Local Histogram Separation Energy Implementation

Question

I am working in level set method, specially Lankton method paper . I try to implement Histogram Separation (HS) Energy problem (Part III.C). It based on Bhattacharyya to control the evolution of contour. To understand it, the first we consider global method in which given an input image and a contour. The contour divides the image into inside and outside region. The Bhattacharyya distance is calculated by

B=sqrt (P_in.*P_out)

where P_in and P_pout are pdf of inside and outside regions. To applied Bhattacharyya for global level set you can see source code at here . Now we return the Lankton paper. It is local level set. In which, he divides the image into small region by Ball function. Then, the contour will separate these regions into inside and outside region. Each small regions have P_in and P_out. And we can calculate Bhattacharyya distance. I done that step. But I cannot implement final step as formual. Can you help me??? and Av and Au is area of inside and outside of these regions. This is my main code. You can download at source code

  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
Ain=zeros(size(idx)); Aout=zeros(size(idx)); 
B=zeros(size(idx));integral=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;

  vpts = find(P>0);             %local exterior
  Aout(i) = length(vpts)+eps;

  %% Bha distance
  p = imhist(I(upts))/ Ain(i) + eps; % leave histograms unsmoothed
  q = imhist(I(vpts)) / Aout(i) + eps;
  B(i) = sum(sqrt(p.* q));
  term2= sqrt(p./q)/Aout(i) - sqrt(q./p)/Ain(i); %Problem in here===I don't know how to code the integral term 
  integral(i) =sum(term2(:));
end   

F =-B./2.*(1./Ain - 1./Aout) - integral./2;

Answer 1

I tried this - no idea if its correct - its has no histogram smoothing (I dont think it is necessary)

if type==3  % Set up for bhatt

F=zeros(size(idx,1),2);

for i = 1:numel(idx)  

img2 = img(yneg(i):ypos(i),xneg(i):xpos(i)); 
P = phi(yneg(i):ypos(i),xneg(i):xpos(i)); 

upts = find(P<=0);            %local interior
Ain = length(upts)+eps;
[u,~] = hist(img2(upts),1:256);

vpts = find(P>0);             %local exterior
Aout = length(vpts)+eps;
 [v,~] = hist(img2(vpts),1:256); 

   Ap = Ain;
   Aq = Aout;
   In=Ap;
   Out=Aq;
    try
     p = ((u))  ./ Ap + eps;
     q = ((v)) ./ Aq + eps;
     catch
     g  
    end


 B = sum(sqrt(p .* q));

 F(i)=B.*((1/numel(In))-(1/numel(Out)))+(0.5.*(1/numel(In)*(q(img(idx(i))+1)...      /p(img(idx(i))+1))))-(0.5.*(1/numel(Out)*(p(img(idx(i))+1)/q(img(idx(i))+1))));
end