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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 130-137.

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

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ter Haar Romeny, FEV

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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:

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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.

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ter Haar Romeny, FEV Abdominal MRA Maximum intensity projection No 3D information Overlapping organs

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ter Haar Romeny, FEV Vesselness measure Based on eigenvalue analysis of Hessian: two low eigenvalues one high eigenvalue

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ter Haar Romeny, FEV 2D Example: DSA

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ter Haar Romeny, FEV Scale integration

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ter Haar Romeny, FEV Closest Vessel Projection

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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

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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.

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ter Haar Romeny, FEV Original data

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ter Haar Romeny, FEV Dark current noise

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ter Haar Romeny, FEV Noise subtracted from data

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

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ter Haar Romeny, FEV

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

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

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

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

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

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ter Haar Romeny, FEV Canceling transparency artifacts The effect of transparency is theoretically a convolution with an exponent; s denotes the tissue’s transparency. - 6 - 4 - 224 z 0.2 0.4 0.6 0.8 1 f(z)f(z)

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ter Haar Romeny, FEV Canceling transparency artifacts In the Fourier domain; The solid line is the real part, the dashed line the imaginary part.

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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.

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ter Haar Romeny, FEV Canceling transparency artifacts The new 0 th order Gaussian filter k(z) (in z-direction) becomes: - 4 - 224 z 0.1 0.2 0.3 0.4 0.5 k(z)(z)

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

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