Automating Transfer Function Design Based on Topology Analysis

Weber, Günther; Scheuermann, Gerik

doi:10.1007/978-3-662-07443-5_18

Cited by 6 publications

(6 citation statements)

References 9 publications

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“…We have compared our results with those obtained with the transfer functions described in Weber and Scheuermann [41], which had originally been developed by Fujishiro et al [42].…”

Section: Transfer Function Designmentioning

confidence: 91%

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The Topological Effects of Smoothing

Shafii

Dillard

Hlawitschka

et al. 2012

IEEE Trans. Visual. Comput. Graphics

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Abstract-Scientific data sets generated by numerical simulations or experimental measurements often contain a substantial amount of noise. Smoothing the data removes noise but can have potentially drastic effects on the qualitative nature of the data, thereby influencing its characterization and visualization via topological analysis, for example. We propose a method to track topological changes throughout the smoothing process. As a pre-processing step, we over-smooth the data and collect a list of topological events, specifically the creation and destruction of extremal points. During rendering, it is possible to select the number of topological events by interactively manipulating a merging parameter. The result that a specific amount of smoothing has on the topology of the data is illustrated using a topology-derived transfer function that relates region connectivity of the smoothed data to the original regions of the unsmoothed data. This approach enables visual as well as quantitative analysis of the topological effects of smoothing.

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“…We have compared our results with those obtained with the transfer functions described in Weber and Scheuermann [41], which had originally been developed by Fujishiro et al [42].…”

Section: Transfer Function Designmentioning

confidence: 91%

“…In addition, this effort was supported by the National Science Foundation through grant CCF-0702817. We thank our colleagues from the Institute for Data Analysis and Visualization (IDAV), Department of Computer Science, UC Davis and Gunther Weber for providing code from his publication [41].…”

Section: Acknowledgementsmentioning

confidence: 99%

The Topological Effects of Smoothing

Shafii

Dillard

Hlawitschka

et al. 2012

IEEE Trans. Visual. Comput. Graphics

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“…Another approach commonly used for regular grids is what we call an analytic approach. In this case, there is no attempt at simulating the concept of critical point in the discrete case, but the approach relies on the general idea of fitting an approximating function, sometimes globally discontinuous, on the vertices of the grid (at which the field values are known) [Watson et al 1985;Schneider and Wood 2004;Schneider 2005;Weber and Scheuermann 2004;Weber et al 2003]. Critical points are then usually detected through analytical techniques.…”

Section: S Biasotti Et Almentioning

confidence: 99%

“…As in the case of simplicial models, the problem of computing a Morse-Smale complex from 3D regular models has not been studied extensively. There are few algorithms that extract critical points Weber et al 2002Weber et al , 2003Weber and Scheuermann 2004;Papaleo 2004]. Weber et al [2002] and Papaleo [2004] use Banchoff 's definition of critical points in the discrete case presented in Section 3.2.2, Soille [1991] Regular Morse complex Meyer [1994] Regular Morse complex Takahashi et al [1995] Simplicial (2D) Morse-Smale complex Bajaj and Schikore [1998] Simplicial (2D) Morse-Smale complex Bajaj et al [1998] Regular (2D) Morse-Smale complex Bajaj et al [1998] Regular (3D) 1-skeleton of the Morse-Smale complex Mangan and Whitaker [1999] Simplicial (2D) Morse complexes Stoev and Strasser [2000] Simplicial (2D/3D) Morse complexes Edelsbrunner et al [2001] Simplicial (2D) Morse-Smale complex Dey et al [2003] Simplicial (3D) Morse complexes (stable manifolds) Danovaro et al [2003a] Simplicial (2D) Morse complexes Danovaro et al [2003b] Simplicial (2D/3D) Morse complexes Bremer et al [2003] Simplicial (2D) Morse-Smale complex Weber et al [2003] Regular (3D) Critical regions for maxima and minima Cazals et al [2003] Simplicial (2D) Morse-Smale complex Edelsbrunner et al [2003a] Simplicial (3D) Morse-Smale complex Ni et al [2004] Simplicial (2D) Morse complexes Pascucci [2004] Simplicial (2D) Morse-Smale complex Schneider and Regular (2D) Morse-Smale complex Schneider [2005] Regular (2D) Morse-Smale complex Magillo et al [2007] Simplicial (2D) Morse complex while used different approach, as discussed above in this section for the 2D case.…”

