## Thursday, January 20, 2011

### Chan Vese Segmentation Algorithm

Attached is the Chan-Vese segmentation algorithm written in C++ by Robert Crandall. Just run make then run the binary "segment" which will process the test.pgm file and create CVoutEdges.pgm and CVoutRegions.pgm files. In the attached zip you can also find his project paper file ECE532_ProjectPaper.pdf.

Code

1. FUCKING SWEET DUDE!!!

2. Do you have a file "SimpleCVsegment.m" implementation the Gibou & Fedkiw’s ODE method, which is also written by Robert Crabdall? Thanks

3. I dont unfortunately.

4. % Perform a simplified version of Chan-Vese segmentation algorithm, as
% described in "Solving Chan-Vese..." paper by He & Osher

function phi = SimpleCVsegment(I,phi0,dt,numIts,epsilon)

function f = myFunc(t,y)
f = PhiT(y,reshape(I,numel(I),1),epsilon);
end

% Set up coefficients for 4th order Runge-Kutta method
A = [0 0 0 0; 1/2 0 0 0; 0 1/2 0 0; 0 0 1 0];
b = [1/6 1/3 1/3 1/6]';
c = [0 1/2 1/2 1]';

% Solve segmentation problem using a fixed number of steps of
[m,n] = size(phi0);
phi = reshape(phi0,m*n,1);
for i = 1:numIts
phi = RKstep(0,phi,dt,@myFunc,A,b,c);
end

phi = reshape(phi,m,n);
end

5. function phit = PhiT(phi,I,epsilon)

[c1,c2] = GetAvgs(I,phi,epsilon);

phit = (-(I-c1).^2+(I-c2).^2);

end

6. function y_next = RKstep(tin, yin, dt, rhs, A, b, c)

[s, m] = size(b);
n = length(yin);
K = zeros(n,s);

for i = 1:s
K(:,i) = rhs(tin + c(i)*dt, yin + dt*(K*A(i,:)'));
end

% Each column of y_next is the solution calculated using the
% corresponding column of b
y_next = yin*ones(1,m) + dt*(K*b);
end

7. % Compute c1 and c2 as used in the Chan-Vese segmentation algorithm.
% c1 and c2 are given by
% c1 = integral(u0*H(phi))dxdy/integral(H(phi))dxdy
% c2 = integral(u0*(1-H(phi))dxdy/integral(1-H(phi))dxdy
%
% If epsilon == 0, we define H as the usual Heaviside function. Then c1 is
% the average of the image pixels over the set where phi is >= 0, and c2 is
% the average over {phi < 0}.
% If epsilon > 0, we use a smoothed version of the Heaviside function with
% parameter epsilon.

function [c1, c2] = GetAvgs(I,phi,epsilon)

% Non-smoothed calculation
if (0 == epsilon)
n1 = length(find(phi>=0));
n2 = length(find(phi<0));
Iplus = I.*(phi>=0);
Iminus = I.*(phi<0);
c1 = sum(sum(Iplus))/n1;
c2 = sum(sum(Iminus))/n2;

% Smoothed calculation
else
H_phi = .5*(1+(2/pi)*atan2(phi,epsilon));
c1 = sum(sum(I.*H_phi))/sum(sum(H_phi));
c2 = sum(sum(I.*(1-H_phi)))./sum(sum(1-H_phi));
end
end