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Indo-Swedish joint network project

Robust topological methods for analysis of dynamic large-scale data for modern material design.






About

This is an ongoing collaboration between Indian Institute of Science, Bangalore and Linköping University, Sweden with the goal to develop methods for topological feature extraction, tracking, and comparison for large scale dynamic data from material imaging and molecular simulations integrated in a visual analysis pipeline that aids domain scientists in analyzing their data. This project is funded jointly by the Swedish Research Council (Vetenskapsrådet) and the Department of Science and Technology, India under a joint network grant VR 2018-07085 and DST/INT/SWD/VR/P-02/2019






People

Principal Investigators



Prof. Vijay Natarajan
Professor

Dept. of Computer Science and Automation
IISc Bangalore.

Prof. Ingrid Hotz
Professor

Dept. of Science and Technology
Linköping University Sweden.






Project Partners



Prof. Mathieu Linares
Associate Professor

Laboratory of Organic Electronics, Dept. of Science and Technology
Linköping University Sweden.

Prof. Tejas G. Murthy
Professor

Dept. of Civil Engineering
IISc Bangalore.

Dr. Talha Bin Masood
Principal Research Engineer

Dept. of Science and Technology
Linköping University Sweden.







Other Contributors



Dr. Saurabh Singh

Post-Doctoral Fellow

IISc Bangalore.

Dr. Alexei Abrikossov
Post-Doctoral Fellow

Dept. of Science and Technology
Linköping University Sweden.

Karran Pandey
Project Assistant

Visualization and Graphics Lab
IISc Bangalore.

Raghavendra G. Sridharamurthy
Ph.D. Student

Dept. of Computer Science and Automation
IISc Bangalore.

Mohit Sharma
Ph.D. Student

Dept. of Computer Science and Automation
IISc Bangalore.

Dinesh Rathod
Masters Student

Dept. of Computer Science and Automation
IISc Bangalore.

Manasa Bhat K.I
Ph.D. Student

Dept. of Civil Engineering
IISc Bangalore.

Bhupendra Chand
Ph.D. Student

Dept. of Civil Engineering
IISc Bangalore.

Signe Sidwall Thygesen
Ph.D. Student

Dept. of Science and Technology
Linköping University Sweden.

Farhan Rasheed
Ph.D. Student

Dept. of Science and Technology
Linköping University Sweden.






Projects

Visual analysis of electronic densities and transitions in molecules.

Morse theory-based segmentation and fabric quantification of granular materials.

MorseGram : A software tool for segmenting 3D Xray CT scanned granular materials.






Publications


Multi-scale visual analysis of cycle characteristics in spatially-embedded graphs.


Farhan Rasheed, Talha Bin Masood, Tejas G. Murthy, Vijay Natarajan, and Ingrid Hotz (2023)
Visual Informatics (CGI 2023), 7 (3), 2023, 49-58.

 We present a visual analysis environment based on a multi-scale partitioning of a 2d domain into regions bounded by cycles in weighted planar embedded graphs. The work has been inspired by an application in granular materials research, where the question of scale plays a fundamental role in the analysis of material properties. We propose an efficient algorithm to extract the hierarchical cycle structure using persistent homology. The core of the algorithm is a filtration on a dual graph exploiting Alexander’s duality. The resulting partitioning is the basis for the derivation of statistical properties that can be explored in a visual environment. We demonstrate the proposed pipeline on a few synthetic and one real-world dataset.

https://doi.org/10.1016/j.visinf.2023.06.005


Breakage analysis of angular sands using Morse theory- based segmentation.


Manasa Bhat K I, Dinesh Rathod, Bhupendra Chand, Tejas Murthy and Vijay Natarajan (2023)
International Symposium on Machine Learning and Big Data in Geoscience, 2023.

 Macro-scale behavior of cohesive granular materials on mechanical loading is primarily due to interplay of binder disintegration and interparticle interactions. When a cohesive granular ensemble is loaded, initially there is progressive degradation of bonds, followed by rearrangement of particles, and on further loading, there is breakage/fragmentation of particles. Under high stress conditions, the micromechanics of these materials are significantly influenced by fragmentation of particles since it alters the grading and morphology of particles. Conventionally, the degree of breakage of particles is measured using sieve analysis and measures such as grain size distributions, void ratio and density. Although these are useful measures to confirm the presence of breakage of particles at global-scale, it does not provide particle-scale information. The prevalence of X-ray Computed Tomography (XRCT) and robust image segmentation algorithms has made micro-scale characterization of breakage and tracking of sequence of breakage events possible. In this research, we study the breakage events in a cohesive granular sample at micro-scale using a robust morse theory-based algorithm.




Continuous Scatterplot Operators for Bivariate Analysis and Study of Electronic Transitions.


