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Parallel Computation of 2D Morse-Smale Complexes
Oct. 2012 (vol. 18 no. 10)
pp. 1757-1770
Nithin Shivashankar, Indian Institute of Science, Bangalore
Senthilnathan M, Indian Institute of Science, Bangalore
Vijay Natarajan, Indian Institute of Science, Bangalore
The Morse-Smale complex is a useful topological data structure for the analysis and visualization of scalar data. This paper describes an algorithm that processes all mesh elements of the domain in parallel to compute the Morse-Smale complex of large 2D datasets at interactive speeds. We employ a reformulation of the Morse-Smale complex using Forman's Discrete Morse Theory and achieve scalability by computing the discrete gradient using local accesses only. We also introduce a novel approach to merge gradient paths that ensures accurate geometry of the computed complex. We demonstrate that our algorithm performs well on both multicore environments and on massively parallel architectures such as the GPU.

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Index Terms:
Manifolds,Geometry,Vectors,Data visualization,Algorithm design and analysis,Parallel algorithms,2D scalar functions.,Topology-based methods,discrete Morse theory,large datasets,gradient pairs,multicore
Citation:
Nithin Shivashankar, Senthilnathan M, Vijay Natarajan, "Parallel Computation of 2D Morse-Smale Complexes," IEEE Transactions on Visualization and Computer Graphics, vol. 18, no. 10, pp. 1757-1770, Oct. 2012, doi:10.1109/TVCG.2011.284
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