Direct Feature Visualization Using Morse-Smale Complexes

@article{Gyulassy2012DirectFV,
  title={Direct Feature Visualization Using Morse-Smale Complexes},
  author={Attila Gyulassy and Natallia Kotava and Mark Kim and Charles D. Hansen and Hans Hagen and Valerio Pascucci},
  journal={IEEE Transactions on Visualization and Computer Graphics},
  year={2012},
  volume={18},
  pages={1549-1562}
}
In this paper, we characterize the range of features that can be extracted from an Morse-Smale complex and describe a unified query language to extract them. We provide a visual dictionary to guide users when defining features in terms of these queries. We demonstrate our topology-rich visualization pipeline in a tool that interactively queries the MS complex to extract features at multiple resolutions, assigns rendering attributes, and combines traditional volume visualization with the… Expand
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References

SHOWING 1-10 OF 51 REFERENCES
Query-driven visualization of large data sets
We present a practical and general-purpose approach to large and complex visual data analysis where visualization processing, rendering and subsequent human interpretation is constrained to theExpand
Topology-based simplification for feature extraction from 3D scalar fields
TLDR
A combinatorial algorithm is designed that simplifies the Morse-Smale complex by repeated application of two atomic operations that remove pairs of critical points of the function and a visualization of the simplified topology is presented. Expand
High-Level User Interfaces for Transfer Function Design with Semantics
TLDR
This paper presents new ideas to facilitate the specification of optical properties for direct volume rendering and introduces an additional level of abstraction for parametric models of transfer functions. Expand
A topological approach to simplification of three-dimensional scalar functions
This paper describes an efficient combinatorial method for simplification of topological features in a 3D scalar function. The Morse-Smale complex, which provides a succinct representation of aExpand
Simplifying flexible isosurfaces using local geometric measures
TLDR
This work defines local geometric measures for individual contours, such as surface area and contained volume, and provides an algorithm to compute these measures in a contour tree, and combines this with a flexible isosurface interface to allow users to explore individualcontours of a dataset interactively. Expand
A Practical Approach to Morse-Smale Complex Computation: Scalability and Generality
TLDR
A new algorithm and easily extensible framework for computing MS complexes for large scale data of any dimension where scalar values are given at the vertices of a closure-finite and weak topology (CW) complex, therefore enabling computation on a wide variety of meshes such as regular grids, simplicial meshes, and adaptive multiresolution (AMR) meshes is described. Expand
The TOPORRERY: computation and presentation of multi-resolution topology
TLDR
A new metaphor for visualizing the Contour Tree borrowed from the classical design of a mechanical orrery is proposed, replaced with a hierarchy of maxima, minima and saddles that can be interactively filtered, both uniformly and adaptively, by importance with respect to a given metric. Expand
Size-based Transfer Functions: A New Volume Exploration Technique
  • Carlos D. Correa, K. Ma
  • Computer Science, Medicine
  • IEEE Transactions on Visualization and Computer Graphics
  • 2008
TLDR
This paper introduces size-based transfer functions, which map the local scale of features to color and opacity, and shows that they can improve classification and enhance volume rendering techniques, such as maximum intensity projection. Expand
Robust on-line computation of Reeb graphs: simplicity and speed
TLDR
An on-line algorithm is introduced that reads a stream of elements and continuously maintains the Reeb graph of all elements already reed and is robust in handling non-manifold meshes and general in its applicability to input models of any dimension. Expand
A topological hierarchy for functions on triangulated surfaces
TLDR
This work combines topological and geometric methods to construct a multiresolution representation for a function over a two-dimensional domain and uses this data structure to extract topologically valid approximations that satisfy error bounds provided at runtime. Expand
...
1
2
3
4
5
...