Building 3D Surface Network From 2D Curve Networks with Application to Anatomical Modeling

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Building 3D Surface Network From 2D Curve
Networks with Application to Anatomical Modeling

• Tao Ju
• Washington University in St. Louis

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Brain Atlases

• A roadmap of the brain
• Models the partitioning of anatomical regions
• Mapping 2D data from individual brains onto a
  common atlas

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Atlas-based Brain Database

• Geometric database of gene expressions Ju et al.
  2003
• 2D brain atlas represented as subdivision meshes
• Gene data from different brains mapped onto a
  same atlas
• Online tools for spatial queries
• Identify genes with specific expressions in
  specified regions

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3D Mouse Brain Atlas

• Surface network partitioning anatomical regions
• Mapping 3D data from different brains to common
  atlas
• From 2D tissue sections
• Better resolution than 3D imaging, e.g. MRI.

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Building 3D Atlas
Curve Network
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Previous Work

• Connecting 2D curves to 3D surfaces
• Keppel 1975 Fuch et al.1977 Ganapathy and
  Denneh 1982 Boissonnat 1988/1992 Meyers et
  al.1992 Welzl and Wolfers 1994 Bajaj et al.
  1996 Oliva et al.1996 Barequet et al.
  1996/2000/2003
• Surface between 2 materials
• Gaps and self-intersections for gt2 materials

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Goal

• Automatically builds error-free surfaces for
  multiple materials
• Geometric correctness

• Allows convenient user interaction
• Topology correctness

• Volumetric Approach
• Avoid voxelization Weinstein 2004

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Step 1- Projection

• Project curve networks from two sections
  orthogonally onto a common plane
• Partitions the plane into disjoint regions
• Each region forms a wedge in space

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Step 2 - Topology Graph

• A wedge is partitioned vertically into layers
• Nodes within a wedge and between neighboring
  wedges are connected by edges
• Nodes/edges determine how volumes are formed

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Step 3 - Polygonalization

• Build polygonal boundaries of volumes
• Triangulation induces splitting of wedges into
  triangular prisms
• Topology graph split into topology grid
• Polygons dual to edges in the grid connecting
  different materials

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Automatic Surface Construction

• Synthetic example

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Automatic Surface Construction

• Reconstruction of Cortex and Olfactory Bulb

First twenty anno-tated sections
Surface network
Wire frame view of Cortex
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Topology Modification
Default Graph
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Example

• Connecting broken structures in Ventricles

Automatic construction
After topology change
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Polygonal Mouse Brain Atlas
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Polygonal Mouse Brain Atlas
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Polygonal Mouse Brain Atlas
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Acknowledgement

• Prof. Joe Warren at Rice University
• Collaborators
• Baylor College of Medicine
• James Carson, Gregor Eichele, Christina Thaller,
  Wah Chiu
• University of Houston
• Ioannis Kakadiaris, Musodiq Bello