# Semi-automatic 3D construction of liver using single view CT images

##### References

3,039 citations

1,947 citations

### "Semi-automatic 3D construction of l..." refers background or methods in this paper

...The level set contour evolves on the basis of minimizing an energy function that is defined as [3]: ( ) ( ) ( ) ( ) f D f L f A f ε μ λ α = + + where 0 μ > is a constant, ( ) D f is the distance regularization term, 0 λ > is the co-efficient of the line integral ( ) L f and α is the co-efficient of the area integral ( ) A f By including the distance regularization, edge indicator, dirac delta and heaviside function in the energy minimization equation (2), we arrive at the following equation [3]: ( ) ( ) ( ) | | ( ) f p f dX e f f dX eH f dX ε ε μ λ δ α Ω Ω Ω = ∇ + ∇ + − ∫ ∫ ∫ where p is a double well potential function, ∇ is the gradient of the zero level set Γ and e is the edge indicator function defined as [1]: e = 2 1 1 | * | G I + ∇ G is the Gaussian kernel with a standard deviation σ , I is the image and (*) is the convolution operator....

[...]

...) div is the divergence operator and p d is a function given by [3]:...

[...]

...The solution to this energy minimization function is obtained by solving the gradient flow given below [3]....

[...]

...The initial user defined contour 0 f is a step function defined as [3]:...

[...]