Fast Similarity Search in Scalar Fields using Merging Histograms

Saikia, Himangshu; Seidel, Hans‐Peter; Weinkauf, Tino

doi:10.1007/978-3-319-44684-4_7

Cited by 12 publications

(9 citation statements)

References 18 publications

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“…Simple and practical similarity measures that are not metrics have also been studied. Saikia et al [7] propose a measure that compares histograms constructed based on the merge trees. As in the case of bottleneck distance, this measure ignores the topological structure during comparison.…”

Section: Related Workmentioning

confidence: 99%

“…A careful study of similarities and differences between the topology-based representations can lead to meaningful comparisons of the underlying scalar fields. Multiple similarity measures (alternatively comparison measures or distance measures) have been proposed to compare scalar fields and topological structures [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13]. However, most of them describe methods to compare these structures globally.…”

Section: Introductionmentioning

confidence: 99%

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Comparative Analysis of Merge Trees using Local Tree Edit Distance

Sridharamurthy,

Natarajan

2021

Preprint

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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 representations of the scalar fields lead to faster and meaningful comparison. While there are many distance or similarity measures to compare topological structures in a global context, there are no known measures for comparing topological structures locally. While the global measures have many applications, they do not directly lend themselves to fine-grained analysis across multiple scales. We define a local variant of the tree edit distance and apply it towards local comparative analysis of merge trees with support for finer analysis. We also present experimental results on time-varying scalar fields, 3D cryo-electron microscopy data, and other synthetic data sets to show the utility of this approach in applications like symmetry detection and feature tracking.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparative Analysis of Merge Trees using Local Tree Edit Distance

Sridharamurthy,

Natarajan

2021

Preprint

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“…The basic premise of pattern matching is to find regions or features that are similar to a designed pattern or a selected region/feature. Such methods exist for a large variety of data types such as images [Low04], geometry [MPWC13], scalar fields [KWKS11, SSW14, SSW15, TN11, TN13, TN14], vector fields [ES03, HEWK03, BHSH14], and multi‐fields [WSW16]. All of these methods address single time steps only, and are not adequate for finding spatio‐temporal similarities: given a pattern, one may find similar features in a number of time steps, but this neglects any temporal evolution, since a progressively changing feature matches a pattern only for a certain amount of time.…”

Section: Related Workmentioning

confidence: 99%

“…To compare the data of two regions we require a signature with enough discriminative power and being invariant against translation and rotation. Saikia et al [SSW15] used the histogram of voxel intensities for this purpose. Birchfield and Rangarajan [BR05] propose spatiograms as a generalization of histograms including higher order moments and apply them in the context of computer vision.…”

Section: Comparison Of Subtree Regionsmentioning

confidence: 99%

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Global Feature Tracking and Similarity Estimation in Time‐Dependent Scalar Fields

Saikia

Weinkauf

2017

Computer Graphics Forum

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We present an algorithm for tracking regions in time‐dependent scalar fields that uses global knowledge from all time steps for determining the tracks. The regions are defined using merge trees, thereby representing a hierarchical segmentation of the data in each time step. The similarity of regions of two consecutive time steps is measured using their volumetric overlap and a histogram difference. The main ingredient of our method is a directed acyclic graph that records all relevant similarity information as follows: the regions of all time steps are the nodes of the graph, the edges represent possible short feature tracks between consecutive time steps, and the edge weights are given by the similarity of the connected regions. We compute a feature track as the global solution of a shortest path problem in the graph. We use these results to steer the – to the best of our knowledge – first algorithm for spatio‐temporal feature similarity estimation. Our algorithm works for 2D and 3D time‐dependent scalar fields. We compare our results to previous work, showcase its robustness to noise, and exemplify its utility using several real‐world data sets.

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Topological Feature Search in Time-Varying Multifield Data

Agarwal

Chattopadhyay

Natarajan

2021

Mathematics and Visualization

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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 the domain scientists. It has been shown in recent works that a single scalar field is insufficient to capture many important topological features in the data, instead one needs to consider topological relationships between multiple scalar fields. In the current paper, we propose a novel method of finding similarity between two multifield data by comparing their respective fiber component distributions. Given a time-varying multifield data, the method computes a metric plot for each pair of histograms at consecutive time stamps to understand the topological changes in the data over time. We validate the method using real and synthetic data. The effectiveness of the proposed method is shown by its ability to capture important topological features that are not always possible to detect using the individual component scalar fields.

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Fast Similarity Search in Scalar Fields using Merging Histograms

Cited by 12 publications

References 18 publications

Comparative Analysis of Merge Trees using Local Tree Edit Distance

Comparative Analysis of Merge Trees using Local Tree Edit Distance

Global Feature Tracking and Similarity Estimation in Time‐Dependent Scalar Fields

Topological Feature Search in Time-Varying Multifield Data

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