Section: Computing a Morse-smale Complexmentioning

confidence: 99%

Describing shapes by geometrical-topological properties of real functions

et al. 2008

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Differential topology, and specifically Morse theory, provide a suitable setting for formalizing and solving several problems related to shape analysis. The fundamental idea behind Morse theory is that of combining the topological exploration of a shape with quantitative measurement of geometrical properties provided by a real function defined on the shape. The added value of approaches based on Morse theory is in the possibility of adopting different functions as shape descriptors according to the properties and invariants that one wishes to analyze. In this sense, Morse theory allows one to construct a general framework for shape characterization, parametrized with respect to the mapping function used, and possibly the space associated with the shape. The mapping function plays the role of a lens through which we look at the properties of the shape, and different functions provide different insights. In the last decade, an increasing number of methods that are rooted in Morse theory and make use of properties of real-valued functions for describing shapes have been proposed in the literature. The methods proposed range from approaches which use the configuration of contours for encoding topographic surfaces to more recent work on size theory and persistent homology. All these have been developed over the years with a specific target domain and it is not trivial to systematize this work and understand the links, similarities, and differences among the different methods. Moreover, different terms have been used to denote the same mathematical constructs, which often overwhelm the understanding of the underlying common framework. The aim of this survey is to provide a clear vision of what has been developed so far, focusing on methods that make use of theoretical frameworks that are developed for classes of real functions rather than for a single function, even if they are applied in a restricted manner. The term geometrical-topological used in the title is meant to underline that both levels of information content are relevant for the applications of shape descriptions: geometrical, or metrical, properties and attributes are crucial for characterizing specific instances of features, while topological properties are necessary to abstract and classify shapes according to invariant aspects of their geometry. The approaches surveyed will be discussed in detail, with respect to theory, computation, and application. Several properties of the shape descriptors will be analyzed and compared. We believe this is a crucial step to exploit fully the potential of such approaches in many applications, as well as to identify important areas of future research.

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“…Here, the opacity TF is designed so that it can emphasize the topological transitions of isosurfaces with respect to the scalar field. (See [29,34].) While the result seems to be better than the previous one, it still suffers from small partial overlaps between the two territories of the proton and hydrogen-atom along with the charge transfer in the projected image.…”

Section: Weight Assignment For Isosurfaces Using Transfer Functionsmentioning

confidence: 83%

A Feature-Driven Approach to Locating Optimal Viewpoints for Volume Visualization

Takahashi¹,

Fujishiro²,

Takeshima³

et al.

VIS 05. IEEE Visualization, 2005.

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The University of Tokyo 0.305 0.988 0.675 0.740 0.013 0.524 0.535 0.738 0.000 0.309 0.687 1.000 + = 0.816 0.571 0.582 0.000 0.241 0.845 1.000 0.361 0.574 0.962 0.557 0.598 Figure 1: Locating optimal viewpoints by individually estimating the visibility quality of each feature subvolume. The value under each image represents its corresponding estimate normalized to [0.0, 1.0]. ABSTRACTOptimal viewpoint selection is an important task because it considerably influences the amount of information contained in the 2D projected images of 3D objects, and thus dominates their first impressions from a psychological point of view. Although several methods have been proposed that calculate the optimal positions of viewpoints especially for 3D surface meshes, none has been done for solid objects such as volumes. This paper presents a new method of locating such optimal viewpoints when visualizing volumes using direct volume rendering. The major idea behind our method is to decompose an entire volume into a set of feature components, and then find a globally optimal viewpoint by finding a compromise between locally optimal viewpoints for the components. As the feature components, the method employs interval volumes and their combinations that characterize the topological transitions of isosurfaces according to the scalar field. Furthermore, opacity transfer functions are also utilized to assign different weights to the decomposed components so that users can emphasize features of specific interest in the volumes. Several examples of volume datasets together with their optimal positions of viewpoints are exhibited in order to demonstrate that the method can effectively guide naive users to find optimal projections of volumes.

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Automating Transfer Function Design Based on Topology Analysis

Cited by 6 publications

References 9 publications

The Topological Effects of Smoothing

The Topological Effects of Smoothing

Describing shapes by geometrical-topological properties of real functions

A Feature-Driven Approach to Locating Optimal Viewpoints for Volume Visualization

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