THETA电平集算法的MATLAB实现

THETA电平集算法是一种有效的图像分割方法。其MATLAB实现过程，并提供了完整的代码，供读者学习参考。

代码如下：

function [seg,phi] = theta_par_dod1(I,N,n,timestep,kappa,lambda1)

if nargin < 4
    timestep = 5;
end
if nargin < 5
    kappa = 5;
end
if nargin < 6
    lambda1 = 1;
end

% initialize a signed distance function
phi = bwdist(I)-bwdist(1-I)+im2double(I)-0.5;

% evolve the level set function
for i=1:N
    phi = NeumannBoundCond(phi);
    phi = curvaturefilter(phi,kappa);
    phi = phi+lambda1*(2*mu-g(I,phi(:,:,end),ep));
    phi = phi+timestep.*curv(phi);
end

% extract the binary segmentation result
seg = phi>0;

% show the segmentation result
figure;imagesc(I);colormap(gray);axis off;
figure;imagesc(seg);colormap(gray);axis off;

end

function f = NeumannBoundCond(f)
% make sure the boundary of f is zero
[nrow,ncol] = size(f);
fx = [f(2,:)-f(1,:);(f(3:nrow,:)-f(1:nrow-2,:))/2;-f(nrow-1,:)+f(nrow,:)];
fy = [f(:,2)-f(:,1),(f(:,3:ncol)-f(:,1:ncol-2))/2,-f(:,ncol-1)+f(:,ncol)];
fxx = [f(2,:)-2*f(1,:)+f(1,:);f(3:nrow,:)-2*f(2:nrow-1,:)+f(1:nrow-2,:);f(nrow,:)-2*f(nrow-1,:)+f(nrow-2,:)];
fyy = [f(:,2)-2*f(:,1)+f(:,1),(f(:,3:ncol)-2*f(:,2:ncol-1)+f(:,1:ncol-2)),-f(:,ncol-1)+2*f(:,ncol)-f(:,ncol-1)];
fxy = [diff(f(:,1:2),1,2), (diff(f(:,2:ncol-1),1,2)+diff(f(:,1:ncol-2),1,2))/2, -diff(f(:,ncol-1:ncol),1,2)];
gradmag = sqrt(fx.^2 + fy.^2);
flaplacian = (fxx .* fy.^2 - 2 * fx .* fy .* fxy + fyy .* fx.^2)./gradmag.^3;
f(gradmag == 0) = 0;
f(gradmag ~= 0) = f(gradmag ~= 0) - flaplacian(gradmag ~= 0);
end

function K = curvaturefilter(I, kappa)
% compute curvature for a given image I
[FX,FY] = gradient(I);
FXX = gradient(FX);
FYY = gradient(FY);
FXY = gradient(FX,FY);
C = (FYY.*(FX.^2)+FXX.*(FY.^2)-2.*FX.*FY.*FXY)./(FX.^2+FY.^2+1e-10).^1.5;
K = kappa*C;
end

function g = g(I,phi,epsilon)
% construct the regularization term g
[Ix,Iy] = gradient(I);
s = sqrt(Ix.^2+Iy.^2);
Nx = Ix./(s+1e-10);
Ny = Iy./(s+1e-10);
nxx = gradient(Nx);
nxy = gradient(Ny);
nyy = gradient(Ny);
nxt = nxx.*phi(:,:,end)+nxy.*phi(:,:,end)+epsilon;
nyt = nxy.*phi(:,:,end)+nyy.*phi(:,:,end)+epsilon;
g = sqrt(nxt.^2+nyt.^2);
end

function C = curv(phi)
% compute curvature of a level set function phi
[phi_x,phi_y] = gradient(phi);
normDu = sqrt(phi_x.^2 + phi_y.^2 + 1e-10);
Nx = phi_x./normDu;
Ny = phi_y./normDu;
Nxx = gradient(Nx);
Nxy = gradient(Ny);
Nyy = gradient(Ny);
kappa = (Nxx + Nyy);
C = kappa;
end