A GPU Parallel Algorithm for Computing Morse-Smale Complexes

The Morse-Smale complex is a well studied topological structure that represents the gradient flow behavior between critical points of a scalar function. It supports multi-scale topological analysis and visualization of feature-rich scientific data. Several parallel algorithms have been proposed towa...

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Bibliographic Details
Published in:IEEE transactions on visualization and computer graphics Vol. 29; no. 9; pp. 3873 - 3887
Main Authors: Subhash, Varshini, Pandey, Karran, Natarajan, Vijay
Format: Journal Article
Language:English
Published: United States IEEE 01.09.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Computation
Critical point
GPU
Gradient flow
Graphics processing units
Indexes
Iterative algorithms
Iterative methods
Manifolds
morse-smale complex
Parallel algorithms
Parallel processing
Point pairs
Runtime
Saddles
Scalar field
shared memory parallel algorithm
Three-dimensional displays
Topology
ISSN:1077-2626, 1941-0506, 1941-0506
Online Access:Get full text
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Summary:The Morse-Smale complex is a well studied topological structure that represents the gradient flow behavior between critical points of a scalar function. It supports multi-scale topological analysis and visualization of feature-rich scientific data. Several parallel algorithms have been proposed towards the fast computation of the 3D Morse-Smale complex. Its computation continues to pose significant algorithmic challenges. In particular, the non-trivial structure of the connections between the saddle critical points are not amenable to parallel computation. This paper describes a fine grained parallel algorithm for computing the Morse-Smale complex and a GPU implementation (g msc ). The algorithm first determines the saddle-saddle reachability via a transformation into a sequence of vector operations, and next computes the paths between saddles by transforming it into a sequence of matrix operations. Computational experiments show that the method achieves up to 8.6× speedup over pyms3d and 6× speedup over TTK, the current shared memory implementations. The paper also presents a comprehensive experimental analysis of different steps of the algorithm and reports on their contribution towards runtime performance. Finally, it introduces a CPU based data parallel algorithm for simplifying the Morse-Smale complex via iterative critical point pair cancellation.
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ISSN:1077-2626
1941-0506
1941-0506
DOI:10.1109/TVCG.2022.3174769