Tomographic Image Reconstruction Using ContentAdaptive Mesh Modeling

1
Tomographic Image Reconstruction Using
Content-Adaptive Mesh Modeling

• H. Can Aras
• Final Presentation
• December 20, 2004

2
Overview

• What is the problem?
• What has been done before the second
  presentation?
• What has been done after the second presentation?
• Enhancements
• Alternative Approaches
• Conclusion

3
CT-Imaging

• A special radiographic technique that uses a
  computer to assimilate multiple X-ray images into
  a 2D cross-sectional image
• Important for viewing the human body and
  diagnostic purposes.
• Quality of CT-Images is important.

4
The Procedure

• The CT machine rotates 180 degrees around the
  patients body, sending out an X-ray beam.
• Sensors positioned at the opposite points of the
  beam record the absorption rates of the varying
  thicknesses of tissue and bone.
• These data are then relayed to a computer that
  turns the information into a picture (CT-Image)
  on a screen.

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Projection Data
SinogramAll projections
ProjectionAll ray-sums in a direction
?
y
P(??t)
t
p
?
x
f(x,y)
t
X-rays
Sinogram
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Problem Aim

• Reconstruction of CT-Images from Projection Data
• There are many algorithms for reconstruction
  (ART, FBP)
• FBP is the most well-known, but not perfect
  especially in case of noisy or incomplete data.
• The aim is to get a better reconstruction of the
  CT image by using a mesh model instead of the
  traditional pixel-based models.

7
Overview

• What is the problem?
• What has been done before the second
  presentation?
• What has been done after the second presentation?
• Enhancements
• Alternative Approaches
• Conclusion

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Approach

• Content-Adaptive Mesh Generation
• Feature Map Extraction (Second derivative)
• Placement of Mesh Nodes (Floyd-Steinberg)
• Connecting Mesh Nodes (Delaunay)
• Estimation of Mesh Nodal Values
• MESH-EM algorithm
• Reconstruction of the Image
• Approximation over each mesh element (triangle)

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Result
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Result (cont.)

• It is difficult to judge which result looks
  better. A physician can tell you.
• Even different physicians can tell you different
  things.
• SNR can be used.
• Other validation techniques can be used, e.g.
  cardiac perfusion detection. This is out of the
  scope of this project.

11
Overview

• What is the problem?
• What has been done before the second
  presentation?
• What has been done after the second presentation?
• Enhancements
• Alternative Approaches
• Conclusion

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Better Filter used for FBP (? 5)
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More Projections (? 2)
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Less Projections (? 10)
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With Smoothing (? 10)
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More Iterations (? 10)
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Synthetic (? 10)
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Brain (? 10)
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Spine (? 10)
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Overview

• What is the problem?
• What has been done before the second
  presentation?
• What has been done after the second presentation?
• Enhancements
• Alternative Approaches
• Conclusion

21
Approach

• Content-Adaptive Mesh Generation
• Feature Map Extraction
• Placement of Mesh Nodes
• Connecting Mesh Nodes
• Estimation of Mesh Nodal Values
• MESH-EM algorithm
• Reconstruction of the Image
• Approximation over each mesh element

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Barycentric Coordinates

• Why not use Barycentric Coordinates instead of
  using a Master Element?
• They are doing the same thing

23
Approach

• Content-Adaptive Mesh Generation
• Feature Map Extraction
• Placement of Mesh Nodes
• Connecting Mesh Nodes
• Estimation of Mesh Nodal Values
• MESH-EM algorithm
• Reconstruction of the Image
• Approximation over each mesh element

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Using Gradient Image (? 5)
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Comparison (? 5)
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Using Watershed Segmentation-I (? 5)
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Using Watershed Segmentation-II (? 5)
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Using Watershed Segmentation-III (? 5)
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Overview

• What is the problem?
• What has been done before the second
  presentation?
• What has been done after the second presentation?
• Enhancements
• Alternative Approaches
• Conclusion

30
Thank you

• Questions?