ter Haar Romeny, FEV Vesselness: Vessel enhancement filtering Better 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

ter Haar Romeny, FEV Vesselness The second order structure is exploited for local shape properties

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

ter Haar Romeny, FEV 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

ter Haar Romeny, FEV Noise subtracted from data

ter Haar Romeny, FEV Frangi’s vessel-likeliness Original data (normal and log-scale) (The images are inverted)

ter Haar Romeny, FEV

Canceling transparency artifacts Point-spread function in z-direction (perpendicular to slices)

ter Haar Romeny, FEV Canceling transparency artifacts Point-spread function in z-direction (perpendicular to slices)

ter Haar Romeny, FEV Canceling transparency artifacts Point-spread function in z-direction (perpendicular to slices)

ter Haar Romeny, FEV Canceling transparency artifacts Point-spread function in z-direction (perpendicular to slices)

ter Haar Romeny, FEV Canceling transparency artifacts Point-spread function in 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 z f(z)f(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.

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.

ter Haar Romeny, FEV Canceling transparency artifacts The new 0 th order Gaussian filter k(z) (in z-direction) becomes: z k(z)(z)

ter Haar Romeny, FEV Canceling transparency artifacts z x Default Gaussian filters Enhanced Gaussian filters