1. Shaohui Huang, Boliang Wang, Xiaoyang Huang

2.  Traditional Active Contour (Snake)  Gradient Vector Flow Snake (GVF Snake)  SEGMENT CT IMAGES  Edge map generation  Contour initialization  Maximum force angle map

5.  The GVF field is defined to be a vector field V(x,y) = (u(x,y),v(x,y)), it comes from the force balance condition by replace the potential force with V(x,y), then we rewrite as

6.  V(x,y) is defined such that it minimizes the energy functional  where f(x,y) is the edge map of the image. GVF field can be obtained by solving following equations

8.  Edge map generation  Contour initialization  Maximum force angle map

9.  Gaussian function with sigma = 1

11.  Two errors with this contour  Over-segment of the liver  Caused by the blur boundary.  Error convergence inside the liver  Caused by the fake boundary.

12.  Canny edge detector

14.  The contour cannot cross the bottleneck of the liver.

15.  Let u, v stand for two GVF forces. Note that u, v are vectors. The angle θ formed by u, v can be calculated as:  A maximum force angle MFA at the coordinate (m,n) is defined as: