extraction of cerebral vasculature from anatomical mri · extraction of cerebral vasculature from...
TRANSCRIPT
Extraction of Cerebral
Vasculature from Anatomical
MRI
Andreas Deistung, University of Jena
Jurgen Reichenbach, University of Jena
Marek Kocinski, TUL
Piotr Szczypinski, TUL
Andrzej Materka, TUL
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The purpose of our research
Vascular Tree Generation
(geometry, flow, pressure drop, viscosity)
3D MRI Data
3D segmentation of a vessel 3D model of a vessel
Pressure drop & flow simulation
comparison
Mesh generation
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What we focus on
3D MRI data(selected cross-section)
The 3D vascular model
Knowledge-Based Extraction of Cerebral Vasculaturefrom Anatomical MRI
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The algorithm
1. Multiscale vessel enhancementa. Gaussian filtering
b. Hessian matrix computation
c. Vesselness function
2. Center-line extractiona. 3D Segmentation
b. Skeletonization
3. Surface smoothing with tube-like deformable models
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Gaussian Filtering
• Derivatives of image L is a convolution with derivatives of Gaussian:
( ) ( ) ( )sGLssL ,, xx
xxx ∂
∂∗=
∂
∂ γ
The D-dimensional Gaussian is defined:
( ) 2
2
2
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1, s
De
s
sG
x
x−
=π
Where γ is a normalization parameter and s is a scale parameter . For a typical diameter of a vessel smin=0.2, smax=2.
maxmin sss ≤≤
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• A Taylor expansion of the image L in the neighborhood of point x0
( ) ( )000000
xxxxxx δδδδ s
T
s
TsLsL ,0,0,, Η+∇+≈+
ss 0,0, , Η∇
where:
is a gradient and Hessian matrix of an imagecomputed at x0 coordinates, at scale s.
Multiscale vessel enhancement
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Multiscale vessel enhancement
• Hessian matrix computed at coordinates x0:
• Eigenvalues are sorted
• The eigenvector of the highest eigenvalueindicate a direction of the vessel at coordinates x0
=
zzzyzx
yzyyyx
xzxyxx
LLL
LLL
LLL
H
123 λλλ ≤≤
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Blob like structures:
Plate-like structures:
Hessian norm: ∑≤
=Η=3
2
j
jFS λ
32
1
λλ
λ
⋅=BR
3
2
λ
λ=AR
3D 2D
2
1
λ
λ=BR
−
Multiscale vessel enhancement
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Vesselness function
( ) ( )γγ ,max 00maxmin
sVVsss ≤≤
=
( )
−−
−
−−=
2
2
2
2
2
2
0
2exp1
2exp
2exp1
0
,
c
SRRsV BA
βαγ
λ2>0 and λ3>0
Vesselness function :
( )
−−
−=
2
2
2
2
0
2exp1
2exp
0
,
c
SRsV B
βγ
λ2 >0
3D case:
2D case:
Finally:
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Multiscale Filtering Results
Slide before filtering Vesselness function representation
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Axial, coronal and sagittal planes of the
multi-scale enhancement filtered volume.
Maximum intensity projections through
the 3D volume.
Multiscale Filtering Results
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3D Visualization Results
Visualisation of a selected vessel after
3D vesselness function thresholding
and data segmentation with flood-fill
(seed growing) algorithm.
The surface is rough and uneven.
Applying a surface smoothing methods
is needed.
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Center-line extraction resultsthe first step for surface smoothing with deformable models
after masking and thresholding
after applying a skeletonization
algorithm
Vesselness function
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Plans for the future work
• Improving a 3D data filtering algorithm,
• Applying tube-like deformable models for surface smoothing,
• Modelling a viscosity, blood flow andpressure drop.
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References:
• Knowledge-Based Extraction of Cerebral Vasculature from Anatomical MRI – L.R.
Ostergaard, O.V. Larsen, J. Haase, F.V. Meer, A.C. Evans, D.L. Collins
• Multiscale vessel enhancement filtering– A.F.Frangi, W.J. Niessen, K.L. Vincken, M.A. Viergever
• Edge Detection and Ridge Detection with Automatic Scale Selection – T.
Lindberg
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Thank you for your attention