Draw energy in active contour method

Question

I have a enrgy equation such as

The algorithm is implement by Lankton and you can download the code and image at code. I want to base on that code to draw the energy function. Note that the F is computed in that code. The my goal energy figure such as

I tried to implement it by that code. But it is not correct answer

  Energy=[];
  %--main loop
  for its = 1:max_its   % Note: no automatic convergence test

    %-- get the curve's narrow band
    idx = find(phi <= 1.2 & phi >= -1.2)';  
    [y x] = ind2sub(size(phi),idx);

    %-- get windows for localized statistics
    xneg = x-rad; xpos = x+rad;      %get subscripts for local regions
    yneg = y-rad; ypos = y+rad;
    xneg(xneg<1)=1; yneg(yneg<1)=1;  %check bounds
    xpos(xpos>dimx)=dimx; ypos(ypos>dimy)=dimy;

    %-- re-initialize u,v,Ain,Aout
    u=zeros(size(idx)); v=zeros(size(idx)); 
    Ain=zeros(size(idx)); Aout=zeros(size(idx)); 
    F_energy=zeros(size(idx));
    %-- compute local stats
    for i = 1:numel(idx)  % for every point in the narrow band
      img = I(yneg(i):ypos(i),xneg(i):xpos(i)); %sub image
      P = phi(yneg(i):ypos(i),xneg(i):xpos(i)); %sub phi

      upts = find(P<=0);            %local interior
      Ain(i) = length(upts)+eps;
      u(i) = sum(img(upts))/Ain(i);

      vpts = find(P>0);             %local exterior
      Aout(i) = length(vpts)+eps;
      v(i) = sum(img(vpts))/Aout(i);
      F_energy(i)=sum((img(upts)-u(i)).^2)+sum((img(vpts)-v(i)).^2); %% Compute the first term in (5) without integrate
    end   

    %-- get image-based forces
    F = -(u-v).*(2.*I(idx)-u-v);
    % Compute the second term in (5) 
    u=phi<=0;
    bw2=bwperim(u);
    Length_phi=sum(sum(bw2));
    Energy=[Energy (sum(F_energy(:))+alpha.*Length_phi)];
    end

Maybe it is so difficult task because the energy function is so complex. However, all thing are implemented by above code, except enrgy term. Hope you can understand and help me draw the enrgy function. Thank in advance

This is my figure result. However, it is not similar the paper result. My result is minimal energy at near zero points. But the paper result is not. What is happen in my code.

Answer 1

Are you sure, that your parameters are similar to these used in original paper? I've observed that energy in each iteration depends on at least two things:

• radius
• initialization mask

The paper indeed confirms that relationship:

The radius of the ball selected by the B(x,y) function is an important parameter to be considered when using localized energies.

and

One limitation of the proposed method is that it has a greater sensitivity to initialization than global region-based methods.

Following picture shows what I've managed to achieve using your code:

Please notice, that in original paper the X-axis unit is second. The code gives us energy in each iteration. Without knowing the duration of one iteration in the original computations (described in the paper) we can't really compare these plots. However, mine is much more similar to the original one.

Here is code for the initialization mask (corresponding to the plot):

I = imread('Mushroom.png');         %-- load the image
m = false(size(I,1),size(I,2));     %-- create initial mask
m(60:100,15:80) = true;             %-- initial mask coordinates

Max iterations: 400
Radius: 20

Hope I've helped.