Parallel Computation of 2D Morse-Smale Complexes

Shivashankar, Nithin; Senthilnathan, M; Natarajan, Vijay

doi:10.1109/tvcg.2011.284

Cited by 55 publications

(48 citation statements)

References 21 publications

(25 reference statements)

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“…There are many algorithms available in the literature to compute the 3D Morse-Smale complex. The algorithms are primarily based on either the quasi Morse-Smale complex formulation [61], [62] or Forman's [63] discrete Morse theory [64], [65], [66], [67]. We use a parallel algorithm based on the latter approach [67] resulting in fast computation even for large datasets.…”

Section: Density Estimation and Filament Modelingmentioning

confidence: 99%

Felix: A Topology Based Framework for Visual Exploration of Cosmic Filaments

Shivashankar

Pranav

Natarajan

et al. 2016

IEEE Trans. Visual. Comput. Graphics

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Abstract-The large-scale structure of the universe is comprised of virialized blob-like clusters, linear filaments, sheet-like walls and huge near empty three-dimensional voids. Characterizing the large scale universe is essential to our understanding of the formation and evolution of galaxies. The density range of clusters, walls and voids are relatively well separated, when compared to filaments, which span a relatively larger range. The large scale filamentary network thus forms an intricate part of the cosmic web. In this paper, we describe Felix, a topology based framework for visual exploration of filaments in the cosmic web. The filamentary structure is represented by the ascending manifold geometry of the 2-saddles in the Morse-Smale complex of the density field. We generate a hierarchy of Morse-Smale complexes and query for filaments based on the density ranges at the end points of the filaments. The query is processed efficiently over the entire hierarchical Morse-Smale complex, allowing for interactive visualization. We apply Felix to computer simulations based on the heuristic Voronoi kinematic model and the standard ΛCDM cosmology, and demonstrate its usefulness through two case studies. First, we extract cosmic filaments within and across cluster like regions in Voronoi kinematic simulation datasets. We demonstrate that we produce similar results to existing structure finders. Second, we extract different classes of filaments based on their density characteristics from the ΛCDM simulation datasets. Filaments that form the spine of the cosmic web, which exist in high density regions in the current epoch, are isolated using Felix. Also, filaments present in void-like regions are isolated and visualized. These filamentary structures are often over shadowed by higher density range filaments and are not easily characterizable and extractable using other filament extraction methodologies.Index Terms-Morse-Smale complexes, tessellations, cosmology theory, cosmic web, large-scale structure of the universe.

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Section: Density Estimation and Filament Modelingmentioning

confidence: 99%

Felix: A Topology Based Framework for Visual Exploration of Cosmic Filaments

Shivashankar

Pranav

Natarajan

et al. 2016

IEEE Trans. Visual. Comput. Graphics

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“…Examples of the first group include parallel computation of the Contour tree [29] and more recently the Morse-Smale complex [17,36,37]. These implementations use variants of the sequential algorithms that are able to compute local fragments of the topological data structure across subdivisions of the domain, and then employ a reduction strategy to generate the global abstraction.…”

Section: Parallel Computation Of Topologymentioning

confidence: 99%

Skeletons for distributed topological computation

Duke

Hosseini

2015

Proceedings of the 4th ACM SIGPLAN Workshop on Functional High-Performance Computing

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Parallel implementation of topological algorithms is highly desirable, but the challenges, from reconstructing algorithms around independent threads through to runtime load balancing, have proven to be formidable. This problem, made all the more acute by the diversity of hardware platforms, has led to new kinds of implementation platform for computational science, with sophisticated runtime systems managing and coordinating large threadcounts to keep processing elements heavily utilized. While simpler and more portable than direct management of threads, these approaches still entangle program logic with resource management. Similar kinds of highly parallel runtime system have also been developed for functional languages. Here, however, language support for higher-order functions allows a cleaner separation between the algorithm and 'skeletons' that express generic patterns of parallel computation. We report results on using this technique to develop a distributed version of the Joint Contour Net, a generalization of the Contour Tree to multifields. We present performance comparisons against a recent Haskell implementation using shared-memory parallelism, and initial work on a skeleton for distributed memory implementation that utilizes an innovative strategy to reduce inter-process communication overheads.

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“…The discrete gradient field is computed using a parallel variant of the method proposed by Gyulassy et al (2008) followed by an efficient computation of the boundary map representing the Morse complex. Finally, the parallel algorithm for computing the discrete gradient field given in Shivashankar et al (2012) is based on a novel description of the discrete Morse function followed by a two-step algorithm computing the cells of the Morse-Smale complex. The algorithms are implemented using a hybrid multi-core implementation.…”

Section: Introductionmentioning

confidence: 99%

Effective homology of k-D digital objects (partially) calculated in parallel

Reina-Molina

Díaz-Pernil

Real

et al. 2016

Pattern Recognition Letters

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In Reina-Molina et al. (2015), a membrane parallel theoretical framework for computing (co)homology information of foreground or background of binary digital images is developed. Starting from this work, we progress here in two senses: (a) providing advanced topological information, such as (co)homology torsion and efficiently answering to any decision or classification problem for sum of k-xels related to be a (co)cycle or a (co)boundary; (b) optimizing the previous framework to be implemented in using GPGPU computing. Discrete Morse theory, Effective Homology Theory and parallel computing techniques are suitably combined for obtaining a homological encoding, called algebraic minimal model, of a Region-Of-Interest (seen as cubical complex) of a presegmented k-D digital image.

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Parallel Computation of 2D Morse-Smale Complexes

Cited by 55 publications

References 21 publications

Felix: A Topology Based Framework for Visual Exploration of Cosmic Filaments

Felix: A Topology Based Framework for Visual Exploration of Cosmic Filaments

Skeletons for distributed topological computation

Effective homology of k-D digital objects (partially) calculated in parallel

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