Transcript Tubeness Plugin - Broad Institute

Tubeness Plugin
Lee Kamentsky
Broad Institute
Tubeness
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Plugin for ImageJ
Designed for 2-D and 3-D images
http://homepages.inf.ed.ac.uk/s9808248/imagej/tubeness/
Y. Sato, S. Nakajima, N. Shiraga, H. Atsumi, S. Yoshida, T. Koller, G.
Gerig, and R. Kikinis, “Three-dimensional multi-scale line filter for
segmentation and visualization of curvilinear structures in medical
images,” Med Image Anal., vol. 2, no. 2, pp. 143-168, June 1998.
Log transformed images, original on left, “Tubeness” on right
Tubeness math
I ( X ), X  ( x, y )
f ( X )  I ( X )  G( X , )
f f
 ( f ( X ))  ( , )
x y
 2 ( I ( X )  G ( X ,  ))
 f
 2 x
 2 ( f ( X ))  
 f
 yx

 axx axy   x 
 x
     1 , 2
a



 y
 yx a yy   y 
1  0, 2  0
f 
xy 

f 
 2 y  Value  2
Eigenvectors & values
λ2
λ1
Info & credits
• More images:
http://www.broadinstitute.org/~leek/tubene
ss/tubeness.html
• Some math:
http://en.wikipedia.org/wiki/Eigenvalue,_ei
genvector_and_eigenspace
• Other math from the paper