Dynamic Cone Beam Reconstruction Using a Variational Level Set - - PowerPoint PPT Presentation

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Dynamic Cone Beam Reconstruction Using a Variational Level Set - - PowerPoint PPT Presentation

Mar 31, 2024 474 likes •697 views

Dynamic Cone Beam Reconstruction Using a Variational Level Set Formulation Andreas Keil 1 , Jakob Vogel 1 , Gnter Lauritsch 2 , Nassir Navab 1 1 Computer Aided Medical Procedures, TU Mnchen, Germany 2 Siemens Healthcare, Forchheim, Germany

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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation

Andreas Keil1, Jakob Vogel1, Günter Lauritsch2, Nassir Navab1

1Computer Aided Medical Procedures, TU München, Germany 2Siemens Healthcare, Forchheim, Germany

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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 2

Outline

Motivation and Assumptions Methods

Level Sets Shape and Motion Models Data Terms

Results and Discussion

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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 3

Motivation :: Clinical

Bringing together pre‐operative 3D imaging (conventional CT, mainly used for rule‐out of stenosis) and intra‐interventional angiography (simultaneous diagnosis and intervention) by enabling 4D reconstruction from cone‐ beam projections.

Image courtesy of Siemens Healthcare

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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 4

Motivation :: Assumptions

Assumption 1: Direct tomographic reconstruction not feasible Perform symbolic reconstruction in a first step (And use recovered motion in subsequent tomographic reconstruction) Assumption 2: Separation of shape reconstruction and motion estimation not feasible (“chicken and egg”) Simultaneously estimate shape and motion

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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 5

Methods :: Sub‐Problems in Our Approach

Vessel Enhancement in 2D Optimization Goal / Data Terms Dynamic Shape Models

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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 6

Methods :: Vessel Enhancement

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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 7

Methods :: Level Sets

  • Level sets re‐introduced by Osher and

Sethian in 1988

  • Implicitly represented contour / shape
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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 8

Methods :: Level Sets

  • Chan and Vese: Active contours without edges. IEEE Trans. Image Process., 10(2):266‐277, 2001
  • http://math.berkeley.edu/~sethian/
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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 9

Methods :: Shape and Motion Models

  • Model shape using level set volume
  • Model motion using B‐splines

parameters

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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 10

Methods :: Dynamic Level Set

Dynamic shape = static shape & motion model shape reg. motion reg.

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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 11

Methods :: Data Terms

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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 12

Methods :: Data Terms

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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 13

Methods :: Data Terms

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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 14

Methods :: Data Terms

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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 15

Methods :: Data Terms (cont’d)

contrary pixel indication (un‐)reconstructed voxel weighted penalty

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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 16

Methods :: Data Terms (cont’d)

contrary pixel indication (un‐)reconstructed voxel weighted penalty

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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 17

Results :: Synthetic Tubular Shapes

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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 18

Results :: Synthetic Coronaries Phantom

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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 19

Results :: Quantitative Evaluation

Positional errors (for rigid motions, gaussian noise of 25%, 3mm voxel spacing): (sub‐voxel accuracy!) Shape errors (for deformable motions, gaussian noise of 30%, 3mm voxel spacing): Sensitivity: 74.2% Specificity: 99.6%

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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 20

Summary

  • Contributions:

– Dynamic level sets for reconstruction – Data terms for level set reconstruction

  • Future work:

– Phantom / real data – Refined motion models (breathing and non‐periodic motions)

  • Applicability to real cardiac cone‐beam CT:

– Mainly depending on vessel extraction in 2D – Reduction of dependency on vessel extraction by

  • combination with tomographic methods
  • closing loop from reconstruction to segmentation
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Dynamic Cone‐Beam Reconstruction Using a Variational Level Set Formulation ‐ Andreas Keil 21

Acknowledgements

Siemens Healthcare ( funding) Moritz Blume (p. 118), Jan Boese, and Martin Brokate ( discussions) Tobias Klug and LRR @ TUM ( multi‐core system) Christopher Rohkohl ( phantom data) Fully3D Student Grant