Volume data mining using 3D field topology analysis

Fujishiro, Issei; Takeshima, Yuriko; Azuma, Taeko; Takahashi, Shigeo

doi:10.1109/38.865879

Cited by 59 publications

(38 citation statements)

References 16 publications

(14 reference statements)

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“…The hyper-Reeb graph can be used, for example, for automatic generation of transfer functions. Fujishiro et al [7] extended this work and used a hyper-Reeb graph for exploration of volume data. In addition to automatic transfer function design, their extended method allows them to generate translucent isosurfaces between critical isovalues.…”

Section: Related Workmentioning

confidence: 99%

“…3.3. Given a list of critical isovalues we construct a corresponding transfer function based on the methods described by Fujishiro et al [7]. The domain of the transfer function corresponds to the range of scalar values [s min , s max ] occurring in a data set.…”

Section: Critical Values Inside a Cellmentioning

confidence: 99%

“…Thus, critical isovalues extracted by Weber et al [12] are also meaningful in a volume rendering context. We use the resulting list of critical isovalues to design transfer functions based on the work presented by Fujishiro et al [5,7]. We generate transfer functions that assign small opacity to all scalar values except those close to critical isovalues.…”

Section: Introductionmentioning

confidence: 99%

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Automating Transfer Function Design Based on Topology Analysis

Weber

Scheuermann

2004

Geometric Modeling for Scientific Visualization

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Summary. Direct Volume Rendering (DVR) is commonly used to visualize scalar fields. Quality and significance of rendered images depend on the choice of appropriate transfer functions that assigns optical properties (e.g., color and opacity) to scalar values. We present a method that automatically generates a transfer function based on the topological behavior of a scalar field. Given a scalar field defined by piecewise trilinear interpolation over a rectilinear grid, we find a set of critical isovalues for which the topology of an isosurface, i.e., a surface representing all locations where the scalar field assumes a certain value v, changes. We then generate a transfer function that emphasizes on scalar values around those critical isovalues. Images rendered using the resulting transfer function reveal the fundamental topological structure of a scalar data set.

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Section: Related Workmentioning

confidence: 99%

Section: Critical Values Inside a Cellmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Automating Transfer Function Design Based on Topology Analysis

Weber

Scheuermann

2004

Geometric Modeling for Scientific Visualization

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“…Since the contour tree usually encapsulates the visual nesting hierarchy of features, previous interfaces [8,19,24] have already exploited this for transfer function design. However, although this hierarchy was used internally, it was not part of the user interface, except in the form of the nesting depth (an integer).…”

Section: User Interfacementioning

confidence: 99%

“…An alternate approach to visualisation is to combine direct volume rendering with contour tree analysis [8]. This combination was initially achieved by computing the nesting depth of a given contour-i.e., the graph distance in the contour tree from a defined exterior contour-and adding it as extra parameter to transfer function design [19].…”

Section: Contour Treementioning

confidence: 99%

Topological Galleries: A High Level User Interface for Topology Controlled Volume Rendering

MacCarthy¹,

Carr²,

Weber³

2011

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Existing topological interfaces to volume rendering are limited by their reliance on sophisticated knowledge of topology by the user. We extend previous work by describing topological galleries, an interface for novice users that is based on the design galleries approach. We report three contributions: an interface based on hierarchical thumbnail galleries to display the containment relationships between topologically identifiable features, the use of the pruning hierarchy instead of branch decomposition for contour tree simplification, and drag-and-drop transfer function assignment for individual components. Initial results suggest that this approach suffers from limitations due to rapid drop-off of feature size in the pruning hierarchy. We explore these limitations by providing statistics of feature size as function of depth in the pruning hierarchy of the contour tree.

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Persistent topology for cryo‐EM data analysis

Xia

Guo

2015

Numer Methods Biomed Eng

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In this work, we introduce persistent homology for the analysis of cryo-electron microscopy (cryo-EM) density maps. We identify the topological fingerprint or topological signature of noise, which is widespread in cryo-EM data. For low signal to noise ratio (SNR) volumetric data, intrinsic topological features of biomolecular structures are indistinguishable from noise. To remove noise, we employ geometric flows which are found to preserve the intrinsic topological fingerprints of cryo-EM structures and diminish the topological signature of noise. In particular, persistent homology enables us to visualize the gradual separation of the topological fingerprints of cryo-EM structures from those of noise during the denoising process, which gives rise to a practical procedure for prescribing a noise threshold to extract cryo-EM structure information from noise contaminated data after certain iterations of the geometric flow equation. To further demonstrate the utility of persistent homology for cryo-EM data analysis, we consider a microtubule intermediate structure (EMD-1129). Three helix models, an alpha-tubulin monomer model, an alphaand beta-tubulin model, and an alpha-and beta-tubulin dimer model, are constructed to fit the cryo-EM data. The least square fitting leads to similarly high correlation coefficients, which indicates that structure determination via optimization is an ill-posed inverse problem. However, these models have dramatically different topological fingerprints. Especially, linkages or connectivities that discriminate one model from another one, play little role in the traditional density fitting or optimization, but are very sensitive and crucial to topological fingerprints. The intrinsic topological features of the microtubule data are identified after topological denoising. By a comparison of the topological fingerprints of the original data and those of three models, we found that the third model is topologically favored. The present work offers persistent homology based new strategies for topological denoising and for resolving ill-posed inverse problems.

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Volume data mining using 3D field topology analysis

Cited by 59 publications

References 16 publications

Automating Transfer Function Design Based on Topology Analysis

Automating Transfer Function Design Based on Topology Analysis

Topological Galleries: A High Level User Interface for Topology Controlled Volume Rendering

Persistent topology for cryo‐EM data analysis

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