A MultiScale Geometric Flow for Segmenting Vasculature in MRI

1
A Multi-Scale Geometric Flow for Segmenting
Vasculature in MRI

• Maxime Descoteaux1, Louis Collins2, Kaleem
  Siddiqi1
• 1Centre for Intelligent Machines School of
  Computer Science
• 2Brain Imaging Center, Montreal Neurological
  Institute
• McGill University, Montréal, Canada

2
Blood vessel segmentation

• Input 3D medical data set
• Output binary volume with 3D vascular tree
• Automatic Segmentation can be used for
• Visualization
• Registration between different modalities
• Image-guided neurosurgery
• Pre-surgical planning
• Large scale clinical studies

3
Angiographic data

• Easier problem sharp bright/dark contrast change
  only at vessel boundaries

4
Anatomical data

• Harder problem several bright/dark contrast
  changes at boundaries of non-vessel structures

Proton density (PD) weighted MRI
5
Previous work

• Aylward Bullitt
• Koller et. al.
• Wink et. al.
• Wilson Noble
• Krissian et. al.
• Lorigo et. al.
• Vasilevskiy Siddiqi

• most show promising results on angiographic data

6
Geometric flows

• Work under restrictive assumptions
• Initialization based on thresholding original
  volume
• No explicit term to model tubular structures
• Do not take into account the multi-scale nature
  of vasculature
• Gradient of image is assumed to be strong ONLY at
  vessel boundaries

7
A multi-scale geometric flow

• Introduce a tubular structure model incorporating
  local vessel centerline orientation and width
• Extend this measure to the implied vessel
  boundaries
• Apply a flux maximizing geometric flow

8
Local shape description

• Hessian matrix
• Encodes shape
• information, i.e., how the normal to the
  iso-intensity manifold changes locally

9
Frangis multi-scale extension

• Consider the Hessian matrix at several scales
  covering the possible vessel widths
• Use derivatives of Lindebergs g-parametrized
  normalized Gaussian kernels over the different
  scales
• gtCompare responses over the different scales s

Lindeberg, IJCV 98
10
Local structure classification
blob vs others
noise vs others
sheet vs others
11
Frangis vesslness measure

• Maximum along centerlines of tubular structures
• Close to zero outside vessel-like regions
• argmax( V(s) ) radius of vessel

for all s
Frangi, MICCAI 98
12
Synthetic branch example
13
Cropped MRA region
14
Vesselness measure
15
Flux maximizing geometric flow

• Used to direct the evolution of a curve/surface
  so that its normals are aligned with a given
  vector field

Vasilevkiy, Siddiqi, PAMI 02
16
Vesselness extension

• Distribute the vesselness measure to
• vessel boundaries gt j distribution

17
Multi-scale geometric flow

• Consider the vector field
• The associated flux maximizing flow

18
MRA segmentation
19
Gadolinium enhanced MRI
20
Qualitative validation
slice of TOF
slice of PC
slice of PD
21
Phase contrast angiography
PC
Vesselness of PC
PC masked by segmentation
22
Time of flight angiography
TOF
Vesselness of TOF
TOF masked by segmentation
23
Proton density weighted MRI
PD
Vesselness of PD
PD masked by segmentation (reversed contrast)
24
PC-PD-TOF comparison
25
Contributions

• A new geometric flow which can extract
  vasculature from standard MRI
• Visualization of the vasculature by an MIP of the
  original volume masked by the segmentation
• Qualitatively, the PD segmentation improves upon
  results obtained from TOF angiography and is very
  similar to that obtained from PC angiography
• Quantitatively

26
Key references

• A. Frangi, W. Niessen, K.L. Vincken, M.A.
  Viergever. Multi-scale vessel enhancement
  filtering. Proc. MICCAI'98, pp.130-137, 1998.
• T. Lindeberg. Edge detection and ridge detection
  with automatic scale selection. International
  Journal of Computer Vision, vol 30(2), 1998.
• A. Vasilevskiy, K. Siddiqi. Flux maximizing
  geometric flows. IEEE Transactions On Pattern
  Analysis and Machine Intelligence, vol. 24, 2002.
• THANK YOU!

27
(No Transcript)
28
Initial curve
29
Final curve
30
Key constructions
synthetic tube
vesselness measure
j-distribution
div(V )
31
Eigen analysis of the Hessian

• We find the direction where there are extreme
• changes in the normal
• 1) smallest e-value is close to zero
• (low curvature along vessel)
• 2) other two e-values are high and very close
• (high curvature of circular cross-section)

32
Eigen analysis of the Hessian
33
MRA example
34
Surface evolution