumor segmentation.

The segmentation of brain tumors is one of the most active areas of medical image analysis. While current methods perform superhuman on benchmark data sets, their applicability in daily clinical practice has not been evaluated. In this work, we investigate the generalization behavior of deep neural networks in this scenario.