Related papers: Extracting Complex Topology from Multivariate Func…
Advances in high-performance computing require new ways to represent large-scale scientific data to support data storage, data transfers, and data analysis within scientific workflows. Multivariate functional approximation (MFA) has…
While the strength of Topological Data Analysis has been explored in many studies on high dimensional numeric data, it is still a challenging task to apply it to text. As the primary goal in topological data analysis is to define and…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Topological simplification of scalar and vector fields is well-established as an effective method for analysing and visualising complex data sets. For multi-field data, topological analysis requires simultaneous advances both mathematically…
Surface extraction from implicit neural representations modelling a single class surface is a well-known task. However, there exist no surface extraction methods from an implicit representation of multiple classes that guarantee topological…
This paper introduces progressive algorithms for the topological analysis of scalar data. Our approach is based on a hierarchical representation of the input data and the fast identification of topologically invariant vertices, which are…
Considering the challenges posed by the space and time complexities in handling extensive scientific volumetric data, various data representations have been developed for the analysis of large-scale scientific data. Multivariate functional…
Integrating high-level context information with low-level details is of central importance in semantic segmentation. Towards this end, most existing segmentation models apply bilinear up-sampling and convolutions to feature maps of…
Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description…
Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…
Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of…
Jacobi sets are an important tool to study the relationship between functions. Defined as the set of all points where the function's gradients are linearly dependent, Jacobi sets extend the notion of critical point to multifields. In…
With the emergence of graph databases, the task of frequent subgraph discovery has been extensively addressed. Although the proposed approaches in the literature have made this task feasible, the number of discovered frequent subgraphs is…
Deep Implicit Functions (DIFs) represent 3D geometry with continuous signed distance functions learned through deep neural nets. Recently DIFs-based methods have been proposed to handle shape reconstruction and dense point correspondences…
Digital terrain models (DTMs) are pivotal in remote sensing, cartography, and landscape management, requiring accurate surface representation and topological information restoration. While topology analysis traditionally relies on smooth…
We present a novel method that can learn a graph representation from multivariate data. In our representation, each node represents a cluster of data points and each edge represents the subset-superset relationship between clusters, which…
We propose a new approach, named PolyMapper, to circumvent the conventional pixel-wise segmentation of (aerial) images and predict objects in a vector representation directly. PolyMapper directly extracts the topological map of a city from…
Multi-modality image fusion aims at fusing modality-specific (complementarity) and modality-shared (correlation) information from multiple source images. To tackle the problem of the neglect of inter-feature relationships, high-frequency…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…
We introduce a framework for the reconstruction and representation of functions in a setting where these objects cannot be directly observed, but only indirect and noisy measurements are available, namely an inverse problem setting. The…