Vesselness: Vessel enhancement filtering

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Vesselness Vessel enhancement filtering

• Better delineation of small vessels
• Preprocessing before MIP
• Preprocessing for segmentation procedure

Frangi, W. J. Niessen, K. L. Vincken, and M. A.
Viergever. Multiscale vessel enhancement
filtering. In Proc. 1st MICCAI, pages 130-137,
1998.
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Vesselness
The second order structure is exploited for local
shape properties
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Deviation of a plate-like structure
Similarity to blob-like structure
Frobenius norm, second-order-like structure
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In the definition of vesselness the three
properties are combined
?1gt0 ? ?2gt0 only bright structures are
detected ?, ? and c control the sensitivity for
?A, ?B and S Frangi uses ? 0.5, ? 0.5, c
0.25 of the max intensity.
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Abdominal MRA

• Maximum intensity projection
• No 3D information
• Overlapping organs

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Vesselness measure

• Based on eigenvalue analysis of Hessian
• two low eigenvalues
• one high eigenvalue

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2D Example DSA
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Scale integration
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Closest Vessel Projection
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Micro-vasculatureCryo-microtome images of the
goat heart

• Very high resolution
• about 404040 µm
• Continuous volume
• Huge stacks (billions of voxels, millions of
  vessels)
• Strange PSF in direction perpendicular to slices
• Scattering
• Broad range of vessel sizes and intensities.

8 cm 2000 pixels
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The Cryomicrotome

• Coronary arteries of a goat heart are filled with
  a fluorescent dye
• Cryo The heart is embedded in a gel and frozen
  (-20C)
• Microtome The machine images the samples
  surface, scrapes off a microscopic thin slice
  (40 µm), images the surface, and so on

a.
b.
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Original data
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Dark current noise
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Noise subtracted from data
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Frangis vessel-likeliness
Original data(normal and log-scale) (The images
are inverted)
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Canceling transparency artifacts
Point-spread function in z-direction (perpendicula
r to slices)
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Canceling transparency artifacts
Point-spread function in z-direction (perpendicula
r to slices)
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Canceling transparency artifacts
Point-spread function in z-direction (perpendicula
r to slices)
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Canceling transparency artifacts
Point-spread function in z-direction (perpendicula
r to slices)
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Canceling transparency artifacts
Point-spread function in z-direction (perpendicula
r to slices)
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Canceling transparency artifacts

• The effect of transparency is theoretically a
  convolution with an exponent
• s denotes the tissues transparency.

f(z)
1
0.8
0.6
0.4
0.2
z
-
-
-
6
4
2
2
4
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Canceling transparency artifacts

• In the Fourier domain
• The solid line is the real part, the dashed line
  the imaginary part.

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Canceling transparency artifacts

• Solution to the problem embed this property in
  the (Gaussian) filters by division in the Fourier
  domain
• Multiplication is convolution, thus division is
  deconvolution.

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Canceling transparency artifacts

• The new 0th order Gaussian filter k(z) (in
  z-direction) becomes

k
(z)
0.5
0.4
0.3
0.2
0.1
z
-
-
4
2
2
4
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Canceling transparency artifacts
Default Gaussian filters
Enhanced Gaussian filters
z
x