Mohit Sharma, Talha Bin Masood, Signe S. Thygesen, Mathieu Linares, Ingrid Hotz and Vijay Natarajan (2023)
IEEE Transactions on Visualization and Computer Graphics, In Press.

 Electronic transitions in molecules due to the absorption or emission of light is a complex quantum mechanical process. Their study plays an important role in the design of novel materials. A common yet challenging task in the study is to determine the nature of electronic transitions, namely which subgroups of the molecule are involved in the transition by donating or accepting electrons, followed by an investigation of the variation in the donor-acceptor behavior for different transitions or conformations of the molecules. In this paper, we present a novel approach for the analysis of a bivariate field and show its applicability to the study of electronic transitions. This approach is based on two novel operators, the continuous scatterplot (CSP) lens operator and the CSP peel operator, that enable effective visual analysis of bivariate fields. Both operators can be applied independently or together to facilitate analysis. The operators motivate the design of control polygon inputs to extract fiber surfaces of interest in the spatial domain. The CSPs are annotated with a quantitative measure to further support the visual analysis. We study different molecular systems and demonstrate how the CSP peel and CSP lens operators help identify and study donor and acceptor characteristics in molecular systems.

https://doi.org/10.1109/TVCG.2023.3237768


Jacobi Set Driven Search for Flexible Fiber Surface Extraction.


Mohit Sharma and Vijay Natarajan (2022)
TopoInVis 2022: Proc. IEEE Workshop on Topological Data Analysis and Visualization, 2022, 49-58.

 Isosurfaces are an important tool for analysis and visualization of univariate scalar fields. Earlier works have demonstrated the presence of interesting isosurfaces at isovalues close to critical values. This motivated the development of efficient methods for computing individual components of isosurfaces restricted to a region of interest. Generalization of isosurfaces to fiber surfaces and critical points to Jacobi sets has resulted in new approaches for analyzing bivariate scalar fields. Unlike isosurfaces, there exists no output sensitive method for computing fiber surfaces. Existing methods traverse through all the tetrahedra in the domain. In this paper, we propose the use of the Jacobi set to identify fiber surface components of interest and present an output sensitive approach for its computation. The Jacobi edges are used to initiate the search towards seed tetrahedra that contain the fiber surface, thereby reducing the search space. This approach also leads to effective analysis of the bivariate field by supporting the identification of relevant fiber surfaces near Jacobi edges.

https://doi.org/10.1109/TopoInVis57755.2022.00012


Level of Detail Exploration of Electronic Transition Ensembles using Hierarchical Clustering.


Signe Sidwall Thygesen, Talha Bin Masood, Mathieu Linares, Vijay Natarajan and Ingrid Hotz (2022)
Computer Graphics Forum (EuroVis 2022), 41(3), 2022, 333-344.

 We present a pipeline for the interactive visual analysis and exploration of molecular electronic transition ensembles. Each ensemble member describes the change in the charge distribution between two different molecular states, together with a set of physical properties. The main targeted tasks of the proposed pipeline are comparison and characterization of electronic transitions and their correlation to physical properties by combining automatic and interactive visual analysis of the ensemble. A quantitative feature vector characterizing the electron charge transfer is introduced that serves as the basis for hierarchical clustering as well as for the visual representations. The interface for the visual exploration consists of four components. A dendrogram provides an overview of the ensemble. It is augmented with a level of detail visual summary for each cluster. A scatterplot using dimensionality reduction provides a second visualization, highlighting ensemble outliers. Parallel coordinates show the correlation with physical parameters. A spatial representation of selected ensemble members supports an in-depth inspection of transitions in a form that is familiar to chemists. All views are linked and can be used to filter and select ensemble members. The usefulness of the pipeline is shown in three different case studies.

https://doi.org/10.1111/cgf.14544


Morse theory-based segmentation and fabric quantification of granular materials.


Karran Pandey, Talha Bin Masood, Saurabh Singh, Ingrid Hotz, Vijay Natarajan and Tejas G. Murthy (2022)
Granular Matter, 24(1), 2022, 27:1-20.

 This article presents a robust Morse theory-based framework for segmenting 3D x-ray computed tomography image (CT) and computing the fabric, relative arrangement of particles, of granular ensembles. The framework includes an algorithm for computing the segmentation, a data structure for storing the segmentation and representing both individual particles and the connectivity network, and visualizations of topological descriptors of the CT image that enable interactive exploration. The Morse theory-based framework produces superior quality segmentation of a granular ensemble as compared to prior approaches based on the watershed transform. The accuracy of the connectivity network also improves. Further, the framework supports the efficient computation of various distribution statistics on the segmentation and the connectivity network. Such a comprehensive characterization and quantification of the fabric of granular ensembles is the first step towards a multiple length scale understanding of the behavior.

