DEFORMABLE MODELS AND THEIR APPLICATION IN SEGMENTATION OF IMAGED PATHOLOGY SPECIMENS - Deformable Models - page 89

Figure 5. The image segmentation result of the nuclei of two Benign (BEN) cells simuta-
neously applying a level set-based deformable model. The top left panel shows the initial
curve, the top right and bottom left panels show two snapshots of the evolving contours,
and the bottom right panel shows the final segmentation results after 1000 iterations. See
attached CD for color version.

Solving (41) is a problem of geodesic computation in a Riemannian space, ac-
cording to ametric induced by the image I . It can be seen that when I ( x, y ) |

is large, the value of the edge detection function g will approach 0 and the energy
term E ( C ) is minimized and the evolution will stop at the boundary of the object.
The geodesic deformable model in [6] actually has a level set formulation,
which established the relationship with these two apparently different approaches:

|∇ G σ ∗

∂ ∂t = |∇ Ψ |·

g ( |∇ I ( C ( s )) | ) · ϕ + ∇ g ( |∇ I ( C ( s )) | ) ·∇ I , Ψ( s, 0)=Ψ 0 ( s ) , (43)

where

ϕ = div ∇

.

I

(44)

|∇ |

I

Applying the FDM, the numerical solution of (43) results in the following
iterative equation:

n +1 n

Ψ =Ψ +∆ t · [ |∇ Ψ |· g ( |∇ I ( C ( s )) | ) · ϕ + ∇ g ( |∇ I ( C ( s )) | ) ·∇ I ] ,

Ψ( s, 0)=Ψ 0 ( s ) , (45)