Vesselness: Vessel enhancement filtering

1. 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.

2. Vesselness The second order structure is exploited for local shape properties

4. Deviation of a plate-like structure: Similarity to blob-like structure: Frobenius norm, second-order-like structure:

5. 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.

6. Abdominal MRA • Maximum intensity projection • No 3D information • Overlapping organs

7. Vesselness measure • Based on eigenvalue analysis of Hessian: • two low eigenvalues • one high eigenvalue

8. 2D Example: DSA

9. Scale integration

10. Closest Vessel Projection

11. Micro-vasculature: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

12. 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.

13. Original data

14. Dark current noise

15. Noise subtracted from data

16. Frangi’s vessel-likeliness Original data(normal and log-scale) (The images are inverted)

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

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

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

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

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

23. Canceling transparency artifacts • The effect of transparency is theoretically a convolution with an exponent; • s denotes the tissue’s transparency. f(z) 1 0.8 0.6 0.4 0.2 z - - - 6 4 2 2 4

24. F (f) 0.4 0.3 0.2 0.1 w 1 2 3 4 5 6 Canceling transparency artifacts • In the Fourier domain; • The solid line is the real part, the dashed line the imaginary part.

25. F (g) 1 0.75 0.5 0.25 w 1 2 3 4 5 6 -0.25 -0.5 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.

26. 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

27. Canceling transparency artifacts Default Gaussian filters Enhanced Gaussian filters z x