Automatic CrossSectioning based on Topological Volume Skeletonization

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Automatic Cross-Sectioning based on Topological
Volume Skeletonization
Smart Graphics 2005

• Yuki Mori,Shigeo Takahashi,Takeo Igarashi
  ,Yuriko Takeshima,Issei Fujishiro
• The University of Tokyo, JST PRESTO,Tohoku
  University

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Introduction
Visualizing the complicated inner structures of
3D volume datasets

• Typical visualization techniques

Isosurface Extraction
Volume Rendering
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Cross-Section

• People frequently use cross-sections to inspect
  the inner structures of a volume dataset

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Our Goal
Automatic generation of cross-sections that
reveal characteristic structures of a volume
dataset
Volume Dataset
Cross-Section
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Our Method

• Extract critical points of field values using 3D
  topology analysis
• Generate cross-section that reveals these
  critical points

scalar field value
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Algorithm
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Algorithm Overview
Volume Dataset
Analyze Topological Structure
Takahashi 2004
Critical Points
Compute Best Fitting Planeto the Points
Displaying Cross-Sections
Visualized Image
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Algorithm Overview
Volume Dataset
Analyze Topological Structure
Takahashi 2004
Critical Points
Compute Best Fitting Planeto the Points
Displaying Cross-Sections
Visualized Image
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Extraction of Critical Points
Critical points where the topology of isosurfaces
changes
critical point
scalar field value
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Extraction of Critical Points
appearance
disappearance
merging
splitting
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Volume Skeleton Tree (VST)
Level-set graph to delineate isosurface
transitions according to scalar field value
Volume
VST
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Example Analytic Function
scalar field value
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Algorithm Overview
Volume Dataset
Analyze Topological Structure
Takahashi 2004
Critical Points
Compute Best Fitting Planeto the Points
Displaying Cross-Sections
Visualized Image
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Finding the Cross-Section as a Best Fitting Plane

• Approximate to points

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Finding the Cross-Section as a Best Fitting Plane

• Calculate the covariance matrix
• Calculate eigenvalues and eigenvectors

where x, y, and z are average of x, y and z
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Finding the Cross-Section as a Best Fitting Plane

• Center of points
• The plane spanned by two major eigenvectors

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Displaying Cross-Sections
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Displaying Cross-Sections

• Volume-rendering of cross-section
• Cutting off a polygon
• 2.5 dimensional Volume Rendering

(a)
(b)
(c)
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a Volume-Rendering of Cross-Section

• Converts each of the field values in a
  cross-section into a suitable color value
• This provides a user with detailed information

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b Cutting Polygonized Isosurface

• Polygonizes isosurfaces associated with critical
  points and cuts them at the given cutting plane
• This method is useful for allowing a user to know
  the cutting planes location

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c 2.5 Dimensional Volume Rendering

• Volume-renders the dataset on the far side of
  the cutting plane
• This method can be expected to provide a
  significant visual effect to be able to embed 2.5
  dimensional information in 2D images

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Demo

• Application to Analytic Function Dataset

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Results

• Application to Real Datasets

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Tooth (medical CT-Scanned Dataset)
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Antiproton-Hydrogen Atom Collision
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Nucleon
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Conclusion and Future Work
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Conclusion

• Method for automatically generating
  characteristic cross-section
• Extract critical points of field values using 3D
  topology analysis
• Generate cross-section that reveals these
  critical points

scalar field value
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Future Work

• Generate cross-sections including curved surface
  and multiple planes
• Try other methods for analyzing inner structures
• Apply to other datasets (vector or tensor field)

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Thank you

• Contact me
• yuki_at_ui.is.s.u-tokyo.ac.jp
• http//www-ui.is.s.u-tokyo.ac.jp/yuki/

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Q and A
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Simplification of VST

• VST pattern to be removed in the simplification
  process

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Why we use differential topology

• Critical points are found to locate local extrema
• Volume Skeleton Tree are constructed to show the
  global configuration of volumetric fields

Critical points
Volume Skeleton Tree
We can control the level of detail of local
features while maintaining the global skeleton
of the whole volume
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References

• S. Takahashi, Y. Takeshima and I. Fujishiro.
  2004. Topological Volume Skeletonization and its
  application to transfer function design.
  Graphical Models, 66(1), 22-49.
• I. Fujishiro, T. Azuma, Y. Takeshima and S.
  Takahashi. 2000. Volume data mining using 3D
  field topology analysis. IEEE Computer Graphics
  and Applications, 20(5), 46-51.
• Meibner, M. Web Page http//www.volvis.org/.
• T. Woo. The National Library of Medicine of the
  National Institutes of Health http//visual.nlm.n
  ih.gov/data.