In recent decades, scientific data has become available in increasing sizes and
precision. Therefore techniques to analyze and summarize the ever increasing
datasets are of vital importance. A common form of scientific data, resulting from
simulations as well as observational sciences, is in the form of scalar-valued function on domains of interest. The Morse-Smale complex is a topological data-structure
used to analyze and summarize the gradient behavior of such scalar functions.
This thesis deals with efficient parallel algorithms to compute the Morse-Smale
complex as well as its application to datasets arising from cosmological sciences as well as structural biology.
The first part of the thesis discusses the contributions towards efficient computation of the Morse-Smale complex of scalar functions de ned on two and three
dimensional datasets. In two dimensions, parallel computation is made possible
via a paralleizable discrete gradient computation algorithm. This algorithm is
extended to work e ciently in three dimensions also. We also describe e cient
algorithms that synergistically leverage modern GPUs and multi-core CPUs to
traverse the gradient field needed for determining the structure and geometry of
the Morse-Smale complex. We conclude this part with theoretical contributions
pertaining to Morse-Smale complex simplification.
The second part of the thesis explores two applications of the Morse-Smale complex. The first is an application of the 3-dimensional hierarchical Morse-Smale complex to interactively explore the filamentary structure of the cosmic web.
The second is an application of the Morse-Smale complex for analysis of shapes
of molecular surfaces. Here, we employ the Morse-Smale complex to determine
alignments between the surfaces of molecules having similar surface architecture.
| Identifer | oai:union.ndltd.org:IISc/oai:etd.ncsi.iisc.ernet.in:2005/3045 |
| Date | January 2014 |
| Creators | Shivashankar, Nithin |
| Contributors | Natarajan, Vijay |
| Source Sets | India Institute of Science |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
| Relation | G26883 |
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