How I can change the circular iteration of active contour example to linear iteration for open contours?

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Here it says that if the end points are not connected the matrix should be simpler.I think by changing only matrix I can achieve the linear iteration. So how i can change the original code to a linear version for open active contours.

Below is the Original code

populating the penta diagonal matrix
A = zeros(m,m);
b = [(2*alpha + 6 *beta) -(alpha + 4*beta) beta];
brow = zeros(1,m);
brow(1,1:3) = brow(1,1:3) + b;
brow(1,m-1:m) = brow(1,m-1:m) + [beta -(alpha + 4*beta)]; % populating a     template row
for i=1:m
  A(i,:) = brow;
  brow = circshift(brow',1)'; % Template row being rotated to egenrate     different rows in pentadiagonal matrix
end
 [L U] = lu(A + gamma .* eye(m,m));
Ainv = inv(U) * inv(L); % Computing Ainv using LU factorization
  end

This code is iterating in circularly but I want to iterate in linear way, means that starting point and ending points are not connected. I will be appreciated if someone can give any thoughts. thanks.

asked 54 secs ago

user3600631

41

How I can change the circular iteration of active contour example to linear iteration for open contours?