Related papers: A Topological Similarity Measure between Multi-Fie…
Distance measures play an important role in shape classification and data analysis problems. Topological distances based on Reeb graphs and persistence diagrams have been employed to obtain effective algorithms in shape matching and scalar…
The problem of computing topological distance between two scalar fields based on Reeb graphs or contour trees has been studied and applied successfully to various problems in topological shape matching, data analysis, and visualization.…
A wide range of data that appear in scientific experiments and simulations are multivariate or multifield in nature, consisting of multiple scalar fields. Topological feature search of such data aims to reveal important properties useful to…
A Reeb graph is a graphical representation of a scalar function on a topological space that encodes the topology of the level sets. A Reeb space is a generalization of the Reeb graph to a multiparameter function. In this paper, we propose…
The Reeb space is a fundamental data structure in computational topology that represents the fiber topology of a multi-field (or multiple scalar fields), extending the level set topology of a scalar field. Efficient algorithms have been…
Measuring similarity between complex objects is a fundamental task in many scientific fields. When objects are represented as graphs, graph similarity/distance measures offer a powerful framework for quantifying structural resemblance.…
The Reeb graph of a scalar function defined on a domain gives a topologically meaningful summary of that domain. Reeb graphs have been shown in the past decade to be of great importance in geometric processing, image processing, computer…
In topological data analysis and visualization, topological descriptors such as persistence diagrams, merge trees, contour trees, Reeb graphs, and Morse-Smale complexes play an essential role in capturing the shape of scalar field data. We…
An important operation in geometry processing is finding the correspondences between pairs of shapes. The Gromov-Hausdorff distance, a measure of dissimilarity between metric spaces, has been found to be highly useful for nonrigid shape…
Reeb graphs are a fundamental structure for analyzing the topological and geometric properties of scalar fields. Comparing Reeb graphs is crucial for advancing research in this domain, yet existing metrics are often computationally…
In many applications involving multi-media data, the definition of similarity between items is integral to several key tasks, e.g., nearest-neighbor retrieval, classification, and recommendation. Data in such regimes typically exhibits…
Mapper is an algorithm that summarizes the topological information contained in a dataset and provides an insightful visualization. It takes as input a point cloud which is possibly high-dimensional, a filter function on it and an open…
Estimating a depth map from multiple views of a scene is a fundamental task in computer vision. As soon as more than two viewpoints are available, one faces the very basic question how to measure similarity across >2 image patches.…
Comparison of data representations is a complex multi-aspect problem that has not enjoyed a complete solution yet. We propose a method for comparing two data representations. We introduce the Representation Topology Divergence (RTD),…
The Reeb space, which generalizes the notion of a Reeb graph, is one of the few tools in topological data analysis and visualization suitable for the study of multivariate scientific datasets. First introduced by Edelsbrunner et al., it…
The Reeb graph has been utilized in various applications including the analysis of scalar fields. Recently, research has been focused on using topological signatures such as the Reeb graph to compare multiple scalar fields by defining…
Extracting the relevant information by exploiting the spatial data warehouse becomes increasingly hard. In fact, because of the enormous amount of data stored in the spatial data warehouse, the user, usually, don't know what part of the…
Comparative analysis of scalar fields is an important problem with various applications including feature-directed visualization and feature tracking in time-varying data. Comparing topological structures that are abstract and succinct…
Persistent homology has been devised as a promising tool for the topological simplification of complex data. However, it is computationally intractable for large data sets. In this work, we introduce multiresolution persistent homology for…
Tabular structures are used to present crucial information in a structured and crisp manner. Detection of such regions is of great importance for proper understanding of a document. Tabular structures can be of various layouts and types.…