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In fact, we can directly update the level set function by Equation 14 after initialization.
By employing a Laplacian operator, we present an operator splitting method to update the level set function.
Based on Equation 14, update the level set function by ϕ n+1/2=ϕ n +Δ t 1·L(ϕ n ).
Instead of attempting to reduce this error directly, we update the level set function Φ forward in time and then backward to get another copy of the level set function, say Φ1.
The topological derivative of the objective functional is approximately derived using a variational approach and the adjoint variable method and is utilized to update the level set function via a time evolutionary reaction-diffusion equation.
Furthermore, considering the regularity of the level set function, we present an operator splitting method to update the level set function, which performs well in maintaining its smoothness and stability.
Finite element method (FEM) is used to solve the Helmholtz equation for acoustic waves, sensitivities are obtained with the adjoint variable method (AVM), and a reaction-diffusion equation is used to update the level set function.
enhance the vessels and extract the rough boundaries of the vessels; initialize the level set function ϕ using (18); update f1 and f2 using (4); update V → (x ) and f(R x)) using (15) and (16): update the level set function ϕ using (17); repeat steps (3) to (5) until the convergence criteria are met.
Besides, we increase a new constraint term which avoids updating the level set function seriously.