[https://doi.org/10.1007/s10035-021-01182-7]


Segmentation Driven Peeling for Visual Analysis of Electronic Transitions.


Mohit Sharma, Talha Bin Masood, Signe S. Thygesen, Mathieu Linares, Ingrid Hotz and Vijay Natarajan (2021)
IEEE VIS 2021, 96-100.

 Electronic transitions in molecules due to absorption or emission of light is a complex quantum mechanical process. Their study plays an important role in the design of novel materials. A common yet challenging task in the study is to determine the nature of those electronic transitions, i.e. which subgroups of the molecule are involved in the transition by donating or accepting electrons, followed by an investigation of the variation in the donor-acceptor behavior for different transitions or conformations of the molecules. In this paper, we present a novel approach towards the study of electronic transitions based on the visual analysis of a bivariate field, namely the electron density in the hole and particle Natural Transition Orbital (NTO). The visual analysis focuses on the continuous scatter plots (CSPs) of the bivariate field linked to their spatial domain. The method supports selections in the CSP visualized as fiber surfaces in the spatial domain, the grouping of atoms, and segmentation of the density fields to peel the CSP. This peeling operator is central to the visual analysis process and helps identify donors and acceptors. We study different molecular systems, identifying local excitation and charge transfer excitations to demonstrate the utility of the method.

[https://doi.org/10.1109/VIS49827.2021.9623300]


Visual Analysis of Electronic Densities and Transitions in Molecules.


T. Bin Masood, S.S. Thygesen, M. Linares, A. I. Abrikosov, V. Natarajan and I. Hotz (2021)
Computer Graphics Forum (EuroVis 2021), 40(3), 2021, 287-298.

 The study of electronic transitions within a molecule connected to the absorption or emission of light is a common task in the process of the design of new materials. The transitions are complex quantum mechanical processes and a detailed analysis requires a breakdown of these processes into components that can be interpreted via characteristic chemical properties. We approach these tasks by providing a detailed analysis of the electron density field. This entails methods to quantify and visualize electron localization and transfer from molecular subgroups combining spatial and abstract representations. The core of our method uses geometric segmentation of the electronic density field coupled with a graph-theoretic formulation of charge transfer between molecular subgroups. The design of the methods has been guided by the goal of providing a generic and objective analysis following fundamental concepts. We illustrate the proposed approach using several case studies involving the study of electronic transitions in different molecular systems.

[https://doi.org/10.1111/cgf.14307]


Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization.


Lin Yan, Talha Bin Masood, Raghavendra Sridharamurthy, Farhan Rasheed, Vijay Natarajan, Ingrid Hotz and Bei Wang (2021)
Computer Graphics Forum, 40: 599-633.

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 present a state-of-the-art report on scalar field comparison using topological descriptors. We provide a taxonomy of existing approaches based on visualization tasks associated with three categories of data: single fields, time-varying fields, and ensembles. These tasks include symmetry detection, periodicity detection, key event/feature detection, feature tracking, clustering, and structure statistics. Our main contributions include the formulation of a set of desirable mathematical and computational properties of comparative measures, and the classification of visualization tasks and applications that are enabled by these measures.

[https://doi.org/10.1111/cgf.14331]


Topological analysis of density fields: An evaluation of segmentation methods.


Alexei I. Abrikosov, Talha Bin Masood, Martin Falk and Ingrid Hotz (2021)
Computers & Graphics, 8: 231-241, ISSN 0097-8493.

Topological and geometric segmentation methods provide powerful concepts for detailed field analysis and visualization. However, when it comes to a quantitative analysis that requires highly accurate geometric segmentation, there is a large discrepancy between the promising theory and the available computational approaches. In this paper, we compare and evaluate various segmentation methods with the aim to identify and quantify the extent of these discrepancies. Thereby, we focus on an application from quantum chemistry: the analysis of electron density fields. It is a scalar quantity that can be experimentally measured or theoretically computed. In the evaluation we consider methods originating from the domain of quantum chemistry and computational topology. We apply the methods to the charge density of a set of crystals and molecules. Therefore, we segment the volumes into atomic regions and derive and compare quantitative measures such as total charge and dipole moments from these regions. As a result, we conclude that an accurate geometry determination can be crucial for correctly segmenting and analyzing a scalar field, here demonstrated on the electron density field.

[https://doi.org/10.1016/j.cag.2021.05.015]

Contact

Vijay Natarajan


Department of Computer Science and Automation
Indian Institute of Science Bangalore
Tel: +91 80 22932909
Fax: +91 80 23602911
Email: vijayn [AT] iisc [DOT] ac [DOT] in