Modeling 3D Stomach

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Modeling 3D Stomach

• Jeonggyu Lee(glaze_at_gatech.edu)
• College of Computing
• Georgia Institute of Technology

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Goal
Set of 2D Images(x,y)
Input
ltSynthesisgt Interpolation Volume Rendering
3D Stomach Model(x,y,z)
Output
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Linear Interpolation - Algorithm

• Key Idea
• Treat each sample as a closed loop.
• Resample two consecutive samples. t 0,1
• Merge them up.

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Linear Interpolation Pros Cons

• Pros
• Have a control over entire model.
• Easy to get a smoothness, etc
• Cons
• Need to extract contours from images.
• Cannot handle topological difference!
• Usually have 1 hole(like a torus)
• Some have more than 2 holes
• Somebody already have done this.
• Fuch 1979, Lawrence 2005

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Voxelization

• Marching Cubes
• Straight forward to get a 3D model
• Works well when samples are good
• Measure of goodness smoothness between samples

Figure from Kitware
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Voxelization Pros Cons

• Pros
• Now we at least have an entire model
• Cons
• Huge of vertices to process(Approx. 1 million)
• Undesirable artifacts(step-edges)

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Where are we?
Set of 2D Images(x,y)
Input
ltSynthesisgt Interpolation Volume Rendering
We have a jaggy 3D model now.
3D Stomach Model(x,y,z)
Output
Hence we are looking for a refinement.
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Where the step-edges come from?
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Where the step-edges come from?
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Refine Subdivide Bulge

• Enhances detail and smoothness of the model
• 1. Subdivide 1 triangle into 4 triangles by
  introducing new vertices.
• 2. Adjust new vertices w.r.t average of
  neighborhood.

Figure generated from Prof. Jarek Rossignacs
MeshViewer
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Refine Subdivide Bulge

• Subdivide 1 triangle into 4 triangles
  byintroducing mid-point.

Figure from Prof. Jarek Rossignacs course note
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Refine Subdivide Bulge

• Move new vertices w.r.t displacement vector

Figure from Prof. Jarek Rossignacs course note
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Subdivide Bulge 1 time - wireframe
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Subdivide Bulge 1 time - solid
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Subdivide Bulge 2 times - wireframe
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Subdivide Bulge 2 times - solid
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Subdivide Bulge Result
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Refine Conclusion

• The refinement is subtle in bigger scale.
• Consumes a lot of memory space
• Need to retry on faster better machines

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Smoothing

• Displaces each vertex by a fraction s of its
  normal
• Same of vertices remains.

• Let Gi be ith point. Let Nvi be the normal of
  the ith point.
• Move Gi aloing Nvi by s where s 0.6, Update
  Nvi
• Move Gi aloing Nvi by s, Update Nvi

Figure generated from Prof. Jarek Rossignacs
MeshViewer
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Smoothing Wireframe
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Smoothing Solid
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Smoothing But in bigger scale
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Smoothing But in bigger scale
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Morphological Simplification

• Removes details
• Roll a ball with a radius R on the boundary
• Introducing tolerance zone.
• Sum of original shape ball r.
• We put a sphere on the every vertex.

Figure from Prof. Jarek Rossignacs course note
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Morphological Simplification Result
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We have to ask.

• Is there actually any enhancement using those
  geometric operations?
• Yes, but subtle.
• Where are those jaggy artifacts from?
• From the Marching cubes displacement.
• i.e. displacement between each cross-sections
• We need to interpolate them smoothly
• Emphasis on the interpolate

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Prior arts Thin-Plate Interpolation

• The key to solve the topological difference when
  interpolating.

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Prior arts Thin-Plate Interpolation
Figure from the Shape Transformation Using
Variational Implicit Functions by Greg Turk James
F. OBrien
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Future work Surgery Planning

• (1)
• (2)

Figure from Prof. Jarek Rossignacs Surgeom
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Conclusion

• Modeling a stomach from samples
• What is missing
• Visual appealing smoothness
• Proper interpolation
• Need to try
• Thin-place interpolation This might be the
  solution
• MAT(Medial Axis Transform)
• Richard computed it.

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Collaborators

• GVU Center
• Prof. Jarek Rossignac
• Kihwan Kim
• Bio-MIBLAB
• Prof. Wang
• Dr. Parry
• Richard