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.

ter Haar Romeny, FEV

VesselnessThe second order structure is exploited for local shape properties

ter Haar Romeny, FEV

ter Haar Romeny, FEV

ter Haar Romeny, FEV

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:

ter Haar Romeny, FEV

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.

ter Haar Romeny, FEV

Abdominal MRA

Maximum intensity projection

No 3D information

Overlapping organs

ter Haar Romeny, FEV

Vesselness measure

Based on eigenvalue

analysis of Hessian:

two low eigenvalues

one high eigenvalue

ter Haar Romeny, FEV

2D Example: DSA

ter Haar Romeny, FEV

Scale integration

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Closest Vessel Projection

ter Haar Romeny, FEV

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

ter Haar Romeny, FEV

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.

ter Haar Romeny, FEV

Original data

ter Haar Romeny, FEV

Dark current noise

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Noise subtracted from data

ter Haar Romeny, FEV

Frangi’svessel-likeliness

Original data(normal and log-scale)

(The images are inverted)

ter Haar Romeny, FEV

ter Haar Romeny, FEV

Canceling transparency artifacts

Point-spread functionin z-direction

(perpendicular to slices)

ter Haar Romeny, FEV

Canceling transparency artifacts

Point-spread functionin z-direction

(perpendicular to slices)

ter Haar Romeny, FEV

Canceling transparency artifacts

Point-spread functionin z-direction

(perpendicular to slices)

ter Haar Romeny, FEV

Canceling transparency artifacts

Point-spread functionin z-direction

(perpendicular to slices)

ter Haar Romeny, FEV

Canceling transparency artifacts

Point-spread functionin z-direction

(perpendicular to slices)

ter Haar Romeny, FEV

Canceling transparency artifacts

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

ter Haar Romeny, FEV

Canceling transparency artifacts

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)

ter Haar Romeny, FEV

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.

)]([

)]([)]([

zfF

zGFzkF

1 2 3 4 5 6w

-0.5

-0.25

0.25

0.5

0.75

1

F (g)

ter Haar Romeny, FEV

Canceling transparency artifacts

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)

ter Haar Romeny, FEV

Canceling transparency artifacts

z

x

DefaultGaussian

filters

EnhancedGaussian

filters