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  1. Extreme wind phenomena play a crucial role in the efficient operation of wind farms for renewable energy generation. However, existing detection methods are computationally expensive and limited to specific coordinates. In real-world scenarios, understanding the occurrence of these phenomena over a large area is essential. Therefore, there is a significant demand for a fast and accurate approach to forecast such events. In this paper, we propose a novel method for detecting wind phenomena using topological analysis, leveraging the gradient of wind speed or critical points in a topological framework. By extracting topological features from the wind speed profile within a defined region, we employ topological distance to identify extreme wind phenomena. Our results demonstrate the effectiveness of utilizing topological features derived from regional wind speed profiles. We validate our approach using high-resolution simulations with the Weather Research and Forecasting model (WRF) over a month in the US East Coast. 
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    Free, publicly-accessible full text available October 22, 2024
  2. This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral component of visualization and analysis pipelines. Although not all topological features present in data are of equal importance. To date, the default definition of feature importance is often assumed and fixed. This work shows how proven explainable deep learning approaches can be adapted for use in topological classification. In doing so, it provides the first technique that illuminates what topological structures are important in each dataset in regards to their class label. In particular, the approach uses a learned metric classifier with a density estimator of the points of a persistence diagram as input. This metric learns how to reweigh this density such that classification accuracy is high. By extracting this weight, an importance field on persistent point density can be created. This provides an intuitive representation of persistence point importance that can be used to drive new visualizations. This work provides two examples: Visualization on each diagram directly and, in the case of sublevel set filtrations on images, directly on the images themselves. This work highlights 
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    Free, publicly-accessible full text available October 22, 2024
  3. This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral component of visualization and analysis pipelines. Although not all topological features present in data are of equal importance. To date, the default definition of feature importance is often assumed and fixed. This work shows how proven explainable deep learning approaches can be adapted for use in topological classification. In doing so, it provides the first technique that illuminates what topological structures are important in each dataset in regards to their class label. In particular, the approach uses a learned metric classifier with a density estimator of the points of a persistence diagram as input. This metric learns how to reweigh this density such that classification accuracy is high. By extracting this weight, an importance field on persistent point density can be created. This provides an intuitive representation of persistence point importance that can be used to drive new visualizations. This work provides two examples: Visualization on each diagram directly and, in the case of sublevel set filtrations on images, directly on the images themselves. This work highlights real-world examples of this approach visualizing the important topological features in graph, 3D shape, and medical image data. 
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    Free, publicly-accessible full text available October 22, 2024
  4. Structured illumination microscopy (SIM) reconstructs optically-sectioned images of a sample from multiple spatially-patterned wide-field images, but the traditional single non-patterned wide-field images are more inexpensively obtained since they do not require generation of specialized illumination patterns. In this work, we translated wide-field fluorescence microscopy images to optically-sectioned SIM images by a Pix2Pix conditional generative adversarial network (cGAN). Our model shows the capability of both 2D cross-modality image translation from wide-field images to optical sections, and further demonstrates potential to recover 3D optically-sectioned volumes from wide-field image stacks. The utility of the model was tested on a variety of samples including fluorescent beads and fresh human tissue samples.

     
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  5. Persistence diagrams have been widely used to quantify the underlying features of filtered topological spaces in data visualization. In many applications, computing distances between diagrams is essential; however, computing these distances has been challenging due to the computational cost. In this paper, we propose a persistence diagram hashing framework that learns a binary code representation of persistence diagrams, which allows for fast computation of distances. This framework is built upon a generative adversarial network (GAN) with a diagram distance loss function to steer the learning process. Instead of using standard representations, we hash diagrams into binary codes, which have natural advantages in large-scale tasks. The training of this model is domain-oblivious in that it can be computed purely from synthetic, randomly created diagrams. As a consequence, our proposed method is directly applicable to various datasets without the need for retraining the model. These binary codes, when compared using fast Hamming distance, better maintain topological similarity properties between datasets than other vectorized representations. To evaluate this method, we apply our framework to the problem of diagram clustering and we compare the quality and performance of our approach to the state-of-the-art. In addition, we show the scalability of our approach on a dataset with 10k persistence diagrams, which is not possible with current techniques. Moreover, our experimental results demonstrate that our method is significantly faster with the potential of less memory usage, while retaining comparable or better quality comparisons. 
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  6. G., Renata Raidou ; Sommer, Björn ; W., Torsten Kuhlen ; Krone, Michael ; Schultz, Thomas ; Wu, Hsiang-Yun (Ed.)
    We introduce a novel multi-modal 3D image registration framework based on 3D user-guided deformation of both volume's shape and intensity values. Being able to apply deformations in 3D gives access to a wide new range of interactions allowing for the registration of images from any acquisition method and of any organ, complete or partial. Our framework uses a state of the art 3D volume rendering method for real-time feedback on the registration accuracy as well as the image deformation. We propose a novel methodological variation to accurately display 3D segmented voxel grids, which is a requirement in a registration context for visualizing a segmented atlas. Our pipeline is implemented in an open-source software (available via GitHub) and was directly used by biologists for registration of mouse brain model autofluorescence acquisition on the Allen Brain Atlas. The latter mapping allows them to retrieve regions of interest properly identified on the segmented atlas in acquired brain datasets and therefore extract only high-resolution images of those areas, avoiding the creation of images too large to be processed. 
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  7. The persistence diagram (PD) is an important tool in topological data analysis for encoding an abstract representation of the homology of a shape at different scales. Different vectorizations of PD summary are commonly used in machine learning applications, however distances between vectorized persistence summaries may differ greatly from the distances between the original PDs. Surprisingly, no research has been carried out in this area before. In this work we compare distances between PDs and between different commonly used vectorizations. Our results give new insights into comparing vectorized persistence summaries and can be used to design better feature-based learning models based on PDs 
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  8. null (Ed.)