# Robust Reference Frame Extraction from Unsteady 2D Vector Fields with Convolutional Neural Networks

ETH Zurich

Above: We developed a novel CNN-based reference frame extraction algorithm that is trained to handle inputs with noise and resampling artifacts. Compared to a linear reference frame optimization [GGT17], our method is more robust to artifacts. The input vector field (w/ and w/o noise) is shown on the left, and the extraction of vortex centers (orange and yellow), compared to a ground truth (blue) is shown on the right. By combining filtering and reference frame extraction via CNNs, vortex extraction becomes more robust. Note that in the experiment above, the CNN has not seen the cylinder flow during training. In fact, it only trained on a synthetic data base that we introduce in the paper.

## abstract

Robust feature extraction is an integral part of scientific visualization. In unsteady vector field analysis, researchers recently directed their attention towards the computation of near-steady reference frames for vortex extraction, which is a numerically challenging endeavor. In this paper, we utilize a convolutional neural network to combine two steps of the visualization pipeline in an end-to-end manner: the filtering and the feature extraction. We use neural networks for the extraction of a steady reference frame for a given unsteady 2D vector field. By conditioning the neural network to noisy inputs and resampling artifacts, we obtain numerically stabler results than existing optimization-based approaches. Supervised deep learning typically requires a large amount of training data. Thus, our second contribution is the creation of a vector field benchmark data set, which is generally useful for any local deep learning-based feature extraction. Based on Vatistas velocity profile, we formulate a parametric vector field mixture model that we parameterize based on numerically-computed example vector fields in near-steady reference frames. Given the parametric model, we can efficiently synthesize thousands of vector fields that serve as input to our deep learning architecture. The proposed network is evaluated on an unseen numerical fluid flow simulation.

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Paper | Slides## Bibtex

```
@article{kim19robust,
author = {Kim, Byungsoo and G{\"u}nther, Tobias},
title = {{Robust Reference Frame Extraction from Unsteady 2D Vector Fields with Convolutional Neural Networks}},
journal = {Computer Graphics Forum (Proc. EuroVis)},
year = {2019},
volume = {38},
number = {3},
}
```