In this work, we present a method to vectorize raster images of line art. Inverting the rasterization procedure is inherently ill‐conditioned, as there exist many possible vector images that could yield the same raster image. However, not all of these vector images are equally useful to the user, especially if performing further edits is desired. We therefore define the problem of computing an instance segmentation of the most likely set of paths that could have created the raster image. Once the segmentation is computed, we use existing vectorization approaches to vectorize each path, and then combine all paths into the final output vector image. To determine which set of paths is most likely, we train a pair of neural networks to provide semantic clues that help resolve ambiguities at intersection and overlap regions. These predictions are made considering the full context of the image, and are then globally combined by solving a Markov Random Field (MRF). We demonstrate the flexibility of our method by generating results on character datasets, a synthetic random line dataset, and a dataset composed of human drawn sketches. For all cases, our system accurately recovers paths that adhere to the semantics of the drawings.

We propose an end‐to‐end trained neural network architecture to robustly predict the complex dynamics of fluid flows with high temporal stability. We focus on single‐phase smoke simulations in 2D and 3D based on the incompressible Navier‐Stokes (NS) equations, which are relevant for a wide range of practical problems. To achieve stable predictions for long‐term flow sequences with linear execution times, a convolutional neural network (CNN) is trained for spatial compression in combination with a temporal prediction network that consists of stacked Long Short‐Term Memory (LSTM) layers. Our core contribution is a novel latent space subdivision (LSS) to separate the respective input quantities into individual parts of the encoded latent space domain. As a result, this allows to distinctively alter the encoded quantities without interfering with the remaining latent space values and hence maximizes external control. By selectively overwriting parts of the predicted latent space points, our proposed method is capable to robustly predict long‐term sequences of complex physics problems, like the flow of fluids. In addition, we highlight the benefits of a recurrent training on the latent space creation, which is performed by the spatial compression network. Furthermore, we thoroughly evaluate and discuss several different components of our method.

This paper introduces the Instructed Glacier Model (IGM) – a model that simulates ice dynamics, mass balance and its coupling to predict the evolution of glaciers, icefields or ice sheets. The novelty of IGM is that it models the ice flow by a Convolutional Neural Network, which is trained from data generated with hybrid SIA + SSA or Stokes ice flow models. By doing so, the most computationally demanding model component is substituted by a cheap emulator. Once trained with representative data, we demonstrate that IGM permits to model mountain glaciers up to 1000 × faster than Stokes ones on Central Processing Units (CPU) with fidelity levels above 90% in terms of ice flow solutions leading to nearly identical transient thickness evolution. Switching to the GPU often permits additional significant speed-ups, especially when emulating Stokes dynamics or/and modelling at high spatial resolution. IGM is an open-source Python code which deals with two-dimensional (2-D) gridded input and output data. Together with a companion library of trained ice flow emulators, IGM permits user-friendly, highly efficient and mechanically state-of-the-art glacier and icefields simulations.

Artistically controlling fluids has always been a challenging task. Optimization techniques rely on approximating simulation states towards target velocity or density field configurations, which are often handcrafted by artists to indirectly control smoke dynamics. Patch synthesis techniques transfer image textures or simulation features to a target flow field. However, these are either limited to adding structural patterns or augmenting coarse flows with turbulent structures, and hence cannot capture the full spectrum of different styles and semantically complex structures. In this paper, we propose the first Transport-based Neural Style Transfer (TNST) algorithm for volumetric smoke data. Our method is able to transfer features from natural images to smoke simulations, enabling general content-aware manipulations ranging from simple patterns to intricate motifs. The proposed algorithm is physically inspired, since it computes the density transport from a source input smoke to a desired target configuration. Our transport-based approach allows direct control over the divergence of the stylization velocity field by optimizing incompressible and irrotational potentials that transport smoke towards stylization. Temporal consistency is ensured by transporting and aligning subsequent stylized velocities, and 3D reconstructions are computed by seamlessly merging stylizations from different camera viewpoints.

Remote magnetic navigation is used for the manipulation of untethered micro and nanorobots, as well as tethered magnetic surgical tools for minimally invasive medicine. Mathematical modeling of the magnetic fields generated by magnetic navigation systems is a fundamental task in the control of such tools for biomedical applications. We describe and compare several existing and newly developed methods for representations of continuous magnetic fields using interpolation in the context of remote magnetic navigation. Clinical-scale electromagnetic navigation systems feature nonlinear magnetization and magnetization interactions between electromagnets, which renders accurate magnetic field modeling challenging. We first introduce a method that can adapt existing linear models to correct for nonlinear magnetization, with similar performance to the current state-of-the-art nonlinear model. Furthermore, we present a method based on convolutional neural networks that is able to improve on the state-of-the-art method by a factor of 5.4.