ter haar romeny, fev vesselness: vessel enhancement filtering better delineation of small vessels...

ter Haar Romeny, FEV

Vesselness: Vessel enhancement

filteringBetter delineation of small vessels

Preprocessing before MIP

Preprocessing for segmentation procedure

A. Frangi, W. J. Niessen, K. L. Vincken, and M. A. Viergever:Multiscale vessel enhancement filtering. Lecture Notes in Computer Science Volume 1496, 1998, pp 130-137.


VesselnessThe second order structure is exploited for local shape properties


This ratio accounts for the deviation from a blob-like structure but cannot distinguish between a line- and a plate-like pattern:

This ratio is essential for distinguishing between plate-like and line-like structures since only in the latter case it will be zero :

Frobenius norm, second-order structureness:


In the definition of vesselness the three properties are combined:

1>0 2>0 : 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.


Abdominal MRA

Maximum intensity projection

No 3D information

Overlapping organs


Vesselness measure

Based on eigenvalue

analysis of Hessian:

two low eigenvalues

one high eigenvalue


2D Example: DSA


Scale integration


Closest Vessel Projection


Micro-vasculature:

E. Bennink - Cryo-microtome images of the goat heart

• Very high resolution:• about 40×40×40 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


The Cryomicrotome

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

a. b.


Original data


Dark current noise


Noise subtracted from data


Frangi’svessel-likeliness

Original data(normal and log-scale)

(The images are inverted)


Canceling transparency artifacts

Point-spread functionin z-direction

(perpendicular to slices)



The effect of transparency is

theoretically a convolution

with an exponent;

s denotes the tissue’s

transparency.

sz

es1

)(zf0,0 sz

0z0

- 6 - 4 - 2 2 4z

0.2

0.4

0.6

0.8

1f(z)

0,0 sz)(z



In the Fourier domain;

The solid line is the real part,

the dashed line the

imaginary part.

si

izfF

)]([

1 2 3 4 5 6w

0.1

0.2

0.3

0.4

F (f)



Solution to the problem: embed

this property in the (Gaussian)

filters by division in the Fourier

domain;

Multiplication is convolution,

thus division is deconvolution.

)]([

)]([)]([

zfF

zGFzkF

1 2 3 4 5 6w

-0.5

-0.25

0.25

0.5

0.75

1

F (g)



The new 0th order Gaussian

filter k(z) (in z-direction)

becomes:

)()()( zGdz

dszGzk

- 4 - 2 2 4z

0.1

0.2

0.3

0.4

0.5

k (z)



z

x

DefaultGaussian

filters

EnhancedGaussian

filters

ter haar romeny, fev vesselness: vessel enhancement filtering better delineation of small vessels...